Multiplying and Dividing Fractions
Multiply across; to divide, multiply by the reciprocal.
About this topic
Multiplying fractions is straightforward: multiply the numerators together and the denominators together. Taking 1/2 of 3/4 gives 3/8, so multiplication can make a number smaller when both factors are below one. You can cancel common factors before multiplying to keep numbers small.
To divide by a fraction, multiply by its reciprocal, the fraction flipped upside down. Dividing by 1/2 asks how many halves fit, which doubles the amount. For example, 3/4 ÷ 3/8 = 3/4 × 8/3 = 2, since cancelling the threes and simplifying 8/4 leaves 2. Mixed numbers should be converted to improper fractions first.
Imagine a recipe that needs 2/3 cup of sugar, but you want to make half the batch. Half of 2/3 is 1/2 × 2/3 = 1/3 cup. In another case, if you have 3 metres of ribbon and each bow needs 3/4 of a metre, then 3 ÷ 3/4 = 3 × 4/3 = 4 bows. An area model, where a unit square is divided into rows and columns, shows why multiplying fractions multiplies both parts.
These skills appear in cooking, construction, scaling drawings and probability of independent events. Students often feel they need a common denominator for multiplication, but that is only for addition and subtraction. Another slip is flipping the wrong fraction when dividing: only the second fraction, the divisor, is inverted.
Key ideas
- Multiply numerators and denominators
- Flip the second fraction to divide
- Cancel common factors early
Quick check
Use cases: where Multiplying and Dividing Fractions helps
- Homework: review the key idea behind Multiplying and Dividing Fractions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Multiplying and Dividing Fractions without notes.
- Visual learning: play with the interactive lab to see how Multiplying and Dividing Fractions changes when you adjust its inputs.
- Teaching a friend: explain Multiplying and Dividing Fractions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Multiplying and Dividing Fractions?
Multiply across; to divide, multiply by the reciprocal.
What will I learn in Multiplying and Dividing Fractions?
Multiply numerators and denominators. Flip the second fraction to divide. Cancel common factors early.
Is Multiplying and Dividing Fractions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Multiplying and Dividing Fractions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Multiplying and Dividing Fractions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.