Top Times Top
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 34 of 58.
(2/5) × (3/7): take a rectangle and cut it into 5 columns and 7 rows, 35 small pieces in all. Shade 2 of the 5 columns, which is 2/5, and 3 of the 7 rows, which is 3/7. Where the two shadings overlap is 2/5 of 3/7.
2 columns of 5 and 3 rows of 7 overlap in 6 of the 35 pieces.
The overlap is 2 columns by 3 rows, 2 × 3 pieces, which is 6, out of 5 × 7, which is 35. So (2/5) × (3/7) is 6/35: multiply the tops, and multiply the bottoms.
Unlike adding, multiplying needs no common denominator. The bottoms multiply because cutting fifths into sevenths makes pieces 35 times smaller than the whole. And a product of two positive fractions below 1 is smaller than both of them, because you are taking a part of a part.
Challenge
Work out (2/3) × (4/5). Multiply top by top and bottom by bottom.
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