# Exercise 2.2

Complete above steps to enable this content

**1.Find:**

Solution:

### a

(a)

Multiply the numerators:1 X 1 =

Multiply the denominators: 4 × 4 =

### b

(b)

Multiply the numerators:1 X 3 =

. Multiply the denominators: 4 × 5 =

**2. Multiply and reduce to lowest form (if possible):**

Solution:

### a

(a)

Convert the whole number 2 to a fraction: 2 =

2 1 Multiply the fractions:

- Multiply the result by
:2 3

### b

(b)

Multiply the numerators:2 X 7 =

. Multiply the denominators: 7 × 9 =

.

### c

(c)

Multiply the numerators:4 X 12 =

. Multiply the denominators: 5 × 7 =

.

**3.Multiply the following fractions:**

### a

Solution:

(a)

1.Multiply the numerators together: 2 × 5 × 1 =

- Multiply the denominators together: 5 × 1 × 4 =
.

The greatest common divisor (GCD) of 10 and 20 is 10.

Dividing both the numerator and the denominator by 10, we get:

### b

(b)6x

Multiply the Numerators: 6 ×

× 7. Multiply the Denominators 1 ×

× 9. Form the Fraction

84 45

Find the greatest common divisor (GCD) of 84 and 45 to simplify the fraction. The GCD is 3.

Divide both the numerator and the denominator by 3:

### c

(c)3x

1.Multiply the Numerators: 3 ×

2.Multiply the Denominators 1 ×

3.Form the Fraction

4.Simplify the Fraction

The fraction

3x

Since

3x

**4. Which is greater:**

### a

**(a)**

**Solution:**

1.Calculate each product:

2.Compare the simplified fractions:

**Therefore,**

### b

**(b)**

**Solution:**

- Calculate each product:

- Compare the simplified fractions:

**Therefore, **

**5.Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is **

**Solution:**

Total number of saplings =

Distance between two adjacent saplings =

Distance between the first and the last sapling = 3 ×

By converting an improper fraction into a mixed fraction, we get

**Thus, the distance between the first and last sapling is 2 x **

**6.Lipika reads a book for 1 x**

**Solution:**

Number of hours taken by Lipika to read a book everyday = 1 x

Number of days taken to read the entire book =

Total number of hours required by her to read the complete book = (

=

**Thus, 10 x **

**7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 x**

**Solution:**

Distance covered by the car using 1 litre of petrol =

By converting a mixed number into improper fractions,2 x

Distance covered by using 2 x 3/4 litres of petrol = 16 km ×

**Thus, 44 km distance will be covered by the car using 2 x 3/4 litres of petrol.**

_*8.(a) (i) Provide the number in the box , such that 2/3 × _ = 10/30.*

**Solution:**

### a

(a) The number in the box can be filled by any number so that the resulting number is 10/30.

(i)2/3 ×

**Therefore, **

(ii) The simplest form of .

_*(b) (i) Provide the number in the box , such that 3/5 × _ = 24/75.*

### b

**Solution:**

(b)The number in the box can be filled by any number so that the resulting number is 24/75.

(i)3/5 ×

**Therefore, **

(ii) As

**Therefore its simplest form is **