Term
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Definition
Negative and positive whole numbers, as well as 0.
{...,-2,-1,0,1,2,...} |
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Definition
Any positive integer that can be multiplied together to get a particular number.
The factors of 16 are: 1, 2, 4, 8, and 16. |
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Definition
Any positive integer that can be multiplied together to get a particular number.
The divisors of 16 are: 1, 2, 4, 8, and 16. |
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Definition
Positive integers that result when you multiply the particular number by any other integer.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, etc. |
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Definition
When one integer is capable of being divided by another integer, resulting in a positive integer.
16 is divisible by 1, 2, 4, 8, and 16. |
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Definition
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Definition
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Definition
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Definition
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Definition
The smallest positive integer that is a multiple of two or more numbers.
The least common multiple of 15 and 50 is 150.
The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, etc.
The multiples of 50 are: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, etc.
The smallest number they have in common is 150. |
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Term
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Definition
The largest positive integer that is a divisor of two or more numbers.
The greatest common divisor of 15 and 50 is 5.
The divisors of 15 are: 1, 3, 5, and 15.
The divisors of 50 are: 1, 2, 5, 10, 25, and 50.
The largest number they have in common is 5. |
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Term
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Definition
The largest positive integer that is a factor of two or more numbers.
The greatest common factor of 15 and 50 is 5.
The factors of 15 are: 1, 3, 5, and 15.
The factors of 50 are: 1, 2, 5, 10, 25, and 50.
The largest number they have in common is 5. |
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Term
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Definition
When one integer is divided by another, and the result is not an integer, the quotient is the largest positive integer that is less than the result.
Another way to put it is that it is the number before the decimal point.
This is only used with the term "remainder" as a way to express the result using only integers.
The quotient of 32 divided by 5 is 6.
This is because 5 times 6 is less than 32 but 5 times 7 is more than 32, AND 5 times 6 is 30, which is 2 less than 32.
The answer is expressed as: "6 remainder 2". |
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Term
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Definition
When integer A is divided by integer B, and the result is not an integer, the remainder is the number that is left over when the quotient is multiplied by B.
This is only used with the term "quotient" as a way to express the result using only integers.
The remainder of 32 divided by 5 is 2.
This is because 5 times 6 is less than 32 but 5 times 7 is more than 32, AND 5 times 6 is 30, which is 2 less than 32.
The answer is expressed as: "6 remainder 2". |
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Term
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Definition
Any integer that is divisible by 2.
{..., -4, -2, 0, 2, 4, ...} |
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Definition
Any integer this is NOT divisible by 2.
{..., -3, -1, 1, 3, ...} |
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Definition
| Any integer greater than 1 that has only two positive divisors (factors): one and itself. |
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Definition
| 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. |
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Term
| How Many Even Prime Numbers Are There, and What Are They? |
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Definition
| 2 is the only even prime number. |
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Term
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Definition
When an integer greater than 1 is expressed by multiplying only prime numbers.
The prime factorization of 16 is: (2)(2)(2)(2).
The prime factorization of 15 is: (3)(5). |
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Definition
When an integer greater than 1 is expressed by multiplying only prime numbers.
The prime divisors of 16 is: (2)(2)(2)(2).
The prime divisors of 15 is: (3)(5). |
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Term
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Definition
| Any integer greater than 1 which is not prime. |
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Term
| First Ten Composite Numbers |
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Definition
| 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18. |
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Term
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Definition
A number which is displayed such that one integer is on top of the another integer, and there is a line between them.
½ is a fraction. |
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Term
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Definition
In a fraction, the integer which is on the top.
The numerator of ½ is 1. |
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Term
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Definition
In a fraction, the integer which is on the bottom.
The numerator of ½ is 2. |
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Term
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Definition
All integers, plus all numbers which can be expressed as a fraction.
-1, 1, 0, 1, and 2 are all rational numbers.
0.5 is also a rational number, because it can be expressed as ½.
Pi is not a rational number, because it cannot be expressed as a fraction. |
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Term
| If a Numerator and a Denominator are Multiplied by the Same Nonzero Integer, What is Special About the Result? |
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Definition
The resulting fraction will be equivalent to the original fraction.
