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Mathematics

Grade5

Easy

Question

Add $2 over 3 and space 1 fifth$ .

$\frac{15}{13}$
$\frac{13}{15}$
$\frac{3}{8}$
$\frac{3}{5}$

hint Hint:

In this question we have to add 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: $13 over 15$

$2 over 3 space equals space 10 over 15 open parentheses Multiply space with space 5 close parentheses 1 fifth space equals space 3 over 15 open parentheses Multiply space with space 3 close parentheses 10 over 15 space plus space 3 over 15 equals 13 over 15$
Step1: First we will write all the prime factors of the denominators
In this question the denominators are $3$ and $5$ .
Factors of $3$ are: $3 to the power of 1$
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 the factor is common in both and so we will multiply it only once
LCM ( $3$ , $5$ ) = $3 to the power of 1 cross times 5 to the power of 1$
LCM ( $3$ , $5$ ) = $15$

Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
So, $15 over 3 space equals space 5$
and $15 over 5 space equals space 3$
So, we will multiply the numerator of $3$ by $5$ and numerator of $5$ by $3$ .
$fraction numerator 2 cross times 5 plus 1 cross times 3 over denominator 15 end fraction space equals space 13 over 15$
So, the sum of $2 over 3 and space 1 fifth$ is $13 over 15$ .

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