Mathematics
Grade5
Easy

Question

A recipe needs 3 over 5 teaspoon black pepper and 2 over 7 red pepper. _____more black pepper is needed than red pepper for this recipe.

  1. 5 over 8
  2. 11 over 35
  3. 8 over 9
  4. 7 over 13

hintHint:

This can be found out by subtracting the fraction 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: 11 over 35


    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:3 over 5 and 2 over 7.
    In this question the denominators are 5 and 7.
    Factors of 5 are:5 to the power of 1
    Factors of 7 are:7 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 multiply all the factors.
    LCM (5,7) = 5 to the power of 1 cross times 7 to the power of 1
    LCM (5,7) = 35
    Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
    So, 35 over 5 equals 7
    and 35 over 7 equals 5
    So, we will multiply the numerator of 5 by 7 and numerator of 7 by 5.
    fraction numerator 3 cross times 7 minus 2 cross times 5 over denominator 35 end fraction equals 11 over 35
    So, The  amount of more red pepper needed is 11 over 35.

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