DIVIDING MIXED NUMBERS

Example 1 :

Find the quotient. Write in simplest form :

9 2/5 ÷ 1 1/3

Solution :

Convert the given mixed numbers to improper fractions.

9 2/5 = 37/5

1 1/3 = 4/3

9 2/5 ÷ 1 1/3 :

= 47/5 ÷ 4/3

Write the division as multiplication by taking reciprocal of the second fraction.

= 47/5 x 3/4

Multiply the numerators and denominators.

= (47 x 3)/(5 x 4)

= 141/20

141/20 is an improper fraction, convert it to mixed number.

=7 1/20

Example 2 :

Find the quotient. Write in simplest form :

6 1/2 ÷ 4 1/5

Solution :

Convert the given mixed numbers to improper fractions.

6 1/2 = 13/2

4 1/5 = 21/5

6 1/2 ÷ 4 1/5 :

= 13/2 ÷ 21/5

Write the division as multiplication by taking reciprocal of the second fraction.

= 13/2 x 5/21

Multiply the numerators and denominators.

= (13 x 5)/(2 x 21)

= 65/42

65/42 is an improper fraction, convert it to mixed number.

= 1 23/42

Example 3 :

Find the quotient. Write in simplest form :

3 1/10 ÷ 2 3/4

Solution :

Convert the given mixed numbers to improper fractions.

3 1/10 = 31/10

2 3/4 = 11/4

3 1/10 ÷ 2 3/4 :

= 31/10 ÷ 11/4

Write the division as multiplication by taking reciprocal of the second fraction.

= 31/10 x 4/11

Multiply the numerators and denominators.

= (31 x 4)/(10 x 11)

= 124/110

= 62/55

62/55 is an improper fraction, convert it to mixed number.

= 1 7/55

Example 4 :

How many 1/4 pound hamburgers can you make from 3 1/2 pounds of ground beef?

Solution :

Quantity of ground beef = 3  1/2 pounds

Quantity of ground beef required = 1/4 pounds 

number of hamburgers can be made = 3  1/2 ÷ 1/4 

= 7/2 ÷ 1/4

= 7/2 x (4/1)

= 14 hamburgers.

Example 5 :

How many 1 3/5 inch thick books can fit on a 14  1/2 inch long bookshelf?

Solution :

Length of bookshelf = 14  1/2 inch

Thickness of books = 1  3/5

Number of books = 14  1/2 ÷ 1  3/5

= (29/2) ÷ (8/5)

= 29/2 x (5/8)

= 145/16

= 9.0625

approximately 9 books can fit in the shelf.

Example 6 :

You have 12 cups of granola and 8 1/2 cups of peanuts to make trail mix. 

What is the greatest number of full batches of trail mix you can make?

Explain how you found your answer.

Solution :

To make one trail mix, we need 2  3/4 cups of granola.

Number of times, we can take gronala from 12 cups

= 12 / ( 2  3/4)

= 12 / (11/4)

= 12 x (4/11)

= 48/11

= 4.3

To make one trail mix, we need 1  1/3 cups of peanuts.

Number of times, we can take peanuts from 8  1/2 cups

= 8  1/2 / (1  1/3)

= (17/2) / (4/3)

= (17/2) x (3/4)

= 51/8

= 6.375

So, approximately 4 trail mix can be made.

Example 7 :

You make skateboard ramps by cutting pieces from a board that is 12 1/2 feet long.

a. Estimate how many ramps you can cut from the board. Is your estimate reasonable? Explain.

b. How many ramps can you cut from the board? How much wood is left over?

Solution :

Length of skate board = 12  1/2 feet

Lenght of one piece = 1  7/8 ft

a) Number of ramps to be cut = 12  1/2 / 1  7/8

= (25/2)/(15/8)

= (25/2) x (8/15)

= 20/3

= 6.6

Number of ramps can be cut is 6.

b) Material required for one piece = 1 7/8

= 15/8

= 1.875

Material required for 6 ramps = 6(1.875)

= 11.25 ft

Original length = 12 1/2 ft

= 25/2

= 12.5 ft

Material left over = 12.5 - 11.25

= 1.25 ft

Divide. Write the answer in simplest form.

Example 8 :

How many inches are in 5 1/2 yards?

Solution :

1 yard = 12 inches

5  1/2 yards = 11/2 yards

11/2 yards = 11/2 x 12

= 66 inches

Example 9 :

You use 1/8 of your battery for every 2/5 of an hour that you video chat. You use 3/4 of your battery video chatting. How long did you video chat?

Solution :

Ratio between battery use and time taken

1/8 : 2/5

To make 2/5 hour as 1 hour, we have to divide by 2/5

= (1/8) x (5/2) : 1

= (5/16) : 1

When 5/16 battery is used the duration of video chatting is 1 hour.

When 3/4 battery is used what is the duration.

(5/16) / 1 = (3/4) / x

x = (3/4) / (5/16)

= 3/4 x 16/5

= 12/5 hours.

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