CONVERTING IMPROPER FRACTIONS TO MIXED NUMBERS

The picture shown below illustrates how to convert an improper fraction to a mixed number.

In each of of the following examples, convert the given improper fraction to mixed number.

Example 1 :

275/3

Solution :

When we divide 275 by 3 as explained in the above picture, 3 goes into 275 by 91 times and we will have 2 left in 275.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 275/3 is

91 2/3

Example 2 :

155/7

Solution :

When we divide 155 by 7 as explained in the above picture, 7 goes into 155 by 22 times and we will have 1 left in 155.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 155/7 is

22 1/7

Example 3 :

782/13

Solution :

When we divide 782 by 13 as explained in the above picture, 13 goes into 782 by 60 times and we will have 2 left in 782.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 782/13 is

60 2/13

Example 4 :

75/8

Solution :

When we divide 75 by 8 as explained in the above picture, 8 goes into 75 by 9 times and we will have 3 left in 75.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 75/8 is

9 3/8

Example 5 :

178/15

Solution :

When we divide 178 by 15 as explained in the above picture, 15 goes into 178 by 11 times and we will have 13 left in 178.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 178/15 is

11 13/15

Example 6 :

The cooking time for a ham is 2/5 of an hour for each pound.

a. How long should you cook a ham that weighs 12  3/4 pounds?

b. Dinner time is 4:45 p.m. What time should you start cooking the ham?

Solution :

Cooking time for a ham = 2/5

= (2/5) x 60

= 2 x 12

= 24 minutes

a) time taken to cook 1 pound of ham will be 24 minutes.

Time taken to cook 12  3/4 pounds of ham =

=  12  3/4 x 24

= (51/4) x 24

= 51 x 6

= 306

= 300 + 6

= 5 hours and 6 minutes

To 12  3/4 pounds of ham, they will take 5 hours and 6 minutes.

b) To figure at what time we have to start cooking to finish the work at 4:45 pm, we have to subtract 5 hours and 1 minute from this time.

= 4 : 45 + 12

= 16 : 45

= 16 : 45 - 5 : 06

= 11 : 39

So, at 11 : 39 am itself they have to start cooking.

Example 7 :

You ask 150 people about their pets. The results show that 9/25 of the people own a dog. Of the people who own a dog, 1/6 of them also own a cat.

a. What fraction of the people own a dog and a cat?

b. How many people own a dog but not a cat? Explain.

Solution :

a)

Total number of people = 150

Number of people who has sog = 2/5 of 150

= (2/5) x 150

= 2 x 30

= 60 people they have dog at home

b) Number of people who has dog, in which 1/6 of the people will have cat.

= 1/6 of 60

= 1/6 x 60

= 10

Number of people who has cat is 10.

Example 8 :

A science experiment calls for 3/4 cup of baking powder. You have 1/3 cup of baking powder. How much more baking powder do you need?

a)  1/4 cup   b)    5/12 cup    c) 4/7 cup    d) 1 1/12 cups

Solution :

Amount of baking powder you need = 3/4

Amount of baking powder you have now = 1/3

Quantity of baking powder we need = 3/4 - 1/3

= (9 - 4)/12

= 5/12 cups 

Example 9 :

A rectangular sheet of paper is 5  2/3 cm long and 3  1/5 cm wide. Find its perimeter. 

Solution :

Length = 5  2/3 cm

Width = 3  1/5 cm

Converting into improper fraction, we get

length = 17/3 cm

Width = 16/5 cm

Perimeter of the rectangle = 2(length + width)

= 2(17/3 + 16/5)

= 2(85 + 48)/15

= 2(133)/15

= 266/15

= 255  11/15

Example 10 :

The recipe requires 3 1/4 cups of flour. Radha has 1  3/8 cups of flour. How many more cups of flour does she need?

Solution :

Amount of flour requires = 3  1/4

Quantity of flour she has = 1  3/8

Amount of flour she needs more = 3  1/4 - 1  3/8

= (3 - 1) + (1/4 - 3/8)

= 2 + (2 - 3)/8

= 2 -1/8

= (16 - 1)/8

= 15/8

= 1  7/8

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