Lesson 12Solving Problems Involving Fractions

Learning Goal

Let’s add, subtract, multiply, and divide fractions.

Learning Targets

  • I can use mathematical expressions to represent and solve word problems that involve fractions.

Warm Up: Operations with Fractions

Problem 1

Without calculating, order the expressions according to their values from least to greatest. Be prepared to explain or show your reasoning.

Activity 1: Situations with and

Problem 1

Here are four situations that involve and .

  • Before calculating, decide if each answer is greater than 1 or less than 1.

  • Write a multiplication equation or division equation for the situation.

  • Answer the question. Show your reasoning. Draw a tape diagram, if needed.

  1. There was liter of water in Andre’s water bottle. Andre drank of the water. How many liters of water did he drink?

  2. The distance from Han’s house to his school is kilometer. Han walked kilometer. What fraction of the distance from his house to the school did Han walk?

  3. Priya’s goal was to collect kilogram of trash. She collected kilogram of trash. How many times her goal was the amount of trash she collected?

  4. Mai’s class volunteered to clean a park with an area of square mile. Before they took a lunch break, the class had cleaned of the park. How many square miles had they cleaned before lunch?

Activity 2: Pairs of Problems

Problem 1

  1. Work with a partner to write equations for the following questions. One person works on the questions labeled A1, B1, …, E1 and the other person works on those labeled A2, B2, …, E2.

    A1. Lin’s bottle holds cups of water. She drank 1 cup of water. What fraction of the water in the bottle did she drink?

    A2. Lin’s bottle holds cups of water. After she drank some, there were cups of water in the bottle. How many cups did she drink?

    B1. Plant A is feet tall. This is as tall as Plant B. How tall is Plant B?

    B2. Plant A is feet tall. Plant C is as tall as Plant A. How tall is Plant C?

    C1. kilogram of berries is put into a container that already has kilogram of berries. How many kilograms are in the container?

    C2. A container with kilogram of berries is full. How many kilograms can the container hold?

    D1. The area of a rectangle is sq cm and one side is cm. How long is the other side?

    D2. The side lengths of a rectangle are cm and cm. What is the area of the rectangle?

    E1. A stack of magazines is inches high. The stack needs to fit into a box that is inches high. How many inches too high is the stack?

    E2. A stack of magazines is inches high. Each magazine is -inch thick. How many magazines are in the stack?

  2. Trade papers with your partner, and check your partner’s equations. If you disagree, work to reach an agreement.

  3. Your teacher will assign 2 or 3 questions for you to answer. For each question:

    • Estimate the answer before calculating it.

    • Find the answer, and show your reasoning.

Activity 3: Baking Cookies

Problem 1

Mai, Kiran, and Clare are baking cookies together. They need cup of flour and cup of butter to make a batch of cookies. They each brought the ingredients they had at home.

  • Mai brought 2 cups of flour and cup of butter.

  • Kiran brought 1 cup of flour and cup of butter.

  • Clare brought cups of flour and cup of butter.

If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of cookies can they make? Explain your reasoning.

Lesson Summary

We can add, subtract, multiply, and divide both whole numbers and fractions. Here is a summary of how we add, subtract, multiply, and divide fractions.

  • To add or subtract fractions, we often look for a common denominator so the pieces involved are the same size. This makes it easy to add or subtract the pieces.

  • To multiply fractions, we often multiply the numerators and the denominators.

  • To divide a number by a fraction , we can simply multiply the number by , which is the reciprocal of .