Unit 8: Multiplying and Dividing Fractions
Multiplying fractions as shrinking, and dividing by a fraction as counting how many pieces fit inside.
6 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Multiplying a Fraction by a Whole Number
- How it worksWalk me through multiplying 5 times 2 sevenths by multiplying the top number and keeping the bottom the same.
- Worked exampleFind the answer to 6 times 3 eighths of a bag of stickers.
- Ties togetherHow does multiplying a fraction by a whole number connect to repeated addition of the same fraction?
Your turn1 of 2
Sam wants 7 times 4 over 8 of a bag of stickers. What is the new numerator of that amount (the denominator stays 8)?What It Means to Multiply Two Fractions
- How it worksWalk me through multiplying 2 thirds by 3 fourths by multiplying straight across the tops and the bottoms.
- Common mistakeWhy doesn't multiplying 1 half by 1 third give you a bigger number than 1 half?
- Common mistakeWhy don't you need a common denominator to multiply 2 thirds by 3 fifths the way you do to add them?
- Worked exampleFind the answer to 3 fourths times 2 fifths of a garden.
- Going furtherWhat happens to the size of the answer if you multiply 1 fourth by a fraction even smaller than 1 fourth?
Your turn1 of 2
A garden is divided so that 2 over 7 of it is for vegetables, and 2 over 5 of that vegetable section is for tomatoes. What is the new numerator for the tomato part of the whole garden?Multiplying Mixed Numbers
- How it worksWalk me through turning 2 and 1 half into an improper fraction before multiplying it by 3 fourths.
- Worked exampleFind the answer to 1 and 1 third times 2 and 1 half cups of flour in a recipe.
- Common mistakeWhy isn't 2 and 1 half times 1 and 1 half equal to 2 and 1 fourth from multiplying the wholes and the fractions separately?
- Going furtherWhat happens when you multiply three mixed numbers, like 1 and 1 half, 2, and 1 and 1 fourth, all together?
Your turn1 of 2
A garden bed is 7 and 1 third metres long and 6 and 1 half metres wide. What is its area in square metres?What It Means to Divide by a Fraction
- How it worksWalk me through dividing 3 by 1 half by counting how many half-pizza slices fit into 3 whole pizzas.
- Worked exampleFind how many fourths fit inside 5 whole chocolate bars.
- Common mistakeWhy does dividing 3 by 1 half give you 6 instead of 1 and a half?
Your turn1 of 2
Amara has 7 whole chocolate bars and cuts each one into pieces that are each 1 over 8 of a bar. How many pieces does she end up with?Dividing Whole Numbers by Fractions
- How it worksWalk me through counting how many fourth-slices fit inside all 4 whole pizzas.
- How it worksHow does multiplying 4 by 4 give you the same answer as counting fourth-slices in 4 pizzas one at a time?
- Worked exampleFind how many thirds fit inside 6 whole chocolate bars.
- Common mistakeWhy doesn't dividing 5 by 1 third give you an answer smaller than 5?
- Going furtherWhat happens to the answer if you divide the same 4 pizzas by an even smaller fraction, like 1 eighth?
Your turn1 of 2
A baker has 7 loaves of bread and slices each loaf into pieces that are each 1 over 8 of a loaf. How many slices does she end up with?Dividing a Fraction by a Fraction
- How it worksWalk me through flipping 1 eighth to 8 over 1 and multiplying it by 3 fourths.
- Common mistakeWhy doesn't dividing 1 half by 1 fourth give you 1 eighth from multiplying straight across?
- Worked exampleFind the answer to 5 sixths divided by 1 third.
- Going furtherWhat happens when you divide a fraction by an equivalent fraction, like 2 fourths divided by 1 half?
Your turn1 of 2
Ravi has 2 over 7 of a pizza left and splits it into pieces that are each 1 third of a whole pizza. How many pieces does he get? (Flip 1 third to 3 over 1 and multiply.)