How To Multiply Fractions Step By Step?
To multiply fractions, you follow three short steps, and none of them involve a common denominator. This is the part that surprises many parents, because adding fractions needs one and multiplying does not. Here is the method your child will use every time.
Step 1: Multiply the numerators. Multiply the two top numbers together to get the new top number.
Step 2: Multiply the denominators. Multiply the two bottom numbers together to get the new bottom number.
Step 3: Simplify. Reduce the answer to its simplest form by dividing the top and bottom by any common factor.
A simple way to remember it: multiply the tops, multiply the bottoms. Everything else is tidying up.
Worked example: multiply two proper fractions.
Take $\frac{2}{3} \times \frac{3}{4}$. Multiply the tops, then the bottoms:
$$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}$$
Now simplify. Both 6 and 12 divide by 6, so:
$$\frac{6}{12} = \frac{1}{2}$$
So $\frac{2}{3} \times \frac{3}{4} = \frac{1}{2}$. The answer is smaller than both fractions you started with, which is the clue to why this works, covered further down.
Why Does Multiplying Fractions Make The Answer Smaller?
Multiplying two proper fractions gives a smaller answer because you are taking a part of a part. When your child reads $\frac{1}{2} \times \frac{1}{3}$, the word to translate is of: it means "half of one third." Half of something already small is smaller still.
The clearest way to show this at home is the area model, and it needs nothing more than a rectangle.
Draw a rectangle and split it into 3 equal columns. Shade one column: that is $\frac{1}{3}$.
Now split the same rectangle into 2 equal rows. Shade one row across.
The piece covered by both shadings is 1 small box out of 6. That box is $\frac{1}{6}$.
$$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$$
The picture and the arithmetic agree: half of one third is one sixth. This is the same "half of a third of the cake" from the top of the page, and it is why the rule multiplies the bottoms as well as the tops.
How Do You Multiply A Fraction By A Whole Number?
To multiply a fraction by a whole number, turn the whole number into a fraction by putting it over 1, then multiply straight across. A whole number always has an invisible denominator of 1.
Worked example: multiply a fraction by a whole number.
Take $\frac{3}{5} \times 4$. Write 4 as $\frac{4}{1}$, then multiply:
$$\frac{3}{5} \times \frac{4}{1} = \frac{3 \times 4}{5 \times 1} = \frac{12}{5}$$
Because 12 is bigger than 5, this is an improper fraction. Convert it to a mixed number so it reads naturally: $12 \div 5 = 2$ remainder $2$, so:
$$\frac{12}{5} = 2\frac{2}{5}$$
A common slip here is multiplying the whole number into both the top and the bottom. Only the numerator gets multiplied, because the whole number sits over 1.
How Do You Multiply Mixed Numbers?
To multiply mixed numbers, convert each one into an improper fraction first, then multiply straight across and simplify. Never multiply the whole-number parts separately from the fraction parts.
To turn a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, $1\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$.
Worked example: multiply two mixed numbers.
Take $1\frac{1}{2} \times 2\frac{1}{3}$. Convert both to improper fractions:
$$1\frac{1}{2} = \frac{3}{2}, \qquad 2\frac{1}{3} = \frac{7}{3}$$
Now multiply straight across:
$$\frac{3}{2} \times \frac{7}{3} = \frac{3 \times 7}{2 \times 3} = \frac{21}{6}$$
Simplify by dividing top and bottom by 3, then convert back to a mixed number:
$$\frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}$$
So $1\frac{1}{2} \times 2\frac{1}{3} = 3\frac{1}{2}$. Your child can sense-check it: roughly "one and a half" times "a bit more than two" should land near three and a half, and it does.
What Is Cross-Cancelling, And Should Your Child Use It?
Cross-cancelling means simplifying before you multiply, by dividing a top number and a bottom number by a shared factor. It keeps the numbers small, so there is less to simplify at the end. It is optional, and it is usually introduced once your child is confident with the basic method.
Worked example: multiply using cross-cancelling.
Take $\frac{4}{9} \times \frac{3}{8}$. Before multiplying, look for shared factors across the two fractions.
The 4 (top) and the 8 (bottom) share a factor of 4: they become 1 and 2.
The 3 (top) and the 9 (bottom) share a factor of 3: they become 1 and 3.
$$\frac{\cancel{4}^{,1}}{\cancel{9}{,3}} \times \frac{\cancel{3}^{,1}}{\cancel{8}{,2}} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$$
The straight-across method gives the same answer: $\frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6}$. Cross-cancelling just gets there with smaller numbers. If it confuses your child, the plain method is always safe.
What Grade Do Kids Learn To Multiply Fractions?
Children usually learn to multiply a fraction by a whole number around age 9 to 10, and to multiply two fractions together around age 10 to 11. The exact grade depends on the curriculum, but the sequence is the same everywhere: whole numbers first, then fraction by fraction, then mixed numbers.
Table: When multiplying fractions appears across three curricula.