In the case of ½, if 1 and 2 are both multiplied by 2, the resulting fraction (2/4) is equivalent to the original. |
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Term
| How Can a Negative Fraction be Expressed? |
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Definition
The negative sign may be placed before the fraction, before the numerator, or before the denominator.
-½ can also be expressed as -1/2 and 1/-2. |
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Term
| Reduction (For Fractions) |
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Definition
When the numerator and the denominator of a fraction have a common denominator, they can be factored and reduced to an equivalent fraction.
In the case of 2/4, 2 can be factored as (1)(2), and 4 can be factored as (1)(2)(2). If we remove the common factors, the result is ½. |
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Term
| How Do You Add Two Fractions with the Same Denominator? |
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Definition
Add the numerators and keep the denominator.
¼ + ¼ = 2/4. This can be reduced to ½. |
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Term
| How Do You Add Two Fractions with Different Denominators? |
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Definition
Find the smallest common denominator, and convert both fractions to the equivalent fraction with that denominator, so that they have the same denominator, then add the numerators together and use the common denominator.
If adding ¼ and ½, the common denominator is 4, so we would convert ½ to 2/4, and leave ¼ as it is. The result would be ¾.
If adding 1/3 and 4/7, the common denominator is 21, so we would convert 1/3 to 7/21, and convert 4/7 to 12/21. The result would be 19/21. |
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Term
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Definition
The common multiple of two denominators.
The common denominator of ¼ and ½ is 4.
The common denominator of 1/3 and 4/7 is 21. |
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Term
| How Do You Subtract Two Fractions with the Same Denominator? |
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Definition
Subtract the numerators and keep the denominator.
¾ - ¼ = 2/4. This can be reduced to ½.
¼ - ¾ = -2/4. This can be reduced to -½. |
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Term
| How Do You Subtract Two Fractions with Different Denominators? |
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Definition
Find the smallest common denominator, and convert both fractions to the equivalent fraction with that denominator, so that they have the same denominator, then subtract the numerators and use the common denominator.
In the case of ½ - ¼, the common denominator is 4, so we would convert ½ to 2/4, and leave ¼ as it is. The result would be ¼.
In the case of 1/3 - 4/7, the common denominator is 21, so we would convert 1/3 to 7/21, and convert 4/7 to 12/21. The result would be -5/21. |
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Term
| How Do You Multiply Two Fractions? |
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Definition
Multiply the two numerators and multiply the two denominators.
½ x ½ = (1)(1)/(2)(2) = ¼.
2/3 x 4/7 = (2)(4)/(3)(7) = 8/21. |
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Term
| How Do You Divide Two Fractions? |
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Definition
Invert the second fraction, then multiply the first fraction by the inverted fraction.
½ ÷ ½ = 1/2 x 2/1 = (1)(2)/(2)(1) = 2/2 (which can be reduced to 1).
2/3 ÷ 4/7 = 2/3 x 7/4 = (2)(7)/(3)(4) = 14/12 (which can be reduced to 7/6). |
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Term
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Definition
A number that consists of an integer and a fraction.
2½ is a mixed number. |
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Term
| How Do You Convert a Mixed Number to an Ordinary Fraction? |
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Definition
Convert the integer to an equivalent fraction, and add it to the fraction part.
2½ = 2 + ½ = (2/1 x 2/2) + ½ = 4/2 + ½ = 5/2 |
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Term
| How Do You Perform Mathematical Operations on Fractions When Either the Numerator or the Denominator is Not an Integer? |
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Definition
As long as neither the numerator nor the denominator are 0, you can treat it as a normal fraction.
x/2 + x/3 = (x/2 x 3/3) + (x/3 x 2/2) = 3x/6 + 2x/6 = 5x/6 |
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Term
| What is a Base (vs an Exponent)? |
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Definition
When an integer has an exponent, the integer is the base.
In the expression 7², 7 is the base. |
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Term
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Definition
An integer which is used to indicate repeated multiplication of a number by itself.
