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.• 1 6http://www.xpmath.com/forums/arcade.php?do=play&gameid=29

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

20/25 = 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 = 24.

2.Add the numerator to this total.• 24 + 1 = 25

3.Write as an improper fraction.• 25/4

http://www.xpmath.com/forums/arcade.php?do=play&gameid=37

Multiplying Mixed Numbers NotesEx: 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 =

2.2 6/7 · 1 2/5 =

3.1 2/3 x 7 1/2 =

Practice:

Dividing Fractions NotesEx: 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 =http://www.xpmath.com/forums/arcade.php?do=play&gameid=28

Dividing Mixed Number NotesEx: 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 5/12 .

3. 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

• 5 2/3

• 8

• 1 6/7

• 1/23

1.3/8 3 =

2.7/8 2/7 =

3.2 1/2 1 2/5 =

Practice

4. 1 2/3 1/2 =

5. 1 1/10 1 5/6

6. 9/10 3

Practice

Find each quotient.

• 6 2/5

• 2/5 3/4

• 9/10 3

• 6 1/4 2 1/2

• 1 1/10 1 5/6