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Fractions

    Introduction

    Fractional Units and Equal Shares

    Fractional Units as Parts of a Whole

    Measuring Using Fractional Units

    Marking Fraction Lengths on the Number Line

    Improper and Mixed Fractions

    Equivalent Fractions

    Comparing Fractions

    Addition and Subtraction of Fractions

    A Pinch of History

    Summary

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Fractions > Equivalent Fractions

Equivalent Fractions

Using a fraction wall to find equal fractional lengths!

In the previous section, you used paper folding to represent various fractions using fractional units. Let us do some more activities with the same paper strips.

What do you observe?

Are the lengths 12 and 24 equal?

Are the lengths 24 and 48 equal?

We can say that 12 24 48

These are ‘equivalent fractions’ that denote the same length, but they are expressed in terms of different fractional units.

Now, check whether 13 and 26 are equivalent fractions or not, using paper strips.

Answer the following questions after looking at the fraction wall:

1

Are the lengths 12 and 36 equal?

,

12 and 36 are equal. When the numerator and denominator of 12 are multiplied by 3, it becomes 36.

Both represent the same portion of a whole, making them fractions.

2

Are 23 and 46 equivalent fractions? Why?

,

23 and 46 are equivalent fractions. When the numerator and denominator of 23 are multiplied by 2, it becomes 46.

Both fractions represent the same part of a whole, ensuring equivalence.

3

How many pieces of length 16 will make a length of 12?

pieces of length 16 will make a length of 12.

Multiplying 3 by 16 equals 36, which simplifies to 12.

This demonstrates how smaller fractions combine to form larger ones.

4

How many pieces of length 16 will make a length of 13?

pieces of length 16 will make a length of 13. Multiplying 2 by 16 equals 26, which simplifies to 13.

This demonstrates the additive nature of smaller fractional parts.

We can extend this idea to make a fraction wall up to the fractional unit 110

1

Are the 36, 48 and 510 equivalent fractions? Why?

,

36, 48, and 510 are equivalent fractions.

Each simplifies to 12 when the numerator and denominator are divided by their greatest common factor. All represent the same portion of a whole.

2

Write two equivalent fractions for 26 .

,

One roti was shared equally by four children.

What fraction of the whole did each child get?

The adjoining picture shows the division of a roti among four children.

Fraction of roti each child got is

You can also express this event through division facts, addition facts, and multiplication facts.

The division fact is 1 ÷ 4 =

The addition fact is 1 = 14 + 14 + 14 +14

The multiplication fact is 1 = × 14

1

1. Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts. Fraction of roti each child gets is.

Division fact: Addition fact: Multiplication fact: Compare your picture and answers with your classmates!

Each child gets roti.

Division fact: 3 ÷ 4 = 34.

Addition fact: 34 + 34 + 34 + 34 = .

Multiplication fact: 4 × 34 = .

Equal sharing ensures fairness.

2

2. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

Anil would get 25 of a cake. Dividing 2 cakes equally among 5 children ensures each receives 25.

This division represents fair sharing, where each fraction corresponds to equal portions of the whole cakes.

1.Are 13 and 27 ; 25 and 27 ; 29 and 627 equivalent? Give reason.

13 27
13 and 27 is not eqivalent fraction why because 7 is not exactly divisible by 3.
25 27.
27 is not equivalent fraction of 25 because 7 is not exactly divisible by 5.
29 627.
29 will be equivalent to 627 because if we multiply 29 by 3 in both numerator and denominator then ans will be 627.

Expressing a fraction in lowest terms (or in its simplest form)

In any fraction, if its numerator and denominator have no common factor except 1, then the fraction is said to be in lowest terms or in its simplest form. In other words, a fraction is said to be in lowest terms if its numerator and denominator are as small as possible.

Any fraction can be expressed in lowest terms by finding an equivalent fraction whose numerator and denominator are as small as possible.

Let’s see how to express fractions in lowest terms.

Is the fraction 1620 in lowest terms? No, 4 is a common factor of 16 and 20. Let us reduce 1620 to lowest terms.

No, 1620 is not in lowest terms. By dividing both the numerator and denominator by 4, we get 45, which is the fraction in its simplest form. This ensures the fraction is fully simplified.