Part 2: Addition and Subtraction

# 2.6: Word problems for adding and subtracting fractions

Notes

In the following, “A/B” represents the fraction “A over B.” For example, “2/3” refers to the fraction “2 over 3” or “two-thirds.”

##### Word problems for adding fractions

**Add To Problem**: The most straightforward type of word problem for adding fractions is to simply add a fraction A/B of an object to a fraction C/D of the same object. For example,

- Arithmetic problem: Solve 3/5 + 1/3.
- Word problem: Desi ate 3/5 of a pie and Kassidy ate 1/3 of a pie. How much pie did Desi and Kassidy eat altogether?
- 3/5 + 1/3 = 14/15, so Desi and Kassidy ate 14/15 of a pie altogether.

##### Word problems for subtracting fractions

**Take From Problem**: One type of word problem for subtracting fractions is to take a fraction C/D of an object from a fraction A/B of the object. For example,

- Arithmetic problem: Solve 3/5 – 1/3.
- Word problem: Desi ate 1/3 of a whole pie from 3/5 of a pie he found in the fridge. How much pie is left?
- 3/5 – 1/3 = 4/15, so there is 4/15 of a pie left.
**Beware:**It would*not*be correct to say “Desi found 3/5 of a pie in the fridge and ate 1/3 of it.” The “it” in this sentence refers to “3/5 of a pie in the fridge,” not to the whole pie. So, in this sentence, Desi eats 1/3 of 3/5 of a pie, which is 1/3 x 3/5 = 1/5 of a whole pie, and there would be 3/5 – 1/5 = 2/5 of a whole pie left.

**Compare Problem**: Another type of word problem for subtracting fractions is to consider the difference between a fraction C/D of an object and a fraction A/B of the object. For example,

- Arithmetic problem: Solve 3/5 – 1/3.
- Word problem: Desi has eaten 3/5 of a pie, while Kassidy has eaten 1/3 of a pie. How much more of a pie has Desi eaten than Kassidy?
- 3/5 – 1/3 = 4/15, so Desi has eaten 4/15 more of a pie than Kassidy.

The video below works through some examples of word problems for adding and subtracting fractions.

Video Tips

Practice Exercises

Do the following exercises to practice matching fraction addition/subtraction problems and word problems.