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 the multiplication problem, A/B x C/D, have the form “A/B of C/D of a unit is how much of a unit?” For example,

**Arithmetic problem:**Solve 3/5 x 1/3 (three-fifths times one-third).**Word problem:**If 1/3 of the students in a class have a pet and 3/5 of the students with a pet have a dog, then what fraction of the students in the class have a dog as a pet?- 3/5 x 1/3 = 1/5, so 1/5 of the students in the class have a dog as a pet.

Here’s a couple more examples:

**Arithmetic problem:**Solve 1/4 x 2/3 (one-quarter times two-thirds).**Word problem:**If a recipe calls for 2/3 of a cup of soy sauce, then how much soy sauce is needed for 1/4 of the recipe?- 1/4 x 2/3 = 1/6, so 1/6 of a cup of soy sauce is needed for 1/4 of the recipe.

**Arithmetic problem:**Solve 1/6 x 3/4 (one-sixth times three-quarters).**Word problem:**If Alastair used 3/4 of a cup of butter to make a cake and he ate 1/6 of the cake, then how much butter did he eat?- 1/6 x 3/4 = 1/8, so Alastair ate 1/8 of a cup of butter.

Pay close attention to the wording for this type of problem:

**Word problem:**If 1/5 of the students in a class have a dog and 1/6 of the students in the class have a cat, then what fraction of the students in the class have a cat and a dog?- Can we solve this by calculating 1/6 x 1/5?
- No, because this assumes that 1/6 of the students in the class that have a dog also have a cat (and we don’t know that). It could be that no students in the class have a cat and a dog!

**Word problem**: If Carina used 6/7 of a bag of chocolate chips to make a batch of brownies and then she ate 2/3 of the batch of brownies, then how many chocolate chips did she eat?- Can we solve this by calculating 2/3 x 6/7?
- No, because this calculates the
*fraction*of a bag of chocolate chips that Carina ate, not the*number*of chocolate chips she ate.

**Word problem**: If Sebastián ate 1/3 of a whole pizza from 3/4 of a pizza left over in the fridge, then how much of a whole pizza did he eat?- Can we solve this by calculating 1/3 x 3/4?
- No, because this would calculate the fraction of a whole pizza that Sebastián ate if he ate 1/3 of the
*leftover*pizza. But he ate 1/3 of a*whole*pizza, which gives us the answer to the question directly with no calculation needed.

The video below works through some examples of word problems for multiplying fractions.

Video Tips

Practice Exercises

Do the following exercises to practice matching fraction multiplication problems and word problems.