Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify and multiply

Picture Method 4/8 of 64 The picture is worth the whole number Divide the picture up into the amount of pieces Label each piece Shade in the amount of pieces Total the amount of pieces

Math Method 1) Put the whole number over 1 (make it a fraction) 2) Cross simplify/reduce: divide out a common factor from the numbers across 3) Re-write the problem 4) Multiply the numerators 5) Multiply the denominators 6) Reduce

In multiplication, “of” = multiply So, 2/3 of 4/6 means 2/3 x 4/6 Simplifying before Multiplying Fractions: –Cross Simplify: Divide out a common factor from the numbers across

Multiplying Fractions Notes Ex: 2 / 3 x 1 / 4 1.Cross reduce/simplify 1/3 x 1/2 2.Multiply the numerators, and then multiply the denominators. 1 x 1 = 3 x 2 = 3.Simplify if possible

Multiplication of Fractions with a Picture Draw a model representing 2 / 3 of 1 / 4.

1. 2 / 3 x 1 / 4 = 2. 5 / 6 of 2 / 5 = 3. 1 / 3 · 9 / 10 = 4. 1 / 4 x 12 = Practice Problems:

Simplest Form: when the only common factor of the numerator and denominator is 1. Ex: 2 / 3 is in simplest form since 2 and 3 have only 1 as a common factor. Write 20 / 25 in simplest form. 20: 1, 2, 4, 5, 10, 20 25: 1, 5, / 25 = 4 / 5  List the factors for the numerator and denominator and find the GCF  Divide the numerator and denominator by the GCF The fraction 20 / 25 written in simplest form is 4 / 5. Reducing Fractions to Simplest Form

Changing a Mixed Number to an Improper Fraction Write 6 ¼ as an improper fraction. 1.Multiply the whole number by the denominator. 6 x 4 = Add the numerator to this total = 25 3.Write as an improper fraction. 25 / 4

Multiplying Mixed Numbers Notes Ex: 2 1 / 7 x 2 2 / 5 1.Change to improper fractions. 15 / 7 x 12 / 5 2.Simplify diagonally (cross simplify) / 7 x 12 / 3.Multiply. 3 / 7 x 12 / 1 = 4.Simplify again. 36 / 7 =

1.1 2 / 5 x 4 1 / 3 = / 7 · 1 2 / 5 = / 3 x 7 1 / 2 = Practice:

Dividing Fractions Notes Ex: 8  4 / 5 1.Find the reciprocal of the second number. The reciprocal of 4 / 5 is 5 / 4. Just FLIP the second number. 2.Change to multiplication and simplify diagonally if you can. 8 / 1 x 5 / 4 3.Multiply. 2 / 1 x 5 / 1 = 4.Simplify. 10 / 1 =

Dividing Mixed Number Notes Ex: 5 1 / 3  2 2 / 5 1.Write each mixed number as an improper fraction. 16 / 3  12 / 5 2.Find the reciprocal of the second number. The reciprocal of 12 / 5 is 5 / Change to multiplication and simplify diagonally if you can. 16 / 3 x 5 / 12 4.Multiply. 4 / 3 x 5 / 3 = 5.Simplify. 20 / 9 =

What is the reciprocal of each number? 9 / / / 7 1 / 23

1. 3 / 8  3 = 2. 7 / 8  2 / 7 = / 2  1 2 / 5 = Practice

/ 3  1 / 2 = / 10  1 5 / / 10  3 Practice

Find each quotient. 6  2 / 5 2 / 5  3 / 4 9 / 10  / 4  2 1 / / 10  1 5 / 6