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Enter a fraction and a whole amount, and this calculator shows you what that fraction of that number is, drawn as a bar model. Questions like "what is 2/3 of 12" are really questions about splitting something into equal parts and then counting some of them, which is much easier to see than to read. The bar model splits the whole into as many parts as the denominator, labels every part with its actual value, and shades the number of parts the numerator asks for, so the answer is something you can point at rather than something you have to trust. It handles the awkward cases too: answers that are not whole numbers come back as exact fractions and mixed numbers, improper fractions like 5/4 draw a second bar to show the overflow past one whole, and the whole itself can be a decimal. Underneath the diagram you get the worked steps in words, multiply by the numerator then divide by the denominator, so students can copy the method rather than just the answer.
Use this when the question gives you an amount and asks for part of it: a discount, a share of a group, a portion of a recipe, or a homework problem in the shape of "what is 3/4 of 20".
Decimals are fine, for example 7.5.
What is 2/3 of 12?
8
A whole number answer.
Four examples covering the cases that trip people up: an even split, an answer that is not a whole number, an improper fraction, and a decimal whole.
3/4 of 20 = 15
A clean whole number answer. Twenty splits into four parts of five, and three of those parts make fifteen.
2/3 of 10 = 6 2/3 (exactly 20/3, or 6.6667... as a decimal)
Ten does not split evenly into thirds, so the answer is a mixed number. Each third is 3 1/3, and two of them make 6 2/3.
5/4 of 12 = 15
An improper fraction asks for more than one whole, so the bar model needs a second bar. Five quarters of twelve is fifteen.
1/4 of 7.5 = 1 7/8 (exactly 15/8, or 1.875 as a decimal)
The whole can be a decimal. A quarter of 7.5 is 1.875, which is 1 7/8 written as a mixed number.
Divide the whole by the denominator to get one part, then multiply by the numerator. For 3/4 of 20: 20 divided by 4 is 5, and 5 times 3 is 15. This is usually the easier order by hand, because the numbers stay small.
Multiply the whole by the numerator, then divide by the denominator. For 3/4 of 20: 20 times 3 is 60, and 60 divided by 4 is 15. This order always works, even when the whole does not divide evenly by the denominator, so it is the safer one to teach as the rule.
Draw a bar model for any fraction on its own, without a whole amount.
Add, subtract, multiply, and divide two fractions with steps.
Reduce an answer like 20/3 or 15/12 to its simplest form.
Turn an answer like 20/3 into 6 2/3.
Check a fraction answer as a decimal.
Pie charts, bars, and number lines for any fraction.
Project the bar model while you talk through the split, then change the whole and let students predict the new answer before you show it.
Generate a diagram for the exact numbers in your question, then print or screenshot it for a handout.
Check both the answer and the method: the steps show whether a wrong answer came from the division or the multiplication.
Common questions about finding a fraction of a number