 # FRACTIONS REVIEW.

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FRACTIONS REVIEW

NUMERATOR DENOMINATOR

To ADD or SUBTRACT fractions with like denominators:
Add or subtract the numerators only. Keep the denominators the same. Simplify (in lowest term) the fraction, if possible. (hint: Find the GCF - What’s the largest number that goes into the numerator and denominator equally?) If you end up with an improper fraction , change it to a mixed number. Why? (hint: Divide the denominator into the numerator)

Try These 2 7 + 3 = 5 7 5 8 - 2 = 3 8 Whole number 9 4 2 - 8 1 = 1 4 + 8 = 9 Denominator 2 1 4 = 4 Improper fraction Numerator

6 4 3 4 Adding mixed numbers with like denominators. 2 1/8 + 2 5/8 1/8
If James has two and one eighth pizzas and Jane has two and five eighths pizzas, how many pizza’s do they have together. 2 1/8 /8 1/8 /8 6/8 Step 1: Add the Fractions 2+2=4 Step 2: Add the whole numbers 4 6 8 Step 3: Combine the whole number and the fraction. 4 3 Step 4: Simplify if possible

Try Some 7 12 = 2 3 5 1 1 6 = 3 4 7 + 1 = 10 5 7 14 8 15 + 7 = 1 9 15 = = 10

+ Adding and Subtracting Unlike Fractions -

+ List the multiples of both denominators. 4: 4, 8, 12, 16, 20
6: 6, 12, 18, 24, 30 Find the least common multiple (LCM). Write new fractions with the LCM as the new denominator. 1 1 4 6 + 1 ? 4 12 6 12 = +

Find the factor you multiply by to get from your original denominator to your new denominator or divide the new denominator by the old . Use that same factor, and multiply it by your original numerator to get a new numerator. 3 ? 4 12 1 ? 6 12 = + 12 ÷ 4 = 3 x 3 12 ÷ 6 = 2 x 1 11 12

Separate the whole number parts from the fraction parts. Find common denominators for the fractions and then add them. Add the whole numbers together. Simplify.

Borrowing When the top numerator is smaller than the bottom numerator, you MUST BORROW! Take one whole from the top whole number. Make that one borrowed into a fraction having the same denominator as your common denominator. Add that numerator to the new numerator. This is now your newer numerator that you will use to subtract from. 3 10 3 10 5 2 11 - 8 10 + 10 13 10 10 = 11 = 4 10 4 8 8 = = 10 10 9 2

Don’t forget to SIMPLIFY!
Let’s Try These 9 3 + 4 5 6 7 4 - 1 2 3 5 9 3 - 4 5 6 Don’t forget to SIMPLIFY!

Multiplying With Fractions

Multiply Fractions: Just Follow These Easy Steps!
Multiply the numerators and write down the answer as your new numerator. Multiply the denominators and write down the answer as your new denominator. Simplify.

Example 3 2 6 1 x = = 9 36 6 4 This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6.

Multiplying by a Whole Number
Turn your whole number into a fraction by placing a 1 as the denominator. If your answer is improper, divide the bottom into the top. 4 5 x 20 1 = 80 16

Simplifying Factors Before you multiply, you can make the problem simpler. You can find the GCF of any numerator and denominator. Find a factor that equally divides the top number and bottom number. Divide and rewrite the problem.

Example 1 In the second fraction, 8 and 16 have a GCF of 8. 1 5 14 5 8 x = 8 ÷ 8 = 1 and 16 ÷ 8 = 2 7 16 2 Now, multiply with the simpler numbers. 5 x 1 = 5 and 7 x 2 = 14.

Or Cross-cancel In the first fraction, the numerator and the denominator of the second fraction have a GCF of 4. 1 4 5 x 16 = In the second fraction, the numerator and the denominator of the first fraction have a GCF of 5. 16 ÷ 4 = 4 and 5 ÷ 5 =1 Now, multiply across. 1 x 1 = 1 and 1x 4 = 4.

To Multiply Mixed Numbers:
Change any mixed numbers to improper fractions. Simplify factors if possible. Multiply numerators by numerators and denominators by denominators. Simplify and/or change improper fractions back into mixed numbers.

Example 1 4 x 6 7 2 9 27 3 = 14 2 14 27 1 - 14 13 1 13 14

Work on These 4 1 6 x 3 5 = 3 1 2 x 8 = x 7 2 1 8 =

÷ Dividing Fractions ÷

To Divide Fractions: Rewrite the first fraction.
Change the division sign to a multiplication sign. Flip the second fraction upside down. Multiply across.

Rewrite as a multiplication problem:
Check this out! 1 3 ÷ 2 Rewrite as a multiplication problem: x =

Your turn! 12 ÷ 3 5 1 3 4 ÷ 2 6 1 4 5 ÷ 6 9

Find common denominator Find new numerator. Add numerators Keep denominators the same Add whole numbers Simplify if possible Find common denominator Find new numerator Top numerator must be larger than bottom. Borrow from whole number if not. Subtract numerators Simplify if possible +++++

Multiplying and Dividing Fractions
Change mixed fraction to improper fraction Simplify fractions or cross-cancel Multiply across (numerators and denominators Simplify if possible Change mixed fraction to improper fraction Change (÷) to (×) Flip the second fraction Simplify fractions or cross-cancel Multiply across (numerators then denominators Simplify if possible x x x x x ÷ ÷ ÷ ÷ ÷

Classwork Try This Interactive Game to Help You Review Operations with Fractions BUG SPLAT HOMEWORK TIME!!! Adding, Subtracting, Multiplying, and Dividing Fractions (Handout)