Bell Work:

What number is ½ of ¾?

Answer:

3/8

Lesson 23:Multiplying and Dividing Mixed

Numbers

To multiply or divide mixed

numbers we first write each

mixed number (or whole number)

as a fraction. A mixed number can

be converted into a fraction.

2 ¼ = 4/4 + 4/4 + ¼ = 9/4

Another way to perform the

conversion is to multiply the whole

number by the denominator and

add the numerator to find the

numerator of the new fraction.

4 x 2 + 1 = 9

2 ¼ = 9/4

If the answer is an improper fraction we

might choose to convert the improper

fraction to a mixed number. We do so

by dividing the numerator by the

denominator.

9/4 = 2 ¼

The remainder becomes the numerator

of the fraction part of the mixed

number.

Example:

Simplify

2 1/3 x 1 1/2

Answer:

2 1/3 x 1 ½

= 7/3 x 3/2

= 21/6

= 3 3/6

= 3 1/2

Example:

Simplify

1 2/3 ÷ 2 1/2

Answer:

1 2/3 ÷ 2 ½

= 5/3 ÷ 5/2

= 5/3 x 2/5

= 10/15

= 2/3

Both of the previous problems

could have been reduced before

multiplying. We may reduce (or

cancel) to eliminate the need to

reduce after multiplying.

Example:

A carpenter is nailing horizontal

boards to the outside surface of a

building. The exposed portion of each

board is 6 ¾ inches. How many rows

of boards are needed to reach to the

top of an 8 foot wall?

Answer:

First convert 8 feet to 96 inches.

96 ÷ 6 ¾ = 96 ÷ 27/4

= 96/1 x 4/27 = 32/1 x 4/9

= 128/9 = 14 2/9

Fourteen boards is not enough. To

reach to the top of the wall the

carpenter will need 15 rows of boards.

Multiplying and Dividing Fractions and Mixed

Numbers1. Write whole numbers or mixed numbers as fractions

2. Multiplying Multiply numerators Multiply denominators

DividingInstead of dividing, multiply by the reciprocal of the divisor

3. Simplify the answer by reducing if possible. Improper fractions may be expressed as whole or mixed numbers

Example:

What is the area of a rectangle

2 ½ inches long and 1 ½

inches wide?

Answer:

3 ¾ inches 2

Example:

A recipe calls for 1 ¾ cups of

milk. How many cups of milk

are needed if the recipe is

doubled?

Answer:

3 ½ cups

HW: Lesson 23 #1-30

Due Next time