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Mathematics

Grade5

Easy

Question

Subtract $4 over 5 space minus space 7 over 15$ .

$\frac{1}{3}$
$\frac{19}{35}$
$\frac{1}{2}$
$\frac{15}{19}$

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: $1 third$

Step1: First we will write all the prime factors of the denominators
In this question the denominators are $5$ and $15$ .
Factors of $5$ are: $5 to the power of 1$
Factors of $15$ are: $3 to the power of 1 cross times 5 to the power of 1$
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 $5$ is common in both $5$ and $15$ so we will multiply it only once with the highest exponent
LCM ( $5$ , $15$ ) = $3 to the power of 1 cross times 5 to the power of 1$
LCM ( $5$ , $15$ ) = $15$
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then subtract them
So, $15 over 5 equals 3$
and $15 over 15 equals 1$
So, we will multiply the numerator of $5$ by $3$ and numerator of $15$ by $1$ .
$fraction numerator 4 cross times 3 minus 7 cross times 1 over denominator 15 end fraction equals 5 over 15$
So, the answer of $4 over 5 space minus space 7 over 15$ is $5 over 15$ which can be reduced to $1 third$ by dividing both numerator and denominator by $5$ .

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