In the expression 7², 2 is the exponent. |
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Term
| When a Negative Number has an Exponent, Will the Result be Positive or Negative? |
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Definition
If the exponent is even, the result will be even.
If the exponent is odd, the result will be odd. |
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Term
| What is the Difference Between -7² and (-7)²? |
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Definition
-7² is the negative of 7², while and (-7)² is -7 to the second power.
-7² = -(7)(7) = -14.
(-7)² = (-7)(-7) = 14. |
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Term
| What Happens When the Exponent is 0? |
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Definition
| If the base is a nonzero numbers, the result is 1. If the base is 0, the result is undefined. |
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Term
| What Happens When an Exponent is Negative? |
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Definition
It is converted to 1 divided by the positive exponent.
7‐² = 1/7² = 1/49 |
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Term
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Definition
The number that, when multiplied by itself, is equal to the given number.
The square root of 4 is 2, because 2 x 2 = 4.
-2 is also a square root of 4, because -2 x -2 = 4. |
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Term
| What is the Square Root of a Negative Number? |
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Definition
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Term
| What Happens if You Square A Square Root? |
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Definition
The result is the base number.
(√4)² = 4. |
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Term
| What Happens if You Try to Get the Square Root of a Squared Number? |
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Definition
The result is the base number.
√(4²) = 4. |
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Term
| How Do You Multiply Two Square Root Numbers? |
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Definition
Multiply the numbers and convert it so that it is the square root of the result.
(√2) x (√3) = √(2 x 3) = √6 |
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Term
| How Do You Divide Two Square Roots? |
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Definition
Convert it to the Square Root of the Fraction.
(√6) ÷ (√3) = √(6 ÷ 3) = √2 |
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Term
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Definition
An integer which is used to indicate repeated multiplication of a number by itself.
In the expression 7², 2 is the exponent. |
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Term
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Definition
In a root, the number of times that the result must be multiplied by itself to get the given number.
The root order of square root, such as √9, is 2. This can also be written as ²√9.
The root order of a cube root, such as ³√27, is 3.
The root order of a fourth root, such as ⁴√81, is 4. |
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Term
| How Many Roots Are There for Odd-Order Roots? |
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Definition
There is exactly one root, even when the number being rooted is negative.
³√27 = 3.
³√(-27) = 3. |
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Term
| How Many Roots Are There for Even-Order Roots? |
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Definition
There are exactly two roots for every positive number being rooted.
There are exactly zero roots for every negative number being rooted.
The fourth roots of 81 are 3 and -3.
However, there is no fourth root of -81, because it is negative. |
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Term
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Definition
In the decimal numbering system, the place value is the distance from the decimal point on either side.
In the case of 9234.167:
9 is in the thousands place, 2 is in the hundreds place, 3 is in the tens place, 4 is in the ones (or units) place, 1 is in the tenths place, 6 is in the hundredths place, and 7 is in the thousandths place. |
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Term
| In Order From Closest to the Decimal to Farthest, What are the First Four Place Values to the Left of the Decimal? |
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Definition
Ones (or Units), Tens, Hundreds, and Thousands.
Note that Tens is NOT the same as Tenths.
In the case of 9234.167:
9 is in the thousands place, 2 is in the hundreds place, 3 is in the tens place, and 4 is in the ones (or units) place. |
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Term
| In Order From Closest to the Decimal to Farthest, What are the First Three Place Values to the Right of the Decimal? |
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Definition
Tenths, Hundredths, and Thousandths.
Note that tenths is NOT the same as tens.
In the case of 9234.167:
1 is in the tenths place, 6 is in the hundredths place, and 7 is in the thousandths place. |
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Term
| How Do You Convert a Decimal to an Equation Using Integers and Fractions if There Are a Finite Number of Digits to the Right of the Decimal? |
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Definition
Each number to the left is multiplied by number indicated in its place value, while each number to the right is divided by the number indicated in its place value, then plus signs are placed between them.
In the case of 9234.167:
9 is multiplied by 1000, 2 is multiplied by 100, 3 is multipled by 10, 4 is multiplied by 1, 1 is divided by 10, 6 is divided by 100, and 7 is divided by 1000. Then all are added together.
