Fraction multiplication
Multiplying a decimal by a fraction looks tricky because the two numbers are written in different formats. The fix is simple: rewrite one of them so both numbers match, then multiply the way you already know. Turn the decimal into a fraction and multiply across, or turn the fraction into a decimal and multiply decimals. This page shows both routes, when each one is faster, and what to do with the answer at the end.
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Interactive tool
Type a decimal times a fraction. The tool solves the problem two ways — turning the decimal into a fraction, and turning the fraction into a decimal — and shows every step of both routes.
Examples: 0.6 x 3/4, 2.5 x 2/3, 1 1/2 x 0.4
Answer
9/20
= 0.45
Rewrite 0.6 as 3/5, multiply by 3/4, and simplify. The exact answer is 9/20, which is 0.45 as a decimal.
Route 1 · fraction method
1. Rewrite the decimal as a fraction
0.6 = 6/10 — 1 decimal place means tenths.
2. Simplify the rewrite
6/10 = 3/5.
3. Multiply across
3/5 × 3/4 = 9/20.
4. Check the lowest terms
9/20 is already in lowest terms.
5. Optional decimal form
9/20 = 0.45.
Route 2 · decimal method
1. Rewrite the fraction as a decimal
3/4 = 0.75.
2. Multiply without the decimal points
6 × 75 = 450.
3. Put the decimal point back
1 place in 0.6 plus 2 in 0.75 is 3, so the product is 0.450.
4. Trim the trailing zeros
0.450 = 0.45.
5. Match it back to a fraction
0.45 = 450/1000 = 9/20.
Worked example
0.5 × 1/4 = 1/2 × 1/4 = 1/8 = 0.125
This problem works through both routes, because 1/4 is also the clean decimal 0.25. Rewrite 0.5 as 1/2 and multiply across, or rewrite 1/4 as 0.25 and multiply decimals. Either way the answer is 1/8, which is 0.125.
Worked example
0.6 × 3/4 = 3/5 × 3/4 = 9/20 = 0.45
This is the standard route. The decimal 0.6 means six tenths, which simplifies to 3/5. Multiplying across gives 9/20, and dividing 9 by 20 turns the answer back into the decimal 0.45.
Worked example
2.5 × 2/3 = 5/2 × 2/3 = 10/6 = 5/3 = 1 2/3
A decimal greater than 1 works the same way: 2.5 means twenty-five tenths, which simplifies to 5/2. The fraction route is required here because 2/3 repeats as a decimal, so switching to decimals would force rounding.
Worked example
0.375 × 2/3 = 3/8 × 2/3 = 6/24 = 1/4 = 0.25
Longer decimals follow the same place-value rule: three digits after the point means thousandths, so 0.375 is 375/1,000, which simplifies to 3/8. The 3s cancel across the product, leaving 1/4, an exact decimal.
This is the standard route, and it always works. Every terminating decimal is a fraction already — 0.6 means six tenths — so write it that way, simplify, and multiply like any two fractions.
0.6 × 3/4
= 3/5 × 3/4
= 9/20
= 0.45
Use this route whenever the fraction’s denominator is not made of 2s and 5s — denominators like 3, 6, 7, or 9. Those fractions never become clean decimals, so the fraction route keeps the answer exact. The multiplying fractions steps are exactly the same once both numbers are fractions.
When the fraction converts to a short decimal, this route is the fastest. Divide the numerator by the denominator, then multiply the two decimals.
3/4 × 0.2
= 0.75 × 0.2
= 0.15
The decimal point is the only place students lose track here. Multiply the whole-number digits first (75 × 2 = 150), then count the total decimal places in the problem (two in 0.75, one in 0.2 — three total) and place the point: 0.150 = 0.15.
Look at the fraction’s denominator before you start. If it is built from 2s and 5s — 2, 4, 5, 8, 10, 20, 25, 50 — the fraction becomes a clean terminating decimal, so either route works and the decimal route is often quicker. If the denominator has any other factor, such as 3, 6, 7, or 9, convert the decimal to a fraction instead; you will avoid a repeating decimal entirely. And if the decimal itself repeats, like 0.333..., always go the fraction route.
Unless the question specifies a form, both are correct — 9/20 and 0.45 name the same amount. Keep the fraction form when the next step involves more fraction work, and switch to a decimal when the context is money, measurement, or a quick estimate. To convert, divide the numerator by the denominator: 9 ÷ 20 = 0.45. Simplify the fraction first either way, because 0.45 is easier to read back from 9/20 than from 18/40.
Review how to convert a decimal to a fractionConvert the mixed number to an improper fraction before anything else, then follow the same two routes. For 1 1/2 × 0.4: write 1 1/2 as 3/2 and 0.4 as 2/5. Multiply across: 3/2 × 2/5 = 6/10 = 3/5. Back in decimal form, 3/5 = 0.6 — and a quick check with 1.5 × 0.4 confirms it.
A repeating decimal such as 0.333... does not stop, so it has no exact place-value fraction like 333/1,000. Recognize it as a fraction instead: 0.333... = 1/3. Then 1/3 × 3/4 = 3/12 = 1/4. Rounding first gives a different answer — 0.33 × 3/4 = 99/400 = 0.2475, not exactly 0.25 — so round only at the very end if the question asks for an approximation.
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