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Mathematics

Grade5

Easy

Question

Kevin ran $2 over 5$ mile on Monday, and $2 over 3$ mile on Tuesday. He run ________ miles altogether.

$\frac{16}{14}$
$\frac{16}{15}$
$\frac{4}{8}$
$\frac{1}{2}$

hint Hint:

This can be found by adding the fractions and 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 by considering the repeated factors only one time with highest exponent

The correct answer is: $16 over 15$

Step1: First we will write all the fractions and then we will write the denominator and then we will use prime factorization method to add the fraction.
Fractions are: $2 over 5$ and $2 over 3$
In this question the denominators are $3 space$ and $5$ .
Factors of $3 space$ 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 there is no common factor so we will multiply all the factors.
LCM ( $3 space$ , $5$ ) = $3 to the power of 1 cross times 5 to the power of 1$
LCM ( $3 space$ , $5$ ) = $15$
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
So, $15 over 3 equals 5$
and $15 over 5 equals 3$
So, we will multiply the numerator of $3 space$ by $5$ and numerator of $5$ by $3 space$ .
$fraction numerator 2 cross times 3 plus 2 cross times 5 over denominator 15 end fraction equals 16 over 15$
So, Kevin ran a total of $16 over 15$ miles.

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