This can be expressed in several ways:
9(1000) + 2(100) + 3(10) + 4(1) + 1/10 + 6/100 + 7/1000.
OR 9(1000) + 2(100) + 3(10) + 4(1) + 1(1/10) + 6(1/100) + 7(1/1000).
OR 9(10³) + 2(10²) + 3(10¹) + 4(10º) + 1(10‐¹) + 6(10‐²) + 7(10‐³).
Any of which may be calculated out to get: 9234167/1000. |
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Term
| How Do You Convert a Decimal to a Fraction if There Are a Finite Number of Digits to the Right of the Decimal? |
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Definition
Every fixed-digit decimal can be converted to an integer divided by a power of 10.
4.1 = 4(1) + 1/10 = 41/10.
34.16 = 3(10) + 4(1) + 1/10 + 6/100 = 3416/100 (which can be reduced to 854/25).
4.167 = 4(1) + 1/10 + 6/100 + 7/1000 = 4167/1000. |
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Term
| How Do You Convert a Fraction to a Decimal? |
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Definition
Divide the numerator by the denominator using long division.
½ = 1 ÷ 2 = 0.5 |
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Term
| What Does it Mean To Say that a Decimal Terminates? |
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Definition
It has a finite number of digits to the right of the decimal.
0.25 is a decimal that terminates. So are 0.5 and 34293298.87892. |
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Term
| What Does it Mean to Say that a Decimal Repeats? |
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Definition
It has an infinitely repeating set of digits to the right of the decimal.
1 ÷ 3 results in a repeating decimal: 0.3333333... (where 3 is infintely repeated).
25 ÷ 6 also results in a repeating decimal: 4.166666... (where 6 is infinitely repeated).
13 ÷ 7 also results in a repeating decimal: 1.857142857142857142... (where 857142 is infinitely repeated). |
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Term
| How is a Repeating Decimal Usually Expressed? |
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Definition
| By place a horizontal line over the repeated digit(s). |
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Term
| What is Special About the Decimals of All Rational Numbers? |
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Definition
| Every rational number can be expressed as a decimal that either terminates or repeats. |
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Term
| What is Special About the Decimals of Every Fraction with Integers in the Numerator and the Denominator? |
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Definition
| All of them can be expressed as a decimal that either terminates or repeats. |
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Term
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Definition
| A decimal that neither terminates nor repeats, such as √2 or π. |
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Term
| When a Decimal Neither Terminates Nor Repeats, What is it Called? |
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Definition
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Term
| Is 0 Negative or Positive? |
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Definition
|
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Term
|
Definition
All rational numbers and all irrational numbers. This includes integers, fractions, and decimals.
It includes both positive and negative numbers.
All square roots are real numbers.
π is also a real number.
The smallest numbers are on the left, while the largest numbers are on the right. |
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Term
| What is the Real Number Line? |
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Definition
A continuous line that is used to represent all real numbers.
The smallest numbers are on the left, and the largest are on the right.
Every real number corresponds to a point on the line. |
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Term
| On the Real Number Line, Which Numbers are Negative? |
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Definition
| All numbers to the left of 0 are negative. 0 is neither negative nor positive. |
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Term
| On the Real Number Line, Which Numbers are Positive? |
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Definition
| All numbers to the right of 0 are positive. 0 is neither negative nor positive. |
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Term
| How Do You Express "X is Less Than Y" Using Symbols? |
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Definition
X < Y
The best way to remember this is to imagine a pac-man eating the larger number. |
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Term
| How Do You Express "X is Greater Than Y" Using Symbols? |
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Definition
X > Y
The best way to remember this is to imagine a pac-man eating the larger number. |
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Term
| In English, How Would You Say X > Y? |
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Definition
X is more than Y.
The best way to remember this is to imagine a pac-man eating the larger number. |
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Term
| In English, How Would You Say X < Y? |
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Definition
X is less than Y.
