FRACTION OF QUANTITIES

In simplest form, state what fraction of:

Problem 1 :

1 metre is 20 cm

Solution :

20 cm as a fraction of 1 metre = 20 cm/ 1 m

= 20 cm/100 cm

= 1/5

Problem 2 :

 2 metres is 78 cm

Solution :

78 cm as a fraction of 2 metres = 78 cm/ 2 m

= 78 cm/200 cm

= 39/100

Problem 3 :

1 kg is 500 g

Solution :

500 g as a fraction of 1 kg = 500 g/ 1 kg

= 500 g/1000 g

= 1/2

Problem 4 :

1 week is 2 days

Solution :

2 days as a fraction of 1 week = 2 days/ 1 week

= 2 days/7 days

= 2/7

Problem 5 :

1 day is 5 hours

Solution :

5 hours as a fraction of 1 day = 5 hours/ 1 day

= 5 hours/24 hours

= 5/24

Problem 6 :

November is two days

Solution :

2 days as a fraction of November = 2 days/30 days

= 1 day/15 days

= 1/15

Problem 7 :

 a decade is one year

Solution :

1 year as a fraction of a decade = 1year/decade

= 1 year/10 years

= 1/10

Problem 8 :

2 dollars is 27 cents

Solution :

27 cents as a fraction of a 2 dollars = 27 cents/2 dollars

= 27 cents/200 cents

= 27/200

Problem 9 :

In a bag there are 12 marbles. 1/2 are blue. How many blue marbles are there ?

Solution :

Total number of marbles = 12

Part of blue marbles = 1/2

Number of blue marbles = 1/2 of 12

= (1/2) x 12

= 6

So, total number of blue marbles is 6.

Problem 10 :

There are 55 dinosaur bones at the local museum. Out of these 2/5 are from a Tyrannosaurus Rex. How many bones would that be ?

Solution :

Total number of dinosaur bones = 55

Part from Tyrannosaurus Rex = 2/5 of 55

= (2/5) x 55

= 2 x 11

= 22

So, the required number of bones is 22.

Problem 11 :

Sara is having a party. Het cake is cut into 24 pieces. 3/4 of the cake is eaten during the party. How many pieces of cake are left.

Solution :

Total number of cakes = 24

part of total eaten = 3/4

Quantity left = 1/4 of total number of pieces

= 1/4 of 24

= (1/4) x 24

= 24/4

 = 6

So, 6 pieces of cake is  left.

Problem 12 :

Over 20 days in February, it rained on 12 days. What fraction of the days were rainy? Simplify your answer

Solution :

Total number of days = 20

Total number of rainy days = 12

Fraction of rainy days = 12/20

= 3/5

Problem 13 :

James earns $800 a month. He spends 1/4 on a rent and 2/5 of food and bills. How much money has he left ?

Solution :

Total earning = $800

Amount spent for rent = 1/4 of 800

= (1/4) x 800

= 200

Amount spent for food = 2/5 of 800

= (2/5) x 800

= 2 x 160

= 320

Amount he spent for rent and food = 200 + 320

= 520

Amount he left = 800 - 520

= 280

So, the required amount he left is $280.

Problem 14 :

Which is larger 

1/2 of 280 or 3/8 of 400

Solution :

So, 3/8 of 400 is 150.

Problem 15 :

Joanne has 300 sweets. She gives 1/2 of the sweets to Erin. Joanne then gives 1/3 of the remaining sweets of William. How many sweets does Joanne have left ?

Solution :

Total number of sweets = 300

number of sweets to Erin = 1/2 of 300

= (1/2) x 300

= 150

Number of sweets to Joanne = 1/3 of 300

= (1/3) x 300

= 100

Problem 16 :

Hannah has $900. She spends 1/3 on books and 2/5 on presents. What fraction of 900 has she left ?

Solution :

Amount Hannah has = $900

Amount spent for books = 1/3 of 900

= 1/3 x 900

= 300

Amount spent for presents = 2/5 of 900

= 2/5 x 900

= 2 x 180

= 360

Amount he left = 900 - (300+360)

= 900 - 660

= 240

Fraction she left = 240/900

= 24/90

= 8/30

= 4/15