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Mathematics

Grade5

Easy

Question

Subtract $6 over 9 space minus space 2 over 5$ .

$\frac{4}{4}$
$\frac{4}{15}$
$\frac{3}{5}$
$\frac{1}{2}$

hint Hint:

In this question we have to subtract two fractions for that we have to make denominator same this can be done by taking LCM. LCM is the least common multiple of two integers. We will use the prime factorization method to find the LCM. In prime factorization method the simply put the factor of each number and then for LCM we take product of factors, but we consider the repeated factors only one time but with highest exponent

The correct answer is: $4 over 15$

Step1: First we will write all the prime factors of the denominators
In this question the denominators are $9$ and $5$ .
Factors of $9$ are: $3 squared$
Factors of $5$ are: $5 to the power of 1$
Step2: For calculating the LCM we will multiply the factors by considering the common factors only one time with the highest exponent.
In this case there is no common factor so we will multiply all the factors
LCM ( $9$ , $5$ ) = $3 squared cross times 5 to the power of 1$
LCM ( $9$ , $5$ ) = $45$
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then subtract them
So, $45 over 9 space equals space 5$
and $45 over 5 space equals space 9$
So, we will multiply the numerator of $9$ by $5$ and numerator of $5$ by $9$ .
$fraction numerator 6 cross times 5 minus 2 cross times 9 over denominator 45 end fraction equals 12 over 45$
So, the answer of $6 over 9 space minus space 2 over 5$ is $12 over 45$ , which can be further simplified by dividing by 3 in both numerator and denominator
$12 over 45 equals 4 over 15$ .

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