Question

reduce the fraction to the lowest terms by dividing by common factors 1.15/21​

Answer 1

Answer:

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Answer 2

Answer

Step-by-step explanation:

Fraction in lowest terms is discussed here.

If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest term.

In other words, a fraction is in its lowest terms or in lowest form, if the HCF of its numerator and denominator is 1.

Observe the fractions represented by the colored portion in the following figures.

Fraction 8/16

Figure A

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In figure A colored part is represented by fraction 816.

Fraction 4/8

Fraction B

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The colored part in figure B is represented by fraction 48.

Fraction 2/4

Fraction C

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In figure C the colored part represents the fraction 24 and

Fraction 1/2

Fraction D

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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

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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