How to Multiply Fractions — Step-by-Step Guide
Multiplying fractions is one of the easiest fraction operations — no common denominators needed. Multiply straight across, simplify, and you're done. This guide walks you through every scenario with clear visuals and worked examples.
To multiply fractions, multiply the numerators (top numbers) together to get the new numerator, then multiply the denominators (bottom numbers) together to get the new denominator. Simplify the result by dividing both by their greatest common factor. For example, 2/3 × 4/5 = 8/15.
What Is the Rule for Multiplying Fractions?
The rule for multiplying fractions is: multiply the numerators together and multiply the denominators together. In mathematical notation, a/b × c/d = (a × c) / (b × d). Unlike addition or subtraction, multiplying fractions does not require finding a common denominator. The process is refreshingly straightforward — just follow three steps.
Multiply the Numerators
Multiply the top numbers of both fractions together. This product becomes the new numerator.
Multiply the Denominators
Multiply the bottom numbers of both fractions together. This product becomes the new denominator.
Simplify the Result
Find the greatest common factor (GCF) of the numerator and denominator, and divide both by it to reduce the fraction to simplest form.
In formula form, the rule looks like this:
Let's see this in action. To multiply 2/3 × 4/5:
Area model: 2/3 × 4/5 means "take 2/3 of 4/5." The overlapping shaded region covers 8 of 15 cells.
This visual confirms our arithmetic. The area model shows that multiplying fractions answers the question "What is a fraction of another fraction?" — you're finding the overlap between two parts of a whole.
What Is Cross-Canceling and How Does It Work?
Cross-canceling (also called cross-simplifying) is a shortcut where you simplify before you multiply by dividing any numerator and an opposite denominator by their greatest common factor. It keeps numbers small, reduces arithmetic errors, and often eliminates the need to simplify at the end. Many students find this technique makes fraction multiplication feel effortless — especially with larger numbers.
Here's how it works: look diagonally across the two fractions. If any numerator and the opposite denominator share a common factor, divide both by that factor before multiplying.
Example: 4/9 × 3/8 with Cross-Canceling
Without cross-canceling, you'd compute 4 × 3 = 12 and 9 × 8 = 72, then simplify 12/72 down to 1/6. Cross-canceling gets you there faster:
Pro tip: Cross-canceling works across any numerator-denominator pair — not just diagonally. If you're multiplying three or more fractions, you can cross-cancel between any numerator and any denominator. The more you simplify early, the easier the final multiplication.
Cross-canceling is especially valuable when working with larger numbers. It's not a separate rule — it's just applying the fundamental principle of simplification at an earlier stage, before the numbers grow. Try our Multiply Fractions Calculator to see cross-canceling in action with your own numbers.
How Do You Multiply Mixed Numbers?
You can't multiply mixed numbers directly — you need to convert them to improper fractions first. Once converted, multiply normally using the same three-step rule.
Convert to Improper Fractions
Multiply the whole number by the denominator, then add the numerator. Place the result over the original denominator.
Multiply the Fractions
Use the standard rule: numerator × numerator and denominator × denominator. Cross-cancel first if you can.
Simplify & Convert Back
Simplify the resulting fraction, then convert it back to a mixed number if the numerator is larger than the denominator.
Multiply 2⅓ × 1½
- Convert 2⅓ to an improper fraction: (2 × 3 + 1) / 3 = 7/3
- Convert 1½ to an improper fraction: (1 × 2 + 1) / 2 = 3/2
- Multiply: 7/3 × 3/2 — cross-cancel the 3s → 7/1 × 1/2 = 7/2
- Convert 7/2 back to a mixed number: 7 ÷ 2 = 3 remainder 1 → 3½
How Do You Multiply a Fraction by a Whole Number?
Any whole number can be written as a fraction with a denominator of 1. Once you do that, multiply normally.
Notice a shortcut: since the whole number has a denominator of 1, you're really just multiplying the numerator by the whole number while keeping the denominator unchanged. This makes intuitive sense — five groups of ¾ gives you 15 quarters, which equals 3¾.
Common mistake: Don't multiply both the numerator and the denominator by the whole number. Only the numerator gets multiplied. The denominator stays the same because you're multiplying by a number over 1, not over the same number.
