A Fraction of a Number
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 20 of 58.
What is three quarters of 20? Taking a fraction of a number is a multiplication, written (3/4) × 20. To work it out, cut 20 into 4 equal parts, as the denominator says: 20 / 4 is 5, so each quarter is 5.
Then take 3 of those parts, as the numerator says: 3 × 5 is 15. So three quarters of 20 is 15. On the board that is two lines after the problem: 3 × 5, then 15.
In short: divide by the bottom, then multiply by the top. That is exactly what the fraction means, since the bottom makes the equal parts and the top counts them, and dividing first keeps the numbers small. The word 'of' after a fraction always means multiply.
Challenge
Work out two thirds of 18, written (2/3) × 18 on the board. Divide by the bottom first and write that line, then finish.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factors & Fractions
1Factors and Multiples
What a Factor IsFactor PairsDivisibility RulesMultiplesPrime or CompositeRecap: Factors and Multiples4What a Fraction Is
Parts of a WholeFractions on the LineA Fraction of a NumberImproper FractionsRecap: What a Fraction Is7Multiplying Fractions
Top Times TopCancel FirstWhole Times FractionA Fraction of a FractionRecap: Multiplying Fractions10Fractions in Stories
Part of a GroupWhat Is LeftSharing a FractionScaling a RecipeRecap: Fraction Stories2Prime Factorization
Factor TreesUsing ExponentsOne Tree per NumberBigger NumbersRecap: Prime Factorization5Equivalent Fractions
Same Amount, New NameSimplifying FractionsSimplify in StepsComparing FractionsRecap: Equivalent Fractions