The best way to remember this is to imagine a pac-man eating the larger number. |
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Term
| What is the Set of Negative and Positive Whole Numbers Called? |
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Definition
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Term
| Fill in the Blank: 4 is a ______ of 16. |
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Definition
|
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Term
| Fill in the Blank: 16 is a ______ of 4. |
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Definition
|
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Term
| Fill in the Blank: 16 is ______ by 4. |
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Definition
|
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Term
| Fill in the Blank: ______ is a Factor of Every Integer. |
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Definition
|
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Term
| Fill in the Blank: The Multiples of ______ Are 1 and -1 Only. |
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Definition
|
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Term
| Fill in the Blank: ______ is a Multiple of Every Integer. |
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Definition
|
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Term
| Fill in the Blank: ______ is a Factor of 0 Only. |
|
Definition
|
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Term
| What is the Smallest Positive Integer that is a Multiple of Two or More Numbers Called? |
|
Definition
| The least common multiple. |
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Term
| What is the Largest Positive Integer that is a Factor of Two or More Numbers? |
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Definition
| The greatest common divisor or the greatest common factor. |
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Term
| Fill in the Blank: When One Integer is Divided by Another, the Result Can Be Expressed as a ______ and a Remainder. |
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Definition
|
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Term
| Fill in the Blank: When One Integer is Divided by Another, the Result Can Be Expressed as a Quotient and a ______. |
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Definition
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Term
| All Integers Which Can be Divided by Two to Produce an Integer are What? |
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Definition
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Term
| All Integers Which Cannot be Divided by Two to Produce an Integer are What? |
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Definition
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Term
| An Integer Greater Than 1 Whose Only Factors are 1 and Itself is Called What? |
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Definition
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Term
| Fill in the Blank: 2 is the Only Even ______ Number. |
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Definition
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Term
| An Integer Greater Than 1 Which is Not Prime is Called What? |
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Definition
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Term
| In a Fraction, What is the Number on Top Called? |
|
Definition
|
|
Term
| In a Fraction, What is the Number on Bottom Called? |
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Definition
|
|
Term
| What is The Set of All Integers Plus All Fractions Called? |
|
Definition
|
|
Term
| Is -½ More or Less Than 1/-2? |
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Definition
| Neither. They are equivalent (equal) to one another. |
|
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Term
| What is the Common Multiple of Two Denominators Called? |
|
Definition
|
|
Term
| Fill in the Blank: A ______ is a Number that Consists of an Integer and a Fraction. |
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Definition
|
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Term
|
Definition
|
|
Term
| What is the Exponent of 7²? |
|
Definition
|
|
Term
| Is -7² More or Less Than (-7)²? |
|
Definition
Less.
-7² = -(7)(7) = -14.
(-7)² = (-7)(-7) = 14.
-14 is Less Than 14. |
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Term
| Fill in the Blank: When ______ is the Exponent of A Nonzero Base, the Result is Always 1. |
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Definition
0
If the base is 0, the result is undefined. |
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Term
|
Definition
|
|
Term
| Fill in the Blank: The Root Order of a Square Root is ______. |
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Definition
|
|
Term
| What is the Root Order of √9? |
|
Definition
|
|
Term
| Fill in the Blank: The Root Order of a Cube Root is ______. |
|
Definition
|
|
Term
| What is the Root Order of ³√343? |
|
Definition
|
|
Term
| What is the Root Order of ⁴√81? |
|
Definition
|
|
Term
| Fill in the Blank: The Root Order of a Fourth Root is ______. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Thousandths Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the Case of 9234.167, 7 is in the ______ Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Thousands Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, 9 is in the ______ Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Ones Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, 4 is in the ______ Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Units Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Tenths Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, 1 is in the ______ Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, ______ is in the Tens Place. |
|
Definition
|
|
Term
| Fill in the Blank: In the case of 9234.167, 2 is in the ______ Place. |
|
Definition
|
|
Term
| Fill in the Blank: If a Number Has a Finite Number of Digits to the Right of the Decimal, it is a ______ Decimal. |
|
Definition
|
|
Term
| Fill in the Blank: If a Number Has an Infinitely Repeating Set of Digits to the Right of the Decimal, it is a ______ Decimal. |
|
Definition
|
|
Term
| Fill in the Blank: Every ______ Number Can be Expressed as a Decimal that Either Terminates or Repeats. |
|
Definition
|
|
Term
| What Number is Neither Negative nor Positive? |
|
Definition
|
|
Term
| What is the Set of All Rational and Irrational Numbers Called? |
|
Definition
|
|
Term
| Fill in the Blank: On the Real Number Line, All Numbers to the Left of 0 are ______. |
|
Definition
|
|
Term
| Fill in the Blank: On the Real Number Line, All Numbers to the Right of 0 are ______. |
|
Definition
|
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Term
|
Definition
The set of all real numbers between two numbers; also the set of all real numbers greater OR less than a given endpoint; also the entire real number line.
