Answer:

In figure D colored part represents 12.

When numerator and denominator of fraction 816 are divided by 2. We get 48 and in the same way 48 gives 24 and then 12.

So, we find that 816, 48, 24 are equal to fraction for 12. Thus, 12 is the simplest or lowest form of all its equivalent fractions like 24, 48, 816, 1632, 3264, …… etc.

Now, if we take all the factors of the numerator 8 and denominator 16 of the fraction 816, we get the following:

All factors of 8 are 1, 2, 4, 8.

All factors of 16 are 1, 2, 4, 8, 16.

We find that highest common factor (HCF) of 8 and 16 is 8.

On dividing both numerator and denominator by highest common factor we get 12.

Since, both numerator and denominator of fraction 12 have no common factor other than 1, we say that the fraction 12 is in its lowest terms or simplest form.

Fraction in Lowest Terms

816 → 48 → 24 → 12

15Save

There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method.

H.C.F. Method

Find the H.C.F. of the numerator and denominator of the given fraction.

In order to reduce a fraction to its lowest terms, we divide its numerator and denominator by their HCF.

Example to reduce a fraction in lowest term, using H.C.F. Method:

1. Reduce the fraction ²¹/₅₆ to its simplest form.

Solution:

Reduce a Fraction

Therefore H.C.F. of 21 and 56 is 7.

We now divide the numerator and denominator of the given fraction by 7.

²¹/₅₆ = 21÷756÷7 = ³/₈.

2. Reduce ⁴⁸/₆₄ to its lowest form.

Solution:

First we find the HCF of 48 and 64 by factorization method.

The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The factors of 64: 1, 2, 4, 8, 16, 32, and 64.

The common factors of 48 and 64 are: 1, 2, 4, 8, 12 and 16.

Therefore, HCF of 48 and 64 is 16.

Now ⁴⁸/₆₄ = 48÷1664÷16

[Dividing numerator and denominator by the HCF of 48 and 64 i.e., 16]

⇒ ⁴⁸/₆₄ = ³/₄

3. Reduce ⁴⁴/₇₂ to its lowest form.

Solution:

First we find the HCF of 44 and 72 by factorization method.

The factors of 44: 1, 2, 4, 11, 22 and 44.

The factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36.

The common factors of 44 and 72 are: 1, 2 and 4.

Therefore, HCF of 44 and 72 is 4.

Now ⁴⁴/₇₂ = 44÷472÷4

[Dividing numerator and denominator by the HCF of 44 and 72 i.e., 4]

⇒ 44/72 = 11/18

Prime Factorization Method

Express both numerator and denominator of the given fraction as the product of prime factors and then cancel the common factors from them.

Example to reduce a fraction in lowest term, using Prime Factorization Method:

Reduce 120360 to the lowest term.

Solution:

Fraction in Lowest Terms

120   =     2 × 2 × 2 × 3 × 5         =   1

360        2 × 2 × 2 × 3 × 3 × 5          3

Solve Examples on Reducing Fractions to Lowest Terms:

1. Express 28140 in the simplest form.

Solution:

Let us find all the factors of both numerator and denominator.

Factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The highest common factor is 28. Now dividing both numerator and denominator by 28, we get 15. The numerator 1 and denominator 5 have no common factors other than 1. So,  15 is the simplest form of 28140.

2. Is 48168 in its simplest form?

Solution:

Let us find HCF of numerator and denominator and then divide both by the highest common factor.

The highest common factor is 2 × 2 × 2 × 3 = 24

Let us divide both numerator and denominator by 24. We get 27.

So, the fraction 48168 is not in its simplest form.

Questions and Answers on Reduce a Fraction to its Simplest Form:

1. Convert the given fractions in lowest form:

(i) 24

(ii) 39

(iii) 416

(iv) 1215

(v) 728

(vi) 610

(vii) 972

(viii) 2436

Answers:

1. (i) 12

(ii) 13

(iii) 14

(iv) 45

(v) 14

(vi) 35

(vii) 18

(viii) 23

2. Match the given fractions:

(i) 1215

(ii) 69

(iii) 836

(iv) 2432

(v) 1525

(a) 34

(b) 29

(c) 35

(d) 45

(e) 23

Answers:

(i) 1215

(ii) 69

(iii) 836

(iv) 2432

(v) 1525

(d) 45

(e) 23

(b) 29

(a) 34

(c) 35

Step-by-step explanation:

Answer:

1.c

2.d

3.e

4.a

5.b

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