Multiply Fractions Calculator
To multiply fractions, multiply the numerators together and the denominators together, then simplify. This free calculator handles proper fractions, improper fractions, and mixed numbers — showing every step including cross-canceling so you can learn while you solve.
Free Fraction Multiplication Tool
How Do You Multiply Fractions?
To multiply fractions, follow three steps: multiply the numerators to get the new numerator, multiply the denominators to get the new denominator, and simplify the result to lowest terms. Unlike addition and subtraction, you do not need a common denominator. This makes fraction multiplication one of the most straightforward fraction operations.
For example, to compute ³⁄₄ × ²⁄₅, multiply 3 × 2 = 6 for the numerator and 4 × 5 = 20 for the denominator, giving you ⁶⁄₂₀. Since both 6 and 20 share a greatest common factor of 2, the simplified answer is ³⁄₁₀. If you'd like a deeper walkthrough with more practice problems, see our full guide on how to multiply fractions.
How Do You Multiply Proper Fractions?
To multiply proper fractions, multiply straight across — numerator times numerator and denominator times denominator — then simplify. A proper fraction has a numerator smaller than its denominator (like ²⁄₃ or ⁵⁄₈). The product of two proper fractions is always smaller than either original fraction, which makes intuitive sense: you're finding a part of a part.
How Do You Multiply Mixed Numbers?
To multiply mixed numbers, first convert each one to an improper fraction, then multiply the fractions as normal. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For instance, 2¹⁄₃ becomes ⁷⁄₃ because (2 × 3) + 1 = 7. Once both values are improper fractions, multiply across and convert the answer back to a mixed number if desired. Our calculator above handles mixed numbers automatically — just enter the whole number in the "Whole" field.
What Is Cross-Canceling and How Does It Save Time?
Cross-canceling is a shortcut where you divide a numerator from one fraction and a denominator from the other by their greatest common factor before multiplying. This keeps the numbers smaller throughout the calculation and often means your answer is already fully simplified at the end — no extra simplification step needed.
Pro Tip: You can cross-cancel diagonally — the numerator of the first fraction with the denominator of the second, or vice versa. For example, in ⁴⁄₉ × ³⁄₈, you can cancel the 4 and 8 (both divisible by 4) and the 3 and 9 (both divisible by 3), giving you ¹⁄₃ × ¹⁄₂ = ¹⁄₆ — no simplifying needed at the end.
Worked Examples
Multiply ²⁄₅ × ³⁄₇
5 × 7 = 35 → denominator
Result: ⁶⁄₃₅ (already in simplest form because 6 and 35 share no common factors).
Multiply ⁶⁄₁₁ × ⁷⁄₁₂
Before multiplying, notice that 6 and 12 share a factor of 6. Cancel to get ¹⁄₁₁ × ⁷⁄₂.
11 × 2 = 22 → denominator
Result: ⁷⁄₂₂. Without cross-canceling you'd compute ⁴²⁄₁₃₂ and need to simplify — far more work.
Multiply 1¹⁄₂ × 2²⁄₃
Convert: 1¹⁄₂ = ³⁄₂ and 2²⁄₃ = ⁸⁄₃.
2 × 3 = 6 → denominator
Simplify ²⁴⁄₆ = 4. Or convert to a mixed number: 4.
Frequently Asked Questions
Multiply the numerators together to get the new numerator, then multiply the denominators together to get the new denominator. Finally, simplify the result if possible. For example, ²⁄₃ × ⁴⁄₅ = ⁸⁄₁₅.
No. Unlike adding or subtracting fractions, you do not need a common denominator when multiplying. Simply multiply straight across — numerator × numerator and denominator × denominator.
Cross-canceling is a shortcut where you simplify diagonal pairs — a numerator from one fraction with a denominator from the other — before multiplying. This keeps the numbers smaller and often means the result is already in simplest form.
Convert each mixed number to an improper fraction first. For example, 2¹⁄₃ becomes ⁷⁄₃ because (2 × 3) + 1 = 7. Then multiply the improper fractions as normal, and convert the result back to a mixed number if needed.
Yes. Multiply all the numerators together and all the denominators together. You can also cross-cancel any numerator with any denominator before multiplying to keep numbers manageable.
Write the whole number as a fraction over 1, then multiply as normal. For example, 3 × ²⁄₅ is the same as ³⁄₁ × ²⁄₅ = ⁶⁄₅, which simplifies to the mixed number 1¹⁄₅. Before simplifying, the denominator always stays the same because you are multiplying it by 1.
When you multiply two numbers that are each less than 1, the result is always smaller than either number. You are finding a fraction of a fraction — a part of a part. For instance, ¹⁄₂ × ¹⁄₃ = ¹⁄₆, which is smaller than both ¹⁄₂ and ¹⁄₃.
²⁄₃ × ³⁄₄ = ⁶⁄₁₂, which simplifies to ¹⁄₂. Even faster: cross-cancel the 3 in the numerator of the second fraction with the 3 in the denominator of the first to get ²⁄₁ × ¹⁄₄ = ²⁄₄ = ¹⁄₂.
No, but they are closely related. To divide fractions, you flip the second fraction (find its reciprocal) and then multiply. So dividing by ²⁄₃ is the same as multiplying by ³⁄₂. Use our divide fractions calculator for division problems.
You should always check whether the result can be simplified, but it is not always necessary. If you cross-cancel before multiplying, the answer is often already in simplest form. Use our simplify fractions calculator to check.
Looking for other operations? Try our master fractions calculator, divide fractions calculator, or learn more with our simplify fractions calculator.