Proportions, Percent of Change (increase/decrease), Percent of Total, Number Theory, Factors and Multiples, Estimation Flashcards

Proportional Relationships and Percents, Proportions: Given a scale, Proportions: Given an Equivalency Statement, Proportions Given a descriptions of similar figures, Proportions: Given similar figures (37 cards)

1
Q

ratio

A

a comparison of two numbers using a fraction, a colon, or the word “to”. Ratios have the same units

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2
Q

rate

A

a ratio with different units

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3
Q

What is the verbal statement for 4 dogs : 3 cats

A

four dogs for every 3 cats

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4
Q

What is the fraction for four dogs for every 3 cats

A

4 dogs/3 cats

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5
Q

What is the colon of 4 dogs/3 cats

A

4 dogs : 3 cats 4:3

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6
Q

What word is commonly used to verbalize a unit rate phrase?

A

per

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7
Q

Unit Rate

A

a rate with a denominator of 1

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8
Q

Ratio example

A

2 feet/3 feet same units

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9
Q

Rate example

A

25 miles/3 hours different units

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10
Q

Proportion

A

3 inches/14 miles=x inches/84.5 miles

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11
Q

How do I know to use a proportion?

A
  • Contains a scale
  • Each of the numbers contains units
  • There are 3 numbers with units, and the problem asks for a 4th number with units.
  • Contains an equivalency statement that represents a rate
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12
Q

How is a scale is typically given?

A

a scale is typically given using a colon

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13
Q

What is the equation for finding the percent of change?

A

new number - original number/original number
then convert the fraction to a decimal and then convert to a percent
if the percent is positive, the percent of change was an increase, if the percent is negative, the percent of change was a decrease.

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14
Q

Examples of counting numbers

A

1,2,3,4,5,6,….

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15
Q

Examples of whole numbers

A

0,1,2,3,4,5,6,…

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16
Q

Integers

A

…,-5,-4,-3,-2,-1,0,1,2,3,4,5,…

17
Q

Rational Numbers

A

any number that can be written as a fraction a/b, where a and b are any integer.

18
Q

True or false: Rational Numbers include all terminating and repeating decimals.

19
Q

Prime

A

A positive integer that only has 1 and itself as factors. Ex. 2,3,13,29

20
Q

Composite

A

A positive integer that has factors other than 1 and itself . Ex. 4,12,27,44

21
Q

Even

A

A number that is divisible by two

22
Q

Odd

A

A number that is not divisible by two

23
Q

Is 1 prime, composite, both, or neither?

A

1 is neither prime nor composite

24
Q

True or False: 2 is not a prime number

A

False, 2 is the only even prime number

25
Is 0 an even or odd number
0 is an even number
26
Is the sum of two even numbers always even or always odd?
the sum of two even numbers is always even
27
True or false: the sum of two odd numbers is always odd
False, the sum of two odd numbers is always even
28
Is the sum of an even and odd number odd or even?
the sum of an even number and an odd number is always an odd number
29
What does prime factorization refer to
it refers to finding all of the prime numbers, that when multiplied together, result in a composite number
30
What is the prime factorization of 24
2x2x2x3 or 2^3x3
31
What is the GCF or Greatest Common Factor
the largest number that divides into all numbers in a given set. The GCF can only be as large as the smallest number in the set
32
What is the LCM or Last Common Multiple
the smallest multiple that all the numbers in a set have in common
33
What are two ways to find Factors and Multiples?
Listing and Factor Trees
34
Estimation
finding a rough calculation or approximation; different estimation strategies are helpful in different situations
35
Compatible Numbers
Estimating by rounding pairs of numbers to numbers that are easy to add, subtract, multiply, or divide Example: 31.8÷5.2 becomes 30÷5, so the estimated value is 6
36
Clustering
Estimating sums or products when all the numbers are close to a single value. Example: 42+38+40+41 becomes 40+40+40+40, so the estimated value is 160
37
Front-End Estimation
Estimating by rounding to the greatest place value or the number in front. Example: 412+58+1,780 would become 400+60+2,000, so the estimated value is 2,460