For example, the interval of 2 and 3 is the set of all real numbers between 2 and 3.
Unless otherwise specified, the endpoints (2 and 3) are not included in the interval. |
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Term
| Fill in the Blank: The Set of All Real Numbers Between 2 and 3 is the ______. |
|
Definition
|
|
Term
| Fill in the Blank: The Set of All Real Numbers Between 1 and 9 is the ______. |
|
Definition
|
|
Term
| 4 < x < 6 is Used to Represent What? |
|
Definition
| The interval (set of all real numbers) between 4 and 6. It does not include the endpoints (4 and 6). |
|
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Term
| Fill in the Blank: Unless Otherwise Specified, the ______ Are Not Included in the Interval. |
|
Definition
|
|
Term
| 4 ≤ x < 6 is Used to Represent What? |
|
Definition
| The interval (set of all real numbers) between 4 and 6, including 4 but not including 6. |
|
|
Term
| 4 < x ≤ 6 is Used to Represent What? |
|
Definition
| The interval (set of all real numbers) between 4 and 6, including 6 but not including 4. |
|
|
Term
| 4 ≤ x ≤ 6 is Used to Represent What? |
|
Definition
| The interval (set of all real numbers) between 4 and 6, including both 4 and 6. |
|
|
Term
| What Does it Mean if an Interval Has Only One Endpoint? |
|
Definition
All real numbers to the right OR left of that endpoint are included in the interval.
x < 2 means all real numbers to the left of the endpoint, not including the endpoint (2).
x > 2 means all real numbers to the right of the endpoint, not including the endpoint (2). |
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| x < 3 is Used to Represent What? |
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Definition
| The set of all real numbers less than (to the left of) 3, not including 3. |
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Term
| x ≤ 3 is Used to Represent What? |
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Definition
| The set of all real numbers less than (to the left of) 3, including 3. |
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Term
| x > 3 is Used to Represent What? |
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Definition
| The set of all real numbers greater than (to the right of) 3, not including 3. |
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Term
| x ≥ 3 is Used to Represent What? |
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Definition
| The set of all real numbers greater than (to the right of) 3, including 3. |
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Term
| Fill in the Blank: The Entire Real Number Line is Considered to Be an ______. |
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Definition
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Definition
The distance between a number and 0 on the number line.
The absolute value is always positive.
The absolute value of a negative number is the same as the absolute value of it's corresponding positive number.
The absolute value of 3 and -3 are both 3.
