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 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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