Worked Examples
Simple Multiplication: 5/6 × 2/7
- Multiply numerators: 5 × 2 = 10
- Multiply denominators: 6 × 7 = 42
- Simplify 10/42: the GCF of 10 and 42 is 2, so divide both by 2
Cross-Canceling: 6/11 × 7/12
- Look for common factors across: 6 and 12 share a factor of 6, so cancel to get 1 and 2
- After canceling: 1/11 × 7/2
- Multiply: 1 × 7 = 7 and 11 × 2 = 22
Mixed Numbers: 3¼ × 2⅔
- Convert: 3¼ = (3 × 4 + 1)/4 = 13/4 and 2⅔ = (2 × 3 + 2)/3 = 8/3
- Cross-cancel: 4 and 8 share a factor of 4, so cancel to get 1 and 2
- After canceling: 13/1 × 2/3 = 26/3
- Convert to mixed number: 26 ÷ 3 = 8 remainder 2
Fraction × Whole Number: 7/10 × 4
- Rewrite: 7/10 × 4/1
- Cross-cancel: 4 and 10 share a factor of 2, so cancel to get 2 and 5
- After canceling: 7/5 × 2/1 = 14/5
- Convert to mixed number: 14 ÷ 5 = 2 remainder 4
Three Fractions: 2/3 × 3/5 × 5/8
- Write all three together: (2 × 3 × 5) / (3 × 5 × 8)
- Cross-cancel: the 3 in the numerator cancels the 3 in the denominator; the 5 in the numerator cancels the 5 in the denominator
- After canceling: (2 × 1 × 1) / (1 × 1 × 8) = 2/8
- Simplify: GCF of 2 and 8 is 2, so 2/8 = 1/4
Practice Problems
Test your skills — try these on paper first, then click "Show Answer" to check your work.
Need instant step-by-step solutions for trickier problems? Use the Multiply Fractions Calculator to check your work and see the simplification process.
When Do You Use Fraction Multiplication in Real Life?
Multiplying fractions appears in everyday situations more often than most people realize. Cooking is the most common example: if a recipe serves 8 and you need to halve it, you're multiplying every ingredient by ½. Scaling a ¾-cup measurement by ½ gives you ¾ × ½ = 3/8 cup.
Other real-world uses include calculating sale prices (finding ¼ off an item means multiplying the price by ¾), determining areas of land or rooms when dimensions involve fractions, splitting shared expenses into fractional portions, and adjusting material quantities in construction or sewing projects. Fraction multiplication is part of the Common Core math standards beginning in 5th grade (CCSS.MATH.CONTENT.5.NF.B.4) because of how frequently it appears in practical problem-solving.
Key Takeaways
1. Multiply straight across: Numerator × numerator for the top; denominator × denominator for the bottom. No common denominator needed.
2. Cross-cancel first: Simplify any numerator with any opposite denominator before multiplying. This keeps numbers small and often gives you the final answer immediately.
3. Convert mixed numbers first: Turn each mixed number into an improper fraction before multiplying, then convert back at the end.
4. Whole numbers go over 1: Write the whole number as a fraction over 1 (e.g., 5 = 5/1), then multiply normally — only the numerator changes.
Frequently Asked Questions
Multiply the numerators (top numbers) together to get the new numerator, and multiply the denominators (bottom numbers) together to get the new denominator. Then simplify the result if possible. For example, 2/3 × 4/5 = 8/15. No common denominator is needed — that's only required for addition and subtraction.
No. Unlike adding or subtracting fractions, multiplication does not require a common denominator. You simply multiply straight across — numerator times numerator and denominator times denominator. This is one of the reasons multiplying fractions is considered easier than adding them.
Cross-canceling is a shortcut where you simplify before multiplying. You divide a numerator of one fraction and the denominator of the other fraction by their greatest common factor. This keeps the numbers smaller and means you often don't need to simplify at the end. It's especially useful with larger numbers. For example, in 4/9 × 3/8, you can cancel the 4 with the 8 (both ÷ 4) and the 3 with the 9 (both ÷ 3) to immediately get 1/3 × 1/2 = 1/6.
First, convert each mixed number to an improper fraction. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Then multiply the improper fractions normally and simplify. Finally, convert back to a mixed number if needed. For example, 2½ × 1⅓ = 5/2 × 4/3 = 20/6 = 10/3 = 3⅓.
Write the whole number as a fraction by placing it over 1, then multiply normally. For example, 3/4 × 5 = 3/4 × 5/1 = 15/4 = 3¾. A handy shortcut: just multiply the numerator by the whole number and keep the denominator the same.
A proper fraction is less than 1, so multiplying by it takes a part of the original value — making the result smaller. Think of it as finding a fraction of a fraction. For example, 1/2 × 1/2 = 1/4, which is half of a half. The area model visualization above shows this nicely: the overlap of two partial regions is always smaller than either region alone.
Yes. Multiply all the numerators together and all the denominators together. For example, 1/2 × 2/3 × 3/4 = (1 × 2 × 3) / (2 × 3 × 4) = 6/24 = 1/4. Cross-canceling across all fractions first makes the arithmetic much easier — in this case, the 2s and 3s cancel completely, leaving just 1/4.
The formula is a/b × c/d = (a × c) / (b × d). Multiply the two numerators for the new top number and the two denominators for the new bottom number. Then simplify by dividing both by their greatest common factor.
Exactly the same way as any other fractions — different denominators don't matter when multiplying. Just multiply straight across: numerator times numerator and denominator times denominator. A common denominator is only needed for adding or subtracting fractions, never for multiplication.
You multiply fractions whenever you need a fraction of something — halving a recipe, calculating a discount (¼ off means multiplying by ¾), scaling measurements in construction, or splitting shared costs into portions. It's one of the most commonly used fraction operations in everyday math.
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