This can also be expressed as: |3| = 3 and |-3| = 3. |
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Term
| What is the Absolute Value of Zero? |
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Definition
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| |-3| is Used to Represent What? |
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Definition
| The absolute value of -3, which is 3. |
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Term
| What is the absolute value of 5? |
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Definition
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Term
| What is the absolute value of -5? |
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Definition
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Term
| |√2| is Used to Represent What? |
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Definition
| The absolute value of √2, which is √2. |
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Term
| For Real Numbers, is A+B Less or Greater Than B+A? |
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Definition
| Neither, they are equivalent. |
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Term
| For Real Numbers, A+B is Equivalent to What? |
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Definition
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Term
| For Real Numbers, is AB Less or Greater Than BA? |
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Definition
| Neither, they are equivalent. |
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Term
| For Real Numbers, AB is Equivalent to What? |
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Definition
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Term
| For Real Numbers, is (A+B)+C Less or Greater Than A+(B+C)? |
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Definition
| Neither, they are equivalent. |
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Term
| For Real Numbers, (A+B)+C is Equivalent to What? |
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Definition
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Term
| For Real Numbers, is (AB)C Less or Greater Than A(BC)? |
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Definition
| Neither, they are equivalent. |
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Term
| For Real Numbers, (AB)C is Equivalent to What? |
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Definition
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Term
| For Real Numbers, A(B+C) is Equivalent to What? |
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Definition
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Term
| For Real Numbers, is A(B+C) Greater or Less Than AB+AC? |
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Definition
| Neither, they are equivalent. |
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Term
| For Real Numbers, What is A+0? |
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Definition
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Term
| For Real Numbers, What is A(0)? |
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Definition
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Term
| For Real Numbers, What is A(1)? |
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Definition
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Term
| For Real Numbers, What Does it Mean if AB=0? |
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Definition
| A is 0, or B is 0, or both A and B are 0. |
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Term
| What is the Result if You Divide a Real Number by 0? |
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Definition
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Term
| If Real Numbers A and B are Both Positive, What Do You Know? |
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Definition
Both their sum and product are positive.
A+B and AB are both positive. |
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Term
| If Real Numbers A and B are Both Negative, What Do You Know? |
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Definition
Their sum is negative, and their product is positive.
A+B is negative, while and AB is positive. |
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Term
| If A is a Positive Real Number and B is a Negative Real Number, What Do You Know? |
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Definition
Their product is negative.
AB is negative. |
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Definition
The absolute value of the sum of two real numbers is less than or equal to the sum of their absolute values.
|A+B| ≤ |A|+|B| |
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Term
| If A and B are Real Numbers, is |A+B| Greater or Less Than |A|+|B|? |
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Definition
Less than or equal to.
|A+B| ≤ |A|+|B| |
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Term
| If Multiplying The Absolute Values of Two Real Numbers, What is it Equivalent To? |
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Definition
The absolute value of their product.
|A||B| = |AB| |
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Term
| What Are the Ways You Can Express The Ratio of A and B? |
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Definition
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Term
| Fill in the Blank: Like Fractions, Ratios Can Be ______ to Lowest Terms. |
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Definition
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Definition
| A way to express the relative sizes of two quantities, often in the form of a fraction where the first quantity is the numerator and the second quantity is the denominator. |
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Term
If Real Number A>1, What Do We Know About the Square of A?
We know it is greater than A. |
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Definition
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Term
| If Real Number A is Greater Than 0 But Less Than 1, What Do We Know About the Square of A? |
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Definition
We know it is less than A.
If 0 < A < 1, than A² < A. |
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Term
| Can More Than Two Positive Quantities be Expressed as a Ratio? |
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Definition
| Yes. The ratio of A, B, and C would be expressed as "A to B to C". |
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Term
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Definition
An equation relating two ratios.
For example, 1/4 = 2/8. |
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Term
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Definition
When two fractions are equivalent to each other, you can multiply the numerator of one by the denominator of the other, then divide by other numerator. The result will be the other denominator.
You can also multiply the numerator of one by the denominator of the other, then divide by the other denominator. The result will be the other numerator.
For example, if you have 1/4 = 2/8, you can do any of the following:
(1x8)/4 = 2
(1x8)/2 = 4
(2x4)/1 = 8
(2x4)/8 = 1
This is useful if either one of the numerators or one of the denominators is unknown. |
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Term
| How Would You Solve for X if You Knew That X/3 Was Equivalent to 4/15? |
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Definition
Cross Multiplication.
(3x4)/15 = X = 0.8 |
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Term
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Definition
| Percent means per hundred or hundredths. |
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Term
| How Would You Express 1/2 as a Percentage? |
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Definition
50%.
(1/2)(50/50) = 50/100 = 50% |
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Term
| How Would You Express 1% as a Fraction? |
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Definition
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Term
| In a Ratio, is the Part the Numerator or the Denominator? |
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Definition
Numerator.
3 is the part of 3/15. |
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Term
| In a Ratio, is the Whole the Numerator or the Denominator? |
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Definition
Denominator.
