Dividing fractions by whole numbers

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Division means splitting or dividing into equal groups or parts. Division is one of the basic arithmetic operations in mathematics. Division is denoted by a cross sign ÷. This mathematical operations is used between different types of numbers such as, integers, whole numbers, fractions, decimals and many more. A whole number is a non-negative, non-decimal number starting from zero. A fraction is a number that can be expressed in p/q form where q ≠ 0. 

Example 1: There is 3/2 liters of juice in a bottle. If the juice is to be distributed in 12 cups. How much juice will each cup have? 
Solution: Total quantity of juice = 3/2 liter.
Number of cups = 12.
Amount of juice in each cup = 3/2 ÷ 12.
(Change to multiplication by reciprocal of 12)
This gives, 3/2 x 1/12 = 3/24 = 1/8.
Hence, each cup contains 1/8 liter of the juice.
Question: Multiple choice question (Pick the correct option.)
What is the answer for the division between the following?
15/4 ÷ 5 = ---------
a)    3                      b) 3/4              c) 1/5              d) None of these.
Correct answer: option b.
Explanation: Here 15/4 is the fraction and 5 is the whole number.
Given 15/4 ÷ 5 (Change to multiplication by the reciprocal of 15.)
This gives 15/4 x 1/5 = 15/20. (The GCF of 15 and 20 is 5)
So dividing by 5 for the numerator and the denominator.
(15 ÷ 5)/(20 ÷ 5) = 3/4.
Hence answer = 3/4.

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