Understanding fractions as division

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Fractions is one of the very basic and important representation in mathematics. A fraction is a number that can be expressed in p/q form. This representation can also be understood as division of two numbers or quantities as the top is the numerator and the bottom is the denominator. The denominator of a fraction can never be equal to zero. Fractions can be further simplified according to the requirement. Different mathematical operations can be used to simplify and solve a given fraction.

Example 1: Amy brought 20 pencils. She uses all the pencils in 5 weeks equally. How many pencils per week did she use?
Solution: Number of pencils brought by Amy = 20.
Number of weeks she took to finish the pencils = 5.
Number of pencils per week = 20/5.
The GCF of 20 and 5 is 5. Dividing the numerator and the denominator by 5.
This gives 20 ÷ 5 /5 ÷ 5 = 4.
Hence, Amy used 4 pencils per week.
 
Question: Multiple choice question (Pick the correct option.)
Simplify the fraction 24/72 to its simplest form?
a)    2/3                   b) 1/6              c) 1/3              d) None of these.
Correct answer: option c.
 Explanation: The given fraction can be further simplified. Write the factors of the numerator and denominator.
This gives: 24 = 8 x 3; 72 = 8 x 9.
Cancelling the common factor 8 gives 24/72 = 3/9.
The fraction can be further simplified by dividing by 3 this gives: 3/9 = 1/3.
Hence answer = 1/3.

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