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
ratio
a comparison of two numbers using a fraction, a colon, or the word “to”. Ratios have the same units
rate
a ratio with different units
What is the verbal statement for 4 dogs : 3 cats
four dogs for every 3 cats
What is the fraction for four dogs for every 3 cats
4 dogs/3 cats
What is the colon of 4 dogs/3 cats
4 dogs : 3 cats 4:3
What word is commonly used to verbalize a unit rate phrase?
per
Unit Rate
a rate with a denominator of 1
Ratio example
2 feet/3 feet same units
Rate example
25 miles/3 hours different units
Proportion
3 inches/14 miles=x inches/84.5 miles
How do I know to use a proportion?
- 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
How is a scale is typically given?
a scale is typically given using a colon
What is the equation for finding the percent of change?
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.
Examples of counting numbers
1,2,3,4,5,6,….
Examples of whole numbers
0,1,2,3,4,5,6,…
Integers
…,-5,-4,-3,-2,-1,0,1,2,3,4,5,…
Rational Numbers
any number that can be written as a fraction a/b, where a and b are any integer.
True or false: Rational Numbers include all terminating and repeating decimals.
True
Prime
A positive integer that only has 1 and itself as factors. Ex. 2,3,13,29
Composite
A positive integer that has factors other than 1 and itself . Ex. 4,12,27,44
Even
A number that is divisible by two
Odd
A number that is not divisible by two
Is 1 prime, composite, both, or neither?
1 is neither prime nor composite
True or False: 2 is not a prime number
False, 2 is the only even prime number
Is 0 an even or odd number
0 is an even number
Is the sum of two even numbers always even or always odd?
the sum of two even numbers is always even
True or false: the sum of two odd numbers is always odd
False, the sum of two odd numbers is always even
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
What does prime factorization refer to
it refers to finding all of the prime numbers, that when multiplied together, result in a composite number
What is the prime factorization of 24
2x2x2x3 or 2^3x3
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
What is the LCM or Last Common Multiple
the smallest multiple that all the numbers in a set have in common
What are two ways to find Factors and Multiples?
Listing and Factor Trees
Estimation
finding a rough calculation or approximation; different estimation strategies are helpful in different situations
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
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
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
