Lesson 16Solving 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
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.
There was
liter of water in Andre’s water bottle. Andre drank of the water. How many liters of water did he drink? 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? 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? 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
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? Trade papers with your partner, and check your partner’s equations. If you disagree, work to reach an agreement.
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
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 .