Three fifths of 20 is 12, because you divide 20 by 5 and multiply the result by 3. This set of worksheets, available as PDFs with a separate answer key, gathers 22 worksheets that train two questions separately, finding the part and finding the whole, and then mix them. For a single calculation use the fraction of a number tool or the find the whole from a fraction one.
| If the student must… | Worksheet | Sample problem |
|---|---|---|
| Find the part | Levels 1 to 3 (and mixed ones in level 4) | 2/3 of 18 = 12 |
| Find the whole | Levels 1 to 4 | 7/15 of the total is 63; the total is 135 |
| Decide what is being asked | Mixed, levels 1 to 4 | They alternate the two cases without warning |
What worksheets there are
There are 22 worksheets of 8, 12, 16 or 20 problems. The denominators go up to 10 in level 1, 12 in level 2, 20 in level 3 and 30 in level 4. In levels 1 to 3 the part calculated is always a whole number. Level 4 has only find-the-whole and mixed worksheets, and some results are not whole numbers, like 3/8 of 10 = 15/4 = 3 3/4. The levels are not grades. In the US, Common Core introduces multiplying a fraction by a whole number in Grade 4 (standard 4.NF.B.4, including word problems), and the limits of 20 and 30 in levels 3 and 4 are a choice made for these worksheets, not a standard (Grade 4, Number and Operations in Fractions, consulted October 17, 2026).
Worked example: 3/5 of 20 with a bar
A bar of 20 squares is divided into 5 equal parts and 3 are colored. How many squares are colored?
- Divide the quantity by the denominator. 20 ÷ 5 = 4, so each part has 4 squares.
- Multiply by the numerator. You take 3 parts, so 4 × 3 = 12.
- Read the answer. 12 squares are colored.
Result: 12 squares.
Check: 12 is 3 parts of 4, and 5 parts of 4 make 20.
A test problem at level 3
“At a tournament, 63 tickets, which are 7/15 of all those sold, were bought in advance. How many tickets were sold in total?” Model answer:
- Write what is known. 7 parts out of 15 are worth 63.
- Find the value of one part with 63 ÷ 7 = 9.
- Multiply by the total number of parts with 9 × 15 = 135.
- Check: 9 × 7 = 63, the given amount.
The direct version would be 5/12 of 96 = 96 ÷ 12 × 5 = 40. If the student multiplies the given amount by the fraction and gets 63 × 7/15 = 147/5, which is 29.4, they have read the data backward. That result is wrong, because the total cannot be less than 63, and that weighs more when grading than a calculation slip in step 2.
Two typical mistakes and how to spot them
The second mistake is using the numerator as the divisor. In 2/3 of 18, dividing by 2 and multiplying by 3 amounts to the wrong calculation 18 × 3/2 = 27, a result greater than 18 for a fraction less than 1. The right way is 18 ÷ 3 × 2 = 12.
Five problems with different questions
Each problem asks for something different. You have to find the part, find the whole, compare and solve two steps. Read what is being asked before choosing the operation.
Practice
- A 48-gallon tank is filled to 5/8. How many gallons does it hold?
- A hiker has walked 28 miles, which is 7/9 of the trail. How long is the whole trail?
- Which is greater, 3/4 of 40 or 5/6 of 42, and by how much?
- A notebook has 60 pages. 3/5 of them are written on and, of the pages left blank, 1/3 are set aside for notes. How many pages are set aside?
- Calculate 3/8 of 10 and write the result as a fraction and as a mixed number.
Show the answers
- 30 gallons, because 48 ÷ 8 = 6 and 6 × 5 = 30.
- 36 miles, because each ninth is 28 ÷ 7 = 4 miles and 4 × 9 = 36.
- 5/6 of 42 is greater, at 35 against 30; the difference is 5.
- 8 pages, because 60 ÷ 5 × 3 = 36 are written on, 60 − 36 = 24 are blank and 24 ÷ 3 = 8.
- 15/4, which is 3 3/4.
For whoever grades
As a rule of thumb, set aside more time for the find-the-whole worksheets than for the find-the-part ones. For a student who stumbles with the calculation, give a drawn bar divided into the parts of the denominator; for a student who is ahead, move on to level 4. Ask for the written check to tell a method mistake from a calculation one.
Keep practicing
The fraction of a number word problems apply it in everyday situations. If you prefer immediate feedback, fraction practice corrects on screen. And when the worksheets run out, the worksheet generator creates a new sheet with other numbers.