CONVERTING MIXED NUMBERS TO IMPROPER FRACTIONS

The process of converting a mixed number to an improper fraction has been clearly explained in the picture shown below.

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

Example 1 :

2 4/7

Solution :

18/7

Example 2 :

12 2/3

Solution :

38/7

Example 3 :

100 4/7

Solution :

704/7

Example 4 :

28 2/5

Solution :

142/5

Example 5 :

1 1/3

Solution :

4/3

Example 6 :

1 1/2

Solution :

3/2

Example 7 :

71 5/6

Solution :

431/6

Example 8 :

3 7/8

Solution :

31/8

Example 9 :

12 8/9

Solution :

116/9

Example 10 :

20 4/7

Solution :

144/7

Example 11 :

Mary bought 3 1/2 m of lace. She used 1 3/4 m of lace for her new dress. How much lace is left with her?

Solution :

Quantity of lace Mary has purchased = 3  1/2 m

Quantity of lace she has used = 1  3/4 m

Quantity of lace left = 3  1/2 - 1 3/4

= (3 - 1) + 1/2 - 3/4

= 2 + (2 - 3) / 4

= 2 -  1/4

= (8 - 1)/4

= 7/4

Example 12 :

Grip size of a tennis racquet is 11  9/80 cm. Express the size as an improper fraction.

Solution :

Given mixed fraction = 11  9/80

Converting into improper fraction = [(11 x 80) + 9]/80

= (880 + 9)/80

= 889/80

Grip size of a tennis racquet is 889/80.

Example 13 :

Express 6  2/3 as an improper fraction

Solution :

Given mixed fraction is 6  2/3

Converting into improper fraction, we get

=  [(6 x 3) + 2]/3

= (18 + 2)/3

= 20/3

Example 14 :

Express 3  2/5 as a decimal.

Solution :

Given mixed fraction is 3  2/5

Whole number is 3. Converting the fraction part as decimal,

2/5 = (2/5) x (2/2)

= 4/10

= 0.4

3 + 2/5 = 3 + 0.4

= 3.4

So, the required decimal is 3.4

Example 15 :

Express 0.041 as a fraction.

Solution :

Given decimal is that 0.041

To convert it as fraction, by observing the number of digits after the decimal, we have 3 digits. So, we have to multiply by 1000.

= 0.041 x (1000/1000)

= 41/1000

Example 16 :

Express 6.03 as a mixed fraction.

Solution :

Given decimal is that 6.03

6.03 = 6 + 0.03

= 6 + (0.03) x (100/100)

= 6 + 3/100

= 6  3/100

Example 17 :

Convert 1537 cm to m and express the result as an improper fraction.

Solution :

1537 cm

100 cm = 1 m

1537 = 1500 + 37

= 15 x 100 + 37

1500 cm = 15 m

37 cm = 37/100 m

= 15  37/100 m

Example 18 :

Convert 2435 m to km and express the result as mixed fraction.

Solution :

= 2435 m

1000 m = 1 km

= 2000 m + 435 m

= (2 x 1000 + 435/1000) 

= 2 km + 0.435 km

= 2  435/1000 km

Example 19 :

Sunil purchased 12  1/2 litres of juice on Monday and 14  3/4 litres of juice on Tuesday. How many litres of juice did he purchase together in two days?

Solution :

Amount of juice purchased on Monday = 12  1/2 liters

Amount of juice purchased on Tuesday = 14 3/4 liters

Quantity of juice purchased together in two days 

= 12  1/2 + 14  3/4

= (12 + 14) + 1/2 + 3/4

= 26 + (2 + 3)/4

= 26 + 5/4

Converting into mixed fraction, we get

= 26 + 1  1/4

= (26 + 1) + 1/4

= 27  1/4

So, amount of juice purchased together is 27  1/4 liters.

Example 20 :

Nasir travelled 3  1/2 km in a bus and then walked 1 1/8 km to reach a town. How much did he travel to reach the town?

Solution :

Distance covered by bus = 3  1/2 km

Distance covered by walk = 1  1/8 km

Total distance covered = 3  1/2 + 1  1/8

= (3 + 1) + 1/2 + 1/8

= 4 + (4 + 1)/8

= 4  5/8

So, the required distance covered is 4  5/8 km.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.