MULTIPLYING INTEGERS AND FRACTIONS

Problem 1 :

3 × 3/6

Solution :

= 3 × 3/6

= (3/1) × (3/6)

= 9/6

HCF of 9 and 6 is 3.

So, dividing the numerator and denominator by 3. We get,

= 3/2

= 1  1/2

Problem 2 :

2/3 × 7

Solution :

= (2/3) × (7/1)

= 14/3

HCF of 14 and 3 is 1.

So, dividing the numerator and denominator by 1. We get,

= 14/3

= 4 2/3

Problem 3 :

(4/7) of 28

Solution :

= (4/7) of 28

The word " of " can be replaced by multiplication sign.. 

= (4/7) x 28

= (4/7) x (28/1)

= (4 x 28) / (7 x 1)

The highest common factor of 28 and 7 is 7.

= 4 x 4

= 16

So, 4/7 of 28 is 16.

Problem 4 :

(3/4) of 124

Solution :

= (3/4) of 124

Here the word of can be replaced by multiplication sign.

= (3/4) x 124

Highest common factor of (4 and 124) is 4.

= 3 x 31

= 93

Problem 5 :

(2/5) of -65

Solution :

= (2/5) of -65

Here the word of can be replaced by multiplication sign.

= (2/5) x 65

Highest common factor of (5 and 65) is 5.

= 3 x (-13)

= -39

Problem 6 :

Find 2/3 of $213 ?

Solution :

= 2/3 of $213

= (2/3) x 213

Dividing 213 by 3, we get

= 2 x 71

= 142

Problem 7 :

Millie calculated that her bicycle cost 1/83 of the cost of her father’s car. If the car cost $ 38014, what did her bicycle cost?

Solution :

Cost of car = $38014

Cost of bicycle = 1/83 of 38014

= (1/83) x 38014

= $458

So, cost of the bicycle is $458.

Problem 8 :

The price of a shirt is 2/13 of the cost of a suit. If the suit costs $292.50, find the cost of the shirt.

Solution :

Cost of suit = $292.50

Price of shirt = 2/13 of 292.50

= (2/13) x 292.50

= $22.5

Problem 9 :

Julie owes Gigi 3/5 of $1336.25. How much does she owe Gigi?

Solution :

Amount given = 3/5 of 1336.25

= (3/5) x 1336.25

= 3 x 267.25

= 801.75

Problem 10 :

2/3 of an amount of money is $519. Find 1/3 of the money

Solution :

Let x be the required money.

2/3 of the money x = 519

x = 519 / (2/3)

x = 519 x (3/2)

x = 778.5

1/3 of x = (1/3) x 778.5

1/3 of x = 259.5