Multiplying Fractions and Mixed Numbers

To multiply fractions, multiply the top numbers together and the bottom numbers together; for mixed numbers, convert them to improper fractions first.

Reading is good — doing is better. Practice Multiplying Fractions and Mixed Numbers as an interactive lesson.

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Definition

Multiplying fractions means finding a part of a part. You line up two fractions, multiply the numerators (top numbers) across, then multiply the denominators (bottom numbers) across to get your answer. When one or both numbers are mixed numbers (like 2 and a half), you change them into improper fractions before you multiply.

Remember the rule

Multiply tops across, multiply bottoms across. Mixed number? Multiply the whole number by the bottom, add the top, put that over the bottom — then multiply.

Key words

Numerator: The top number in a fraction — it tells you how many parts you have.
Denominator: The bottom number in a fraction — it tells you how many equal parts the whole is split into.
Improper Fraction: A fraction where the top number is bigger than or equal to the bottom number, like 7/3.
Mixed Number: A whole number combined with a fraction, like 2 and 1/3.
Product: The answer you get after multiplying.
Simplify: Rewrite a fraction in its smallest form by dividing the top and bottom by the same number.
Convert: Change a number from one form to another, like turning a mixed number into an improper fraction.
Whole Number: A counting number like 1, 2, 3 — no fractions or decimals.

Worked examples

1/2 × 3/4 = ?

→ 3/8 · Multiply 1×3=3 for the top, and 2×4=8 for the bottom.

2/3 × 3/5 = ?

→ 6/15, which simplifies to 2/5 · 6 and 15 can both be divided by 3, so always simplify your answer.

1 1/2 × 2/3 = ?

→ 1. Convert 1 1/2 to 3/2. 2. Multiply: 3/2 × 2/3 = 6/6 = 1 · When the top and bottom are equal the fraction equals 1 — a neat result!

2 1/3 × 1 1/2 = ?

→ 1. Convert: 2 1/3 = 7/3 and 1 1/2 = 3/2. 2. Multiply: 7×3=21 on top, 3×2=6 on bottom = 21/6. 3. Simplify: 21/6 = 3 3/6 = 3 1/2 · Always convert both mixed numbers before you multiply.

4 × 3/5 = ?

→ Write 4 as 4/1, then multiply: 4×3=12 on top, 1×5=5 on bottom = 12/5 = 2 2/5 · Any whole number can be written as itself over 1.

2/5 × 5/6 = ?

→ 10/30, which simplifies to 1/3 · Divide both 10 and 30 by 10 to simplify quickly.

Common mistakes

Forgetting to convert mixed numbers to improper fractions before multiplying — you cannot just multiply the whole number parts and fraction parts separately.
Adding the denominators instead of multiplying them, for example writing 1/2 × 1/3 = 2/5 instead of 1/6.
Forgetting to simplify the answer — always check if the top and bottom share a common factor.
When converting a mixed number, forgetting to add the original numerator after multiplying, for example writing 2 3/4 as 8/4 instead of 11/4.
Multiplying the top by the bottom or mixing up which numbers to multiply together.

FAQs

Why do we convert mixed numbers to improper fractions first?

You need one single fraction to multiply. A mixed number is really addition (2 + 1/3), and you cannot multiply across an addition sign the way you can with a single fraction.

Do I always have to simplify my answer?

Your teacher will almost always expect a simplified or fully reduced answer, so yes — get in the habit of checking whether the top and bottom share any common factor.

Why does multiplying two fractions give a smaller number?

Because you are finding a part of a part. Half of half a pizza is only a quarter of the pizza — less than you started with.

How do I turn a mixed number into an improper fraction?

Multiply the whole number by the denominator, then add the numerator, and put that total over the same denominator. Example: 3 2/5 → (3×5)+2=17, so it becomes 17/5.

Can I simplify before I multiply to make the math easier?

Yes! This is called cross-canceling. If a top number and a bottom number share a common factor, you can divide both by that factor before you multiply — it keeps the numbers smaller.

What if my answer is an improper fraction — do I have to convert it to a mixed number?

Usually yes for a final answer in 5th grade. Divide the top by the bottom: the quotient is your whole number and the remainder goes over the denominator.

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