What does it mean to multiply fractions?

Multiplying fractions means finding the product of two or more fractional amounts. Instead of the complex process needed for adding or subtracting fractions, you simply multiply the numerators together and the denominators together. For example, \frac{2}{3} \times \frac{3}{4} means you're finding what \frac{2}{3} of \frac{3}{4} is.

Do I always have to simplify after multiplying fractions?

Technically no, but it's good practice. Your answer is correct either way, but simplifying gives you the fraction in lowest terms, which is the standard form. For instance, \frac{2}{3} \times \frac{3}{4} = \frac{6}{12}, but \frac{1}{2} is the simplified form. You can also simplify before multiplying to keep numbers manageable.

What if I'm multiplying a fraction by a whole number?

Convert the whole number to a fraction by placing it over 1, then multiply normally. For example, 7 \times \frac{2}{5} = \frac{7}{1} \times \frac{2}{5} = \frac{14}{5}. This works because any whole number can be written as a fraction with denominator 1.

Why is the product of two fractions always smaller than at least one of them?

This happens when both fractions are between 0 and 1. Multiplying a fraction less than 1 by another positive number makes it smaller. However, if one fraction is greater than 1 (like \frac{5}{3}), the product can be larger. For instance, \frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5}, which is larger than \frac{4}{5}.

Multiplying Fractions

Multiply fractions by multiplying numerators and denominators separately, letting you combine fractional amounts and solve fraction problems efficiently.

\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}

Solve a problem with Multiplying Fractions

Type the problem. The solver will use Multiplying Fractions where Multiplying Fractions is the right tool, and tell you when it is not.

What each symbol means

What Multiplying Fractions takes

Symbol	Meaning
$a$	The numerator (top number) of the first fraction; if $a = 0$ , the entire product is 0.
$b$	The denominator (bottom number) of the first fraction; it can never be 0, as division by zero is undefined.
$c$	The numerator (top number) of the second fraction; if $c = 0$ , the entire product is 0.
$d$	The denominator (bottom number) of the second fraction; it can never be 0, as division by zero is undefined.

When to use it

When you need to find the product of two or more fractions, or work with fractional parts of quantities.

Level

Usually taught in: Pre-Algebra

Worked examples

1. Multiply two positive fractions and simplify

Problem

Multiply

\frac{2}{3} \times \frac{3}{4}

$\frac{2}{3} \cdot \frac{3}{4} = \frac{2 \cdot 3}{3 \cdot 4}$
Apply the rule: multiply the numerators and multiply the denominators.
$\frac{6}{12}$
Calculate $2 \times 3 = 6$ in the numerator and $3 \times 4 = 12$ in the denominator.
$\frac{1}{2}$
Simplify by dividing both numerator and denominator by 6, their greatest common factor.

Answer: $\frac{1}{2}$

This basic example shows the complete process: apply the rule, compute the products, and simplify. Since 6 and 12 share a common factor of 6, we reduce to get $\frac{1}{2}$ .

2. Multiply a negative fraction and simplify

Problem

Multiply

\frac{-3}{4} \times \frac{8}{9}

$\frac{-3}{4} \cdot \frac{8}{9} = \frac{(-3) \cdot 8}{4 \cdot 9}$
Apply the multiplication rule; keep the negative sign with the numerator.
$\frac{-24}{36}$
Compute $(-3) \times 8 = -24$ and $4 \times 9 = 36$ .
$\frac{-2}{3}$
Simplify by dividing both numerator and denominator by 12, their greatest common factor.

Answer: $\frac{-2}{3}$

When one fraction is negative, the product is negative. The result simplifies because both numerator and denominator share the factor 12, showing why it's important to always check for common factors.

3. Solve a word problem with fractional amounts

Problem

At a school bake sale, a recipe calls for

\frac{5}{6}

cup of flour. You want to make

\frac{4}{5}

of the recipe. How much flour do you need?

