Understanding fractions as division

Understanding fractions as division 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.