Mathematics
Grade5
Easy

Question

Kevin ate 5 over 9 of a pie. Michael ate 1 halfof a pie. The amount of pie Kevin and Michael ate together is ________.

  1. 6 over 11
  2. 19 over 18
  3. a over 4
  4. 1

hintHint:

In this question we have to add both 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: 19 over 18


    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:5 over 9 and 1 half
    In this question the denominators are 2 and 9.
    Factors of 2 are:2 to the power of 1
    Factors of 9 are:3 squared
    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 (2,9) = 2 to the power of 1 cross times 3 squared
    LCM (2,9) = 18
    Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
    So, 18 over 2 equals 9
    and 18 over 9 equals 2
    So, we will multiply the numerator of 2 by 9 and numerator of 9 by 2.
    fraction numerator 5 cross times 2 plus 1 cross times 9 over denominator 18 end fraction equals 19 over 18
    So, The total amount of pie they ate altogether is 19 over 18.

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