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Mathematics

Grade5

Easy

Question

Subtract $7 over 11 space minus space 1 third$ .

$\frac{8}{11}$
$\frac{8}{14}$
$\frac{4}{7}$
$\frac{10}{33}$

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: $10 over 33$

Step1: First we will write all the prime factors of the denominators
In this question the denominators are $11$ and $3$ .
Factors of $11$ are: $11 to the power of 1$
Factors of $3$ are: $3 to the power of 1$
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 with the highest exponent
LCM ( $11$ , $3$ ) = $3 to the power of 1 cross times 11 to the power of 1$
LCM ( $11$ , $3$ ) = $33$
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then subtract them
So, $33 over 3 equals 11$
and $33 over 11 equals 3$
So, we will multiply the numerator of $11$ by $3$ and numerator of $3$ by $11$ and $3$ .
$fraction numerator 7 cross times 3 minus 1 cross times 11 over denominator 33 end fraction equals 10 over 33$
So, the answer of $7 over 11 space minus space 1 third$ is $10 over 33$ .

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