Fraction Examples: 10 Worked Problems With Answers

Adding and subtracting

The first three fraction examples build up the one difficulty that matters here: denominators that do not match.

1. Same denominatorworked example

3⁄8 + 2⁄8the parts are already the same size
5⁄8add the numerators, keep the denominator

2. One denominator divides the otherworked example

7⁄8 − 1⁄4quarters and eighths
7⁄8 − 2⁄84 divides 8, so only the second needs rewriting
5⁄8subtract the numerators

3. Neither divides the otherworked example

2⁄3 + 1⁄4thirds and quarters
8⁄12 + 3⁄1212 is the least common denominator
11⁄12add, and it is already in lowest terms

Multiplying and dividing

No common denominator is needed here, but cancelling early saves work.

4. Straight multiplicationworked example

3⁄4 × 2⁄5multiply across
6⁄20numerators together, denominators together
3⁄10divide top and bottom by 2

5. Cancelling firstworked example

3⁄4 × 8⁄93 and 9 share 3; 4 and 8 share 4
1⁄1 × 2⁄3cancel before multiplying
2⁄3no simplification left to do

6. Divisionworked example

5⁄6 ÷ 10⁄3how many tenths-of-three fit into five sixths?
5⁄6 × 3⁄10multiply by the reciprocal
15⁄60 = 1⁄4multiply across, then simplify

Mixed numbers

Convert to improper fractions first. It is more writing, but there is no carrying step to forget.

7. Adding mixed numbersworked example

1 ½ + 2 ⅓the sum
3⁄2 + 7⁄3convert both to improper fractions
9⁄6 + 14⁄6common denominator 6
23⁄6 = 3 ⅚add, then convert back

8. Subtracting with a borrowworked example

3 ¼ − 1 ½the quarter is smaller than the half
13⁄4 − 3⁄2improper form avoids borrowing entirely
13⁄4 − 6⁄4common denominator 4
7⁄4 = 1 ¾subtract, then convert back

Simplifying and comparing

Two more worked examples, covering the operations that are not addition, subtraction, multiplying fractions or dividing fractions but turn up in almost every question anyway.

A. Simplifying to lowest termsworked example

36⁄48both are divisible by 12
(36 ÷ 12)⁄(48 ÷ 12)divide top and bottom by the greatest common factor
3⁄4no shared factor remains

B. Comparing two fractionsworked example

3⁄5 or 5⁄8 — which is larger?the question
24⁄40 and 25⁄40rewrite both over 40
5⁄8 is larger25 fortieths beats 24 fortieths

If you only need to know which is bigger and not by how much, cross-multiply instead: 3 × 8 = 24 against 5 × 5 = 25. The larger product sits above the larger fraction.

Word problems

The arithmetic here is easy. Deciding which operation the words describe is the actual task, and 'of' almost always signals multiplication.

9. A fraction of a fractionworked example

⅔ of 3⁄4 of a tank'of' means multiply
2⁄3 × 3⁄4set it up
6⁄12 = 1⁄2half a tank

10. Sharing a quantityworked example

3⁄4 kg shared into portions of 1⁄8 kghow many portions fit?
3⁄4 ÷ 1⁄8'how many fit into' means divide
3⁄4 × 8⁄1 = 6six portions

Questions about fraction examples

What is the hardest part of fraction problems?

For arithmetic, finding the common denominator. For word problems, deciding which operation is being described — most lost marks come from the setup, not the sums.

Should I always convert mixed numbers to improper fractions?

For adding and subtracting, yes — it removes the borrowing step. For multiplying and dividing it is not optional, because the methods only work on improper form.

How do I check a fraction answer?

Estimate first. 2/3 + 1/4 must be a little under 1, so an answer of 11/12 is plausible and an answer of 3/7 is not. This catches wrong methods, not just wrong arithmetic.

Does 'of' always mean multiply?

In fraction problems, almost always. Two thirds of three quarters is 2/3 × 3/4.