# Test Review The test will be on the following: Improper to Mixed

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Test Review The test will be on the following: Improper to Mixed
Mixed to Improper Simplification Adding and subtracting fractions with like and unlike denominators Adding and subtracting mixed numbers with like and unlike denominators Multiplying and dividing fractions Multiplying with Mixed numbers Reciprocal

Rules for Mixed to Improper
Step 1: Multiply the whole number with the denominator. Step 2: Take the answer from step 1 and add it to the numerator. Step 3: Take the answer from step 2 and put it over the original denominator. Ex) = 2 x 5 = = 15

Mixed to Improper 6 1/3 2 1/5 3 2/7 8 1/2

9/3 11/5 23/7 17/2

Changing Improper to Mixed Numbers
Step 1: Divide the denominator into the numerator. Step 2. The quotient is now your Whole number; the remainder is now your numerator and the divisor is now your denominator. Ex) 18 ÷ 5 = 15 3 Answer: 3 3 5 3 Whole number Denominator numerator

Improper to Mixed 8/5 20/9 22/7 13/3

Answers to changing improper to mixed numbers
1 2/5 2 2/9 3 1/7 4 1/3

Simplifying Fractions
In order to simply fractions you need to see what number will go into the numerator and the denominators. You need to get it in the simplest form. Ex) 9 ÷ 3 = 3 ÷ 3 = 1 36 ÷ 3 = 12 ÷ 3 = 4

Simplification of Fractions
20/24 2/8 3/9 36/63

5/6 1/3 4/7

Adding and Subtracting with like denominators
Step 1: The denominators are the same then just bring the denominator straight down Step2: Then add or subtract the numerators Step 3: Simplify your answer Ex) = 16 ÷ 2 = 8 = ÷

Adding and Subtracting with Like denominators
3/ /8 = 10/12 – 4/12 = 9/ /11 = 10/ /15 =

8/8 = 1 6/12 = ½ 17/11 = 1 6/11 9/15 = 3/5

/10 = 37 13/ /18 = 2 3/ /10 = 7 3/ /5 =

1/10 13 6/18 = /3 6 4/10 = 6 2/5 16 5/5 = = 17

Renaming to Subtract 2 ½ - 1 ¾ = 8 2/9 - 2 7/9 = 3 2/6 - 1 2/3 =
2 ½ ¾ = 8 2/ /9 = 3 2/ /3 = 7 ¼ /12 =

Adding and Subtracting with Unlike denominators
¾ - ½ = 1/ /12 = 5/6 - ¾ = ½ + 3/7 =

Adding and Subtracting Mixed Numbers with Unlike Denominators
7 1/ /3 = 2 1/ /8 = 8 5/ ¾ = 6 6/ ½ =

Comparing Fractions When comparing fractions we use the butterfly
method. You go diagonally across from the denominator to the numerator and multiply and put the number at the top of the numerator and compare those numbers. 5 27 < 35

Comparing Fractions 3/5 ____ 4/9 4/7 ___ ¾ 2/3 ____ 5/8 3/25 ___ 6/50

> < =

Multiplying Fractions
Step 1: Multiply the numerators Step 2: Multiply the denominators Step 3: Simplify if necessary Ex) x = ÷ 3 = 4 ÷

Multiplying Fractions
3/8 x 2/9 = 6/4 x 3/2 = 8/11 x 5/4 = 5/7 x 14/5 =

1/12 9/4 = 2 ¼ 10/11 14/7 = 2

Multiplying Mixed Numbers
Step 1: Change all mixed numbers into improper fractions Step 2: Multiply the numerators Step 3: Multiply the denominators Step 4: Simplify if necessary Ex) x = x = ÷ = 16 = 5 1 ÷

Multiplying with Mixed Numbers

24/21 = 8/7 = 1 1/7 160/ 45 = 32/9 = 3 5/9 230/ 24 = 115/12 = 9 7/12 35/4 = 8 3/4

Reciprocal To find the reciprocal of a number you are just
flipping the fraction. The denominator becomes the numerator and the numerator becomes the denominator. Ex) = 5

Reciprocal of Fractions
8/9 = 2/5 = 3/10 = 7 =

Answer to Reciprocal 9/8 5/2 10/3 1/7

Dividing Fractions Step 1: Keep the first fraction the same (Keep It)
Step 2: Change division to multiplication (Change It) Step 3: Take the reciprocal of the second fraction (flip it) Step 4: Multiply numerators Step 5: Multiply denominators Step 6: Simplify if necessary Ex) ÷ = x 5 = = 1 1

Dividing Fractions ÷ 2/3 = 6/5 ÷ 3/9 = 7/8 ÷ 5 = 11/5 ÷ 6/5 =

15/2 = 7 ½ 18/5 = 3 3/5 7/40 11/6 = 1 5/6

Dividing Fractions Step 1: All mixed numbers must be made improper
Step 2: Keep the first fraction the same (Keep It) Step 3: Change division to multiplication (Change It) Step 4: Take the reciprocal of the second fraction (flip it) Step 5: Multiply numerators Step 6: Multiply denominators Step 7: Simplify if necessary Ex) ÷ = 10 ÷ 18 = 10 x 5 = 50 ÷ 2 = 25 ÷

Dividing with Mixed Numbers
/5 ÷ 2 2/3 = 3 2/9 ÷ 4 1/5 = 7 1/6 ÷ 2 3/5 = 3 ¼ ÷ 2 ½ =