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

Problem 11 :

Your friend has 12 CDs and 3/4 of them are pop music. How many CDs are pop music?

Solution :

Total number of CDs = 12

Number of CD's for pop music = 3/4 of 12

= 3/4 ⋅ 12

= (3 ⋅ 12)/4

= 3 ⋅ 3

= 9 CDs

So, number of CDs of pop music is 9.

Problem 12 :

A batch of oatmeal muffins calls for 2/3 cup of oats. How many cups of oats do you need to make four batches of muffins?

Solution :

A batch of oatmeal muffin calls = 2/3 cups of oats

Number of batches = 4

Number of cups of oats need = 2/3 of 4 

= 8/3

= 2  2/3 cups

Problem 13 :

There are 365 days in a year and rain falls on 2/5 of the days. How many days does it rain during the year?

Solution :

Number of days in a year = 365

Number of days raining during the year = 2/5 of 365

= 2/5 x 365

= (2 x 365)/5

= 2 x 73

= 146 days

So, the number of days raining in a year is 146 days.

Problem 14 :

A rectangular picnic shelter is 75 feet long by 60 feet wide. A model of the shelter is 1/15 as wide and 1/15 as long as the actual shelter. What is the area, in square feet, of the model of the shelter?

Solution :

Original length = 75 feet

Length of model shelter = 1/15 of 75

= 1/15 ⋅ 75

= 5 feet

Original width = 60

Width of model shelter = 1/15 of 60

= 1/15 ⋅ 60

= 4 feet

Area of model shelter = 5 x 4

= 20 square feet

Problem 15 :

You spend 1/3 of your money and your friend spends 1/2 of her money shopping. Is it possible that you spend more money than your friend? Explain your reasoning.

Solution :

The question doesnot say that both you and your friend has the same money initially.

If your initial amount of money is significantly larger than your friend's, it is possible you can spend more money than your friend.