Post on 23-Dec-2015
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