Skill | US (CCSS) | UK (National Curriculum) | India (NCERT) |
|---|---|---|---|
Fraction × whole number | Grade 4 (4.NF.B.4) | Year 5 | Class 7 |
Fraction × fraction | Grade 5 (5.NF.B.4) | Year 6 | Class 7 |
Mixed numbers | Grade 5 (5.NF.B.6) | Year 6 | Class 7 |
If your child is in one of these grades and finding it hard, that is expected, not a warning sign. Multiplying fractions asks a child to hold several ideas at once, and it settles with practice on real quantities.
Why Does This Method Work?
The three-step rule is not an arbitrary trick. It falls out directly from what a fraction and the word "of" actually mean, and it helps your child to know that.
Multiplying tops counts the parts. In $\frac{2}{3} \times \frac{3}{4}$, the numerators count how many parts you are taking, so they multiply together.
Multiplying bottoms counts the pieces. The denominators count how many equal pieces the whole is cut into, and cutting into thirds and then into quarters makes twelfths.
"Of" means multiply. "One half of one third" is $\frac{1}{2} \times \frac{1}{3}$, the same phrase your child meets when sharing food or halving a recipe.
No common denominator is needed. Common denominators line up pieces for adding. Multiplication makes new, smaller pieces, so that step simply does not apply.
When your child can say why the method works, they stop guessing between the addition rule and the multiplication rule, which is where most fraction errors begin. For more on why this topic feels harder than it should, see why are fractions so hard.
What Are The Most Common Mistakes With Multiplying Fractions?
These are the errors teachers and parents see most often, drawn from documented student misconceptions. Naming them ahead of time is the easiest way to help your child sidestep them.
Finding a common denominator that is not needed.
Where it slips in:
A child has just learned to add fractions, where a common denominator is required, and carries that habit into multiplication.
Don't do this:
Do not stop to find a common denominator before multiplying. It wastes time and often leads to a wrong answer.
The correct way:
Multiply straight across, tops together and bottoms together. Common denominators are only for adding and subtracting.
Forgetting to convert mixed numbers first.
Where it slips in:
Faced with $1\frac{1}{2} \times 2\frac{1}{3}$, a child multiplies the whole numbers and the fractions separately, or adds the whole number onto the numerator.
Don't do this:
Do not multiply the parts of a mixed number on their own, and do not add the whole number to the top.
The correct way:
Convert each mixed number into an improper fraction first, so $1\frac{1}{2}$ becomes $\frac{3}{2}$, then multiply straight across.
Multiplying a whole number into the top and the bottom.
Where it slips in:
When computing $\frac{3}{5} \times 4$, a child multiplies both the numerator and the denominator by 4.
Don't do this:
Do not multiply the denominator by the whole number. That changes the size of the pieces.
The correct way:
Write the whole number over 1, so only the numerator is multiplied: $\frac{3}{5} \times \frac{4}{1} = \frac{12}{5}$.
Leaving the answer unsimplified.
Where it slips in:
A child finishes with a correct but bulky fraction such as $\frac{6}{12}$ and stops there.
Don't do this:
Do not treat an unsimplified fraction as finished when the question asks for simplest form.
The correct way:
Divide the top and bottom by their common factor, so $\frac{6}{12}$ becomes $\frac{1}{2}$.
When Should You Get Extra Help?
Most children work through fraction multiplication with steady practice and a few good conversations at the kitchen table. A little frustration is part of learning it. Consider reaching out for extra support when the signs point to a foundation gap rather than a passing rough patch.
Your child mixes up the multiply rule and the add rule even after several weeks of practice.
Simpler ideas underneath keep tripping them up, such as what a fraction means or basic times tables.
Homework on fractions regularly ends in tears or avoidance.
Your child has started saying "I'm just bad at fractions" or "I'm not a math person."
If the struggle sits under fractions in earlier arithmetic, more fraction worksheets will not fix it. Working out where the real gap is comes first. Our guide on when a child struggling with math needs support walks through this honestly, and how to teach math to kids covers the at-home habits that help most.
Where Can Your Child Get Extra Help With Multiplying Fractions?
If you would like structured support beyond home practice, these Bhanzu pages match the grade bands where multiplying fractions is taught.
4th Grade math tutoring: for the fraction-by-whole-number stage.
5th Grade math tutoring: for multiplying fraction by fraction and mixed numbers.
Elementary math tutoring: for rebuilding the arithmetic that sits under fractions.
Math classes for kids: live small-group classes that teach the why before the how.
Where Should You Go Next?
Multiplying fractions is one step in a longer fractions journey, and a few natural doors open from here.
Mental math with fractions. Build the quick sense-checking that catches wrong answers before they are written down.
Fractions, decimals and percentages. See how multiplying fractions connects to the wider number system your child will use for years.
How to teach math to kids. The everyday habits that make any math topic, fractions included, stick at home.
If your child learns best with a live guide, a Bhanzu trainer teaches fractions starting from the "why" (the area model and the meaning of "of") rather than the rule alone, in the math classes for kids.
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