$\frac{4}{5} \cdot \frac{5}{6} = \frac{4 \cdot 5}{5 \cdot 6}$
Set up the multiplication: find $\frac{4}{5}$ of $\frac{5}{6}$ cup by multiplying the fractions.
$\frac{20}{30}$
Multiply the numerators: $4 \times 5 = 20$ . Multiply the denominators: $5 \times 6 = 30$ .
$\frac{2}{3}$
Simplify by dividing both numerator and denominator by 10, their greatest common factor.

Answer: $\frac{2}{3} \text{ cup}$

Real-world problems often ask for a fraction of a fraction. Multiplying fractions gives us the exact amount needed without having to visualize or measure fractional parts separately.

Common mistakes

Where Multiplying Fractions usually goes wrong

The mistake	Why it is wrong	The fix
Writing $\frac{2}{3} \times \frac{4}{5} = \frac{2+4}{3+5} = \frac{6}{8} = \frac{3}{4}$ .	Students sometimes confuse multiplication of fractions with addition, which does require adding numerators and finding common denominators.	Multiply the numerators and denominators: $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$ .
Writing $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}$ .	Cross-multiplication is used in proportion problems and equations, not for multiplying fractions directly.	Multiply straight across: numerator times numerator and denominator times denominator. $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$ .
Writing $\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 9}{8 \times 4} = \frac{27}{32}$ .	Students sometimes incorrectly pair numerators and denominators, mixing up which numbers to multiply together.	Multiply numerator by numerator and denominator by denominator: $\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 4}{8 \times 9} = \frac{12}{72} = \frac{1}{6}$ .

Tips and when to use something else

You can simplify before multiplying by canceling common factors between any numerator and any denominator — this keeps numbers smaller and is often faster.
If you're multiplying a whole number by a fraction, first rewrite the whole number as a fraction: $5 \times \frac{3}{4} = \frac{5}{1} \times \frac{3}{4} = \frac{15}{4}$ .
For word problems involving 'of', use Multiplying Fractions: 'one-half of one-third' means $\frac{1}{2} \times \frac{1}{3}$ .
If you need to find how many times one fraction goes into another, use Dividing Fractions instead, which means multiply by the reciprocal.

Related formulas

Simplifying FractionsSimplify a fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common factor.Dividing FractionsDividing fractions means flipping the second fraction and multiplying instead — it lets you split quantities into equal groups.ReciprocalA reciprocal flips a fraction—multiply a number by its reciprocal and you always get 1, helping you solve fraction equations.Adding FractionsAdd fractions with different denominators by finding a common denominator, then combining the numerators to get your answer.Mixed Number to Improper FractionConvert a mixed number into an improper fraction so you can multiply, divide, or compare it with other fractions in calculations.

Frequently asked questions

What does it mean to multiply fractions?: Multiplying fractions means finding the product of two or more fractional amounts. Instead of the complex process needed for adding or subtracting fractions, you simply multiply the numerators together and the denominators together. For example, $\frac{2}{3} \times \frac{3}{4}$ means you're finding what $\frac{2}{3}$ of $\frac{3}{4}$ is.
Do I always have to simplify after multiplying fractions?: Technically no, but it's good practice. Your answer is correct either way, but simplifying gives you the fraction in lowest terms, which is the standard form. For instance, $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12}$ , but $\frac{1}{2}$ is the simplified form. You can also simplify before multiplying to keep numbers manageable.
What if I'm multiplying a fraction by a whole number?: Convert the whole number to a fraction by placing it over 1, then multiply normally. For example, $7 \times \frac{2}{5} = \frac{7}{1} \times \frac{2}{5} = \frac{14}{5}$ . This works because any whole number can be written as a fraction with denominator 1.
Why is the product of two fractions always smaller than at least one of them?: This happens when both fractions are between 0 and 1. Multiplying a fraction less than 1 by another positive number makes it smaller. However, if one fraction is greater than 1 (like $\frac{5}{3}$ ), the product can be larger. For instance, $\frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5}$ , which is larger than $\frac{4}{5}$ .

Need a different method?

The full solver is not scoped to one formula — type any problem and it will pick the method.

Open the math solver

Reviewed 2026-09-18