2.6: Word problems for adding and subtracting fractions

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.