# Dividing whole numbers by fractions

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The basic arithmetic operations used in math between different types of numbers are addition, subtraction, multiplication and division. 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 ÷. 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 denominator is not equal to zero q ≠ 0.

Example 1: A wooden log of 10 inches is divided into half inch logs. How many such logs are made?
Solution: Length of the wooden log = 10 inches.
The log needs to be further cut into 1/2 inch logs.
Number of logs divided into = 10 ÷ 1/2.
(Change to multiplication by reciprocal of 1/2)
This gives, 10 x 2 = 20.
Hence, the wooden log is divided into 20 half inch logs.

Question: Multiple choice question (Pick the correct option.)
What is the answer for the division between the following?
15 ÷ 3/2 = ---------
a)    10                    b) 12               c) 15               d) None of these.
Correct answer: option a.
Explanation: Here 3/2 is the fraction and 15 is the whole number.
Given 15 ÷ 3/2 (Change to multiplication by the reciprocal of 3/2.)
This gives 15 x 2/3 = 30/3. (The GCF of 30 and 3 is 3)
So dividing by 3 for the numerator and the denominator.
(30 ÷ 3)/(3 ÷ 3) = 10.
Hence answer = 10.