15 is the whole of 3/15. |
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Term
| What is a Part (vs a Whole)? |
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Definition
The Numerator of a Ratio.
3 is the part of 3/15. |
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Term
| What is a Whole (vs a Part)? |
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Definition
The Denominator of a Ratio.
15 is the whole of 3/15. |
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Term
| How Would You Express .067 as a Percentage? |
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Definition
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Term
| How Would You Express 15% as a Decimal (Without the % Sign)? |
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Definition
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Term
| How Do You Find the Part to a Whole? |
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Definition
There are two ways:
1) Multiply the whole by the decimal equivalent of the percent.
2) Set up a proportion, with the percent A expressed as A/100 and cross-multiply by x divided by the whole. |
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Term
| If the Whole is 15 and the Part is 3, What is the Percent? |
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Definition
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Term
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Definition
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Term
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Definition
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Term
| How Do You Get 20% of 440? |
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Definition
Two Ways:
1) Decimal equivalent and multiplication.
(440)(.20) = 88
2) Proportions and cross-multiplication.
x/440 = 20/100
x = (20)(440)/100 = 8800/100 = 88, so 20% of 440 is 88. |
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Term
| Given the Percent and Part, How Do You Calculate the Whole? |
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Definition
There are two ways:
1) Divide the part by the decimal equivalent of the percent.
2) Set up a proportion, with the percent A expressed as A/100 and cross-multiply by the part divided by x. |
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Term
| If the Percent is 20% and the Part is 3, How Do You Calculate the Whole? |
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Definition
Two ways:
1) Decimal equivalent and division.
3/0.20 = 15
2) Proportions and cross-multiplication.
3/x = 20/100
x=(3)(100)/20 = 300/20 = 15 |
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Term
| What is the Base of a Percent? |
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Definition
The whole of that percent.
In the case of "3 is 20% of 15", the base would be 15. |
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Term
| Is the Part Greater or Less Than the Whole? |
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Definition
It can be either (or even equal).
If it is smaller, the percent will be less than 100%.
If it is larger, the percent will be more than 100%.
If it is equal, the percent will be 100%. |
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Term
| Is the Part Greater or Less Than the Base? |
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Definition
It can be either (or even equal).
If it is smaller, the percent will be less than 100%.
If it is larger, the percent will be more than 100%.
If it is equal, the percent will be 100%. |
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Term
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Definition
| The amount of change as a percentage of an initial positive amount, when a quantity changes from that initial positive amount to another positive amount. |
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Term
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Definition
| The amount of change as a percentage of an initial positive amount, when a quantity changes from that initial positive amount to a greater positive amount. |
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Term
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Definition
| The amount of change as a percentage of an initial positive amount, when a quantity changes from that initial positive amount to a smaller positive amount. |
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Term
| How Do You Find the Percent Change? |
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Definition
Divide the change by the base.
To calculate the percent change from 10 to 45:
(45-10)/10 = 35/10 = 3.5 = 350% |
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Term
| How Do You Find the Percent Increase? |
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Definition
Divide the amount of increase by the base.
To calculate the percent increase from 15 to 45:
(45-15)/15 = 30/15 = 2.0 = 200% |
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Term
| How Do You Find the Percent Decrease? |
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Definition
Divide the amount of decrease by the base.
To calculate the percent decrease from 65 to 13:
(65-13)/65 = 52/65 = 0.8 = 80% |
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Term
| If a Quantity Increases From 120 to 300, What is the Percent Increase? |
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Definition
| (300-120)/120 = 180/120 = 1.5 = 150% |
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Term
| If a Quantity Changes From 120 to 300, What is the Percent Change? |
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Definition
| (300-120)/120 = 180/120 = 1.5 = 150% |
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Term
| If a Quantity Decreases From 300 to 120, What is the Percent Decrease? |
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Definition
| (300-120)/300 = 180/300 = 0.6 = 60% |
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Term
| When Computing the Percent Increase, Which Number is the Base? |
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Definition
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Term
| When Computing the Percent Decrease, Which Number is the Base? |
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Definition
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