The bar model, known as the Singapore method, draws the whole as a bar and cuts it into equal parts, so a word problem becomes one division and one multiplication. With 3/4 of 20, the bar has four cells of 5, and three of them make 15. The fraction of a number calculator checks this direct case. If you only want to draw a fraction, with no data, see how to draw fractions; here the bar is used to solve problems.
What to draw for each kind of problem
Almost every fraction problem with bars falls into one of four types. What changes is which number you write on the bar and what you are asked for.
| Type | Example | What to draw | Calculation |
|---|---|---|---|
| Part of a known whole | 3/4 of 20 | The whole in 4 cells | 20 ÷ 4 × 3 = 15 |
| Whole from a part | 3/8 is 21 | 8 cells, 3 marked with 21 | 21 ÷ 3 × 8 = 56 |
| Comparing two quantities | Maya has 2/5 of what Ethan has; together, 35 | Two bars with the same cell | 35 ÷ 7 = 5; 10 and 25 |
| Fractions of the remainder | 1/4 is spent, then 1/3 of what is left; 3/4 × 2/3 leaves half the total, which is 30 | One bar and its remainder | 30 ÷ 1/2 = 60 |
The table shows that the question decides the drawing: when the whole is known, divide by the denominator, and when a part is known, divide by its number of cells. The model is a way to organize your thinking, not a new formula.
How to draw the bar
The procedure is the same for all four types and has four steps.
- Decide which quantity is the whole, that is, what the full 1 of the fraction refers to.
- Draw a bar for that whole and write its value above it, or a question mark if you are looking for it.
- Divide it into as many equal cells as the denominator says and shade the number of cells the numerator says.
- Work out what one cell is worth and multiply by the number of cells the problem asks for.
The first step is the one that goes wrong most often, because a fraction is always a fraction of something. “2/7 of what there is” and “2/7 of half” describe bars of different sizes, and if two fractions refer to different wholes they cannot share the same bar.
Worked example: if 2/7 is 18, what is the whole?
A part (18) and the fraction it represents (2/7) are known, and the whole is asked for. This is the inverse of finding the part.
- Draw the whole bar. The denominator 7 gives seven equal cells, and the whole is what you are looking for.
- Shade two cells. The numerator 2 says how many, and together they are worth 18.
- Find one cell. Two cells are worth 18, so one is worth 18 ÷ 2 = 9.
- Rebuild the whole. Seven cells are worth 7 × 9 = 63.
18 ÷ 2 = 9; 9 × 7 = 63
Answer. The whole is 63.
Check. 63 ÷ 7 × 2 = 18, which is the number in the problem. Dividing 7 by 2 would be a mistake, because the 18 matches two cells and not the whole.
The find the whole from a fraction calculator does that same division and returns the exact total. The drawing helps you decide beforehand which number is the numerator and which is the denominator.
Comparing two quantities with two bars
Grace has 3/4 of what Noah has, and together they have 56. Draw two bars with cells of the same size: 3 for Grace and 4 for Noah. There are 3 + 4 = 7 cells worth 56, so one cell is worth 56 ÷ 7 = 8. Grace has 3 × 8 = 24 and Noah has 4 × 8 = 32. To check, 24 + 32 = 56 and 24 is 3/4 of 32.
56 ÷ 7 = 8; 3 × 8 = 24; 4 × 8 = 32
If the given number were the difference instead of the sum, the drawing would be the same: Noah has one cell more than Grace, so that one cell is worth the difference. Quantities shared in a fixed ratio can also be worked out with proportional sharing and sharing with fractions.
When the second fraction is taken from the remainder
In “1/3 is spent and then half of what is left; 30 remains,” each fraction applies to a different whole. Draw the bar in six cells: the first spending takes 2, 4 are left, and half of the remainder is another 2. That leaves 2 cells, worth 30, so one is worth 15 and the whole is 6 × 15 = 90. In fractions, 2/3 × 1/2 = 1/3 of the whole is left, and 30 ÷ 1/3 = 90.
30 ÷ 2 = 15; 15 × 6 = 90
The guide on fraction of the remainder problems covers more cases of this kind, with three or more chained steps.
From the drawing to algebra
In middle school the cell is called x and the bar becomes an equation. In the first example, two cells are 2x = 18, so x = 9 and the whole is 7x = 63. In the Grace and Noah example, 3x + 4x = 56 gives x = 8. The drawing decides which equation to write, and algebra solves it. When the data are already fractions, equations with fractions give the exact value of x.
When the bar is not the right tool
The bar works when all the quantities have a fixed ratio and fit in a few cells. If the problem is not proportional or has many unknowns, move to algebra or the rule of three. To tell which of two fractions is greater, the compare fractions tool is enough, with no drawing, and the general guide to fraction word problems helps you recognize the family each problem belongs to.
Practice
- Find 2/3 of 27 with a bar.
- If 4/9 of a number is 20, what is the number?
- Ava and Jack have 54 together, and Ava has 5/4 of what Jack has. How much does each have?
See the answers
- 18, because one cell is worth 27 ÷ 3 = 9 and two cells are 18.
- 45, because four cells are worth 20, one is worth 5, and all nine are worth 45.
- Ava 30 and Jack 24, because there are 5 + 4 = 9 cells of 6.
For more exercises with solutions, see the worked fraction exercises or create new sheets with the fraction worksheet generator. If you would rather see a fraction drawn without data, the visual fractions tool and the visuals hub offer other ways to see it.
Sources
The Common Core State Standards for Mathematics, standard 3.NF.A.1, says to understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (accessed October 17, 2026). The standard does not cover the bar model: the problems in this guide are checked with the calculations shown.