Denominators 2–12 (3 fractions)

20 denominators 2–12 (3 fractions) problems with an answer key. Print with your browser; the answers print on a separate page.

Name: ____________________ Date: __________

1/2 + 1/2 + 1/3 = ______
5/7 + 3/8 + 1/9 = ______
2/10 + 1/10 + 7/12 = ______
4/5 + 1/2 + 1/8 = ______
1/9 + 1/10 + 3/9 = ______
3/10 + 2/4 + 5/7 = ______
1/8 + 7/9 + 5/8 = ______
4/5 + 2/3 + 1/6 = ______
1/7 + 2/10 + 1/3 = ______
1/2 + 9/11 + 5/7 = ______
4/5 + 4/8 + 4/5 = ______
3/5 + 7/9 + 1/12 = ______
1/12 + 1/6 + 5/12 = ______
9/11 + 2/6 + 2/7 = ______
1/2 + 1/2 + 7/12 = ______
5/12 + 3/4 + 7/10 = ______
1/2 + 5/11 + 1/11 = ______
9/12 + 3/8 + 1/2 = ______
1/7 + 8/10 + 2/5 = ______
1/11 + 4/10 + 7/8 = ______

How to use this worksheet

Print it, set a time limit if you like, and mark it with the key. Press “New worksheet” for a fresh set of numbers at the same level: every set is different, so it works for repeated practice and for a whole class.

Worked example: 1/2 + 1/2 + 1/3

Here is the method for the first problem on this sheet, step by step. The same steps work for every problem at this level.

The denominators are different. Find the lowest common multiple of 2 and 3: it is 6.
Rewrite each fraction over 6: 1/2 = 3/6, 1/2 = 3/6, 1/3 = 2/6.
Add the numerators: 3 + 3 + 2 = 8, giving 8/6.
Simplify by dividing the top and bottom by 2: the answer is 4/3.

What this level practises

Denominators 2–12 (3 fractions) is usually taught in grade 5. This sheet has 20 problems, and every answer is given in simplest form. Work through the sheet without a calculator, then mark it with the key: the aim is accuracy first and speed second.

Tips for adding fractions

Only the numerators are added; the denominator says what size the pieces are and stays the same.
With different denominators, rewrite the fractions with a common denominator first. The lowest common multiple keeps the numbers small.
Simplify the answer by dividing the top and bottom by their greatest common factor.
Drawing the fractions as bars or circles helps children see why the pieces must be the same size before adding.

Printing

Use your browser’s print command. The menus, buttons and ads are left off the printout, and the answer key starts on a new page so it can be kept back. For a whole class, print one sheet, press “New worksheet” and print again to give each group different numbers.

Other levels

Answer key

1/2 + 1/2 + 1/3 = 4/3
5/7 + 3/8 + 1/9 = 605/504
2/10 + 1/10 + 7/12 = 53/60
4/5 + 1/2 + 1/8 = 57/40
1/9 + 1/10 + 3/9 = 49/90
3/10 + 2/4 + 5/7 = 53/35
1/8 + 7/9 + 5/8 = 55/36
4/5 + 2/3 + 1/6 = 49/30
1/7 + 2/10 + 1/3 = 71/105
1/2 + 9/11 + 5/7 = 313/154
4/5 + 4/8 + 4/5 = 21/10
3/5 + 7/9 + 1/12 = 263/180
1/12 + 1/6 + 5/12 = 2/3
9/11 + 2/6 + 2/7 = 332/231
1/2 + 1/2 + 7/12 = 19/12
5/12 + 3/4 + 7/10 = 28/15
1/2 + 5/11 + 1/11 = 23/22
9/12 + 3/8 + 1/2 = 13/8
1/7 + 8/10 + 2/5 = 47/35
1/11 + 4/10 + 7/8 = 601/440

Questions

What grade is denominators 2–12 (3 fractions) for?

It is usually taught in grade 5, but the right level is the one a child can finish with few mistakes. Move on when a sheet feels easy.

Can I print a different worksheet?

Yes. Press “New worksheet” for a fresh set of numbers at the same level; each set has its own answer key, so you can print as many as you need.

Are the answers checked?

The answers are worked out by the same program that makes the problems, so the key always matches the sheet. The worked example above shows the method.

How long should a worksheet take?

Most children finish 20 problems at a comfortable level in ten to fifteen minutes. If it takes much longer, try an easier level first.