DIVIDING FRACTIONS!

Divide a whole number by a unit fraction

2 WAYS!METHOD #1 of dividing fractions:

Create equivalent fractions and create a common denominator for both fractions.

Using the newly created equivalent fractions, divide across

LET’s WATCH! http://www.mathplayground.com/howto_divide_fractions.h

tml http://learnzillion.com/lessons/206-divide-fractions-by-frac

tions-using-the-common-denominator http://learnzillion.com/lessons/1250-divide-a-fraction-by-a-

whole-number http://learnzillion.com/lessons/1263-divide-a-whole-numbe

r-by-a-nonunit-fraction http://learnzillion.com/lessons/1251-divide-a-fraction-by-a-

fraction

Let’s Practice!2 divided by 1/4:

2/1 divided by 1/4:Common denominator: 4

8/4 divided by 1/4 = 8

Two numbers are reciprocals if their product is 1. A reciprocal of a number (fraction) is when you “flip” the fraction’s numerator and denominator.EXAMPLE: 3/4 The reciprocal is: 4/3

Let’s Watch and Practice!http://learnzillion.com/lessons/1315-understand-

why-dividing-by-a-number-gives-the-same-result-as-multiplying-by-its-reciprocal

http://learnzillion.com/lessons/1290-understand-reciprocals-by-thinking-about-inverse-relationship-between-multiplication-and-division

http://learnzillion.com/lessons/1323-solve-division-of-fractions-problems-using-reciprocals

http://learnzillion.com/lessons/356-divide-fractions-by-fractions-using-the-reciprocal

Look at the relationship between thefractions and . If you switch the numerator and denominator of a fraction,you will find its reciprocal. Dividing by a number is the same as multiplying by itsreciprocal.

34__ 4

3__

24 ÷ 4 = 6 24 • = 614__

Additional Example 1A: Finding Reciprocals

Find the reciprocal.

19__

19__ • = 1 Think: of what number is 1?

19__1

9__

19__ • 9 = 1 of is 1. 1

9__ 9

1__

The reciprocal of is 9.19__

Additional Example 1B: Finding Reciprocals

Find the reciprocal.

23__

23__ • =

1Think: of what number is 1?

23__

32__2

3__ • = = 16

6__ of is 1. 2

3__ 3

2__

The reciprocal of is .23__ 3

2__

15__

165__ • =

1Write 3 as . 1

5__

516__16

5__ • = = 180

80__ of is 1.

165__ 5

16__

The reciprocal of is .165__ 5

16__

165__

Additional Example 1C: Finding Reciprocals

Find the reciprocal.

3

Check It Out: Example 1A

Find the reciprocal.

14__

14__ • =

1Think: of what number is 1?

14__

14__ • 4 = 1 of is 1. 1

4__ 4

1__

The reciprocal of is 4.14__

Check It Out: Example 1B

Find the reciprocal.

45__

45__ • =

1Think: of what number is 1?

45__

54__4

5__ • = =

12020__ of is 1. 4

5__ 5

4__

The reciprocal of is .45__ 5

4__

18__

Check It Out: Example 1C

Find the reciprocal.

4

Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

÷ 7 87__

87__ ÷ 7 = •

Rewrite as multiplication using the

reciprocal of 7, . 17__

Multiply by the reciprocal.

87

__ 17__

8 • 17 • 7____ =

The answer is in simplest form.

=

849__

When you divide by a proper fraction, the quotient will be greater than the dividend. For example, since there are 8 halves in 4, 4 ½ = 8.

Caution!

DO NOW

DO NOWA juice container contains 2/4 quart of juice.

Niasia pours 1/3 quart of the juice into a cup. How much juice is left in the container?

There are 334 students in LV MOORE. If 2/5 of the students are girls, how many are boys? (do not leave it as 3/5 are boys – find the actual #)

The recipe for cookies requires 4/5 cup of sugar. If Jonah wants to make 1/3 of the total recipe, how much sugar does he need for the adjusted recipe?

REVIEW!Write an equivalent fraction for: 7/8Compare fractions! < > =

2/3 7/8 5/6 7/18

4/9 + 5/61 5/8 - 2 2/3Calculate the perimeter of a triangle with 3 sides

measuring: 5/6, 7/8, 1 ¾5/11 * 2/36 ½ divided by 6/7

Relationship between multiplication and division (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3

How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?

How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers

÷ 56__

56__ ÷ = •

Rewrite as multiplication using the

reciprocal of , . 32__

Simplify before multiplying.

56

__ 32__

5 • 36 • 2____ =

You can write the answer as a mixed number.

=

54__

23__

23__ 2

3__

1

2Multiply.

= 1

14__

Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers

2 ÷ 1 34__

Write the mixed numbers as

improper fractions. 2 =

and 1 = 1312__

Rewrite as multiplication.

11 • 124 • 13______

=

You can write the answer as a mixed number.

=

3313__

112__

34__

1

3Simplify before multiplying.

= 2

713__

2 ÷ 1 = ÷34

__ 112__ 11

4__ 13

12__ 11

4__

112__

114__ 12

13__ •

Multiply. =

Check It Out: Example 2ADivide. Write each answer in simplest form.

÷ 3 23__

23__ ÷ 3 = •

Rewrite as multiplication using the

reciprocal of 3, . 13__

Multiply by the reciprocal.

23

__ 13__

2 • 13 • 3____ =

The answer is in simplest form.

=

29__

Check It Out: Example 2B

÷ 710__

710__ ÷ = •

Rewrite as multiplication using the

reciprocal of , . 51__

Simplify before multiplying.

710__ 5

1__

7 • 510 • 1____ =

You can write the answer as a mixed number.

=

72__

15__

15__ 1

5__

1

2Multiply.

= 3 12__

Check It Out: Example 2C

3 ÷ 1 23__

Write the mixed numbers as

improper fractions. 3 =

and 1 = . 109__

Rewrite as multiplication.

11 • 93 • 10______

=

You can write the answer as a mixed number.

=

3310__

19__

23__

1

3Simplify before multiplying.

= 3

310__

3 ÷ 1 = ÷23

__ 19__ 11

3__ 10

9__ 11

3__

19__

113__ 9

10__ •

Multiply. =

DO NOWFind the reciprocal.

1. 2.

Divide. Write each answer in simplest form.

3. ÷ 20 4. 3 ÷ 2

5. Rhonda put 2 pounds of pecans into a -pound bag. How many bags did Rhonda fill?

111__ 8

13__

47__ 1

2__ 1

2__

34__ 1

4__

111__ 13

8__

135__ 7

5 __ 2

5__, or 1

11 bags

1. Identify the reciprocal of .

A. –15 C.

B. D. 15

Lesson Quiz for Student Response Systems

2. Identify the reciprocal of .

A. 15 C.

B. 7 D.

Lesson Quiz for Student Response Systems

3. Divide and identify the answer in the simplest form.

A. C.

B. D.

Lesson Quiz for Student Response Systems

4. Divide and identify the answer in the simplest form.

A. C.

B. D.

Lesson Quiz for Student Response Systems

Dividing Fractions

Math Journaling – Explain in words what it means to divide a whole number by a fraction and 2 fractions.

How do you use multiplication to divide any number by a fraction?