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EE.1 Word problems with unit fractions

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What are unit fractions?

Unit fractions are fractions with the number 1 as the numerator (top number) and a whole number as the denominator (bottom number). They show one equal part of a whole.

Examples:
  • 1/2 means one out of two equal parts
  • 1/3 means one out of three equal parts
  • 1/4 means one out of four equal parts
Note

Every unit fraction represents one piece of something divided into equal parts.

How to identify unit fractions in a problem

Look for fractions that have the number 1 on top. They often appear in word problems that talk about “one part” of something shared or divided equally.

Examples:
  • “One slice of pizza when a pizza is cut into 8 equal pieces” → 1/8
  • “One student gets one share when a candy bar is split into 4 equal shares” → 1/4
Note

If the numerator is 1, you are working with a unit fraction. The denominator tells how many equal parts the whole is divided into.

Solving word problems with unit fractions

To solve word problems with unit fractions, read carefully to find what the “whole” is, how many equal parts it is divided into, and how many unit fractions are needed to answer the question.

Example Problem:
  • A chocolate bar is cut into 6 equal pieces. Maria eats 1 piece. What fraction of the chocolate bar did she eat? → She ate 1/6.
  • A rope is divided into 4 equal parts. One part is used. What fraction of the rope was used? → 1/4.
Note

Always connect the problem back to the whole: the denominator shows the total parts, and the numerator 1 shows just one of those parts.

Adding and comparing unit fractions in problems

Sometimes word problems ask you to add unit fractions or compare them. To add, count how many equal unit parts are taken. To compare, remember that the larger the denominator, the smaller each part is.

Examples:
  • “Two friends each eat 1/6 of a pizza.” Together, they ate 2/6 of the pizza.
  • 1/4 is larger than 1/8 because one-fourth is a bigger part than one-eighth of the same whole.
Note

Think: more equal parts means each part is smaller. Fewer equal parts means each part is larger.

Using unit fractions in sentences

Practice using fractions in full sentences to understand them better. This helps explain your thinking clearly in math problems.

Examples:
  • “I ate one out of four equal slices of cake. I ate 1/4 of the cake.”
  • “One out of eight parts of the ribbon was used. That is 1/8 of the ribbon.”
Note

Explaining your answer in words shows you understand the meaning of the unit fraction, not just the numbers.