**Recap of fractions:**

A fraction is defined as a part of a whole number that has been divided into an ** equal **number of parts.

A fraction is written as *a/b* where *a* and *b* are whole numbers. *a *is known as the numerator and *b *is known as the denominator.

**Equivalent fractions**

Equivalent fractions are those fractions that have the same value. In other words, equivalent fractions represent the same parts of a whole.

Consider the following fractions

In the above figure:

The shaded parts (a), (b) and (c) represented by fractions *1/2* , *2/4* and *6/12* are equal. As the shaded parts cover the same area, this means that the fractions *1/2* , *2/4* and *6/12* represent the same part of the whole. Therefore, they are equivalent fractions.

Similarly, the shaded parts (d) and (e) represented by fractions * 1/3* and *2/6* are equal. Therefore, *1/3* and *2/6* are equivalent fractions.

You can find equivalent fractions of a given fraction by multiplying or dividing both the numerator and the denominator of the original fraction by the same number. Note that this number cannot be 0.

- Finding equivalent fractions by multiplication

To find the equivalent fractions of *2/3* we can multiply both the numerator 2 and the denominator 3 by the same number i.e. 2*2 ÷ 3*2 = 4/6

Hence, 4/6 is an equivalent fraction of 2/3

Similarly, if we multiply the numerator and the denominator by the numbers 3, 4, 5 we get the following equivalent fractions respectively:

6/9, 8/12, 10/15

- Finding equivalent fractions by division

To find the equivalent fractions of 12/30 we can divide both the numerator 12 and the denominator 30 by the number 3 as it is a common divisor of 12 and 30 i.e. 12/30 ÷ 30/3 = 4/10

Hence, 4/10 is an equivalent fraction of 12/30

Similarly, if we divide the numerator and the denominator by the numbers 2 and 6 we get the following equivalent fractions respectively:

6/15 , 2/5

**Lowest form of a fraction**

When the numerator and denominator of a fraction have no common factor other than 1 then the fraction is said to be in its lowest or simplest form. In order to find the simplest form of a fraction you must divide the numerator and the denominator by the Highest Common Factor.

For example: Find the simplest form of the fraction 12/30

The HCF of 12 and 30 is 6

Therefore, the simplest form is 12/6 ÷ 30/6 = 2/5

**Equivalent Fractions worksheets**:

Q1: Find the first four equivalent fractions of 3/7

A1: The first four equivalent fractions of 3/7 are:

3*2/7*2 , 3*3/7*3 , 3*4/7*4 , 3*5/7*5

= 6/14 , 9/21, 12/28, 15/35

Q2. Find an equivalent fraction of 5/8 with the numerator 25.

A2: We know that 5 * 5 = 25, hence the equivalent fraction of 5/8 with the numerator 25 can be obtained by multiplying the numerator and denominator by 5

= 5*5 / 8*5 =25/40

Q3. Find an equivalent fraction of 3/4 with the denominator 40.

A3: We know that 4 * 10 = 40, hence the equivalent fraction of 3/4 with the denominator 40 can be obtained by multiplying the numerator and denominator by 10

= 3*10 / 4*10 = 30/40

Q4. Identify which of the following are equivalent fractions

- 3/8 and 21/56
- 4/17 and 1/5
- 7/12 and 14/24
- 6/13 and 6/14

A4. Pairs of equivalent fractions are (a) and (c).

Q5. Reduce the fraction 35/63 to its simplest form.

A5. HCF of 35 and 63 is 7

Therefore, simplest form of 35/63 = 35/7 ÷ 63/7 = 5/9

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