Fractions and Division in Word Problems

Fractions and Division in Word Problems

Math Mission

Opening

Solve word problems involving fractions.

Dog Play Area

Work Time

Dog Play Area

Denzel wants to fence in a rectangular play area for his dog. The play area will extend the entire length of his backyard, which is 813 yards.

  • If he wants his dog to have 50 square yards to play in, how wide does he need to make the play area?

Ask yourself:

  • What is the formula for the area of a rectangle?
  • What measurements does the problem provide?
  • What is the unknown measurement?

Walking to School

Work Time

Walking to School

Martin walks 45 of a mile to school each day. The distance Emma walks to school is 56 of the distance Martin walks.

  • How far does Emma walk?

Ask yourself:

Can you use a number line to model the situation?

Hippopotamus

Work Time

Hippopotamus

The male hippopotamus at the zoo weighs 2 tons. He weighs 112×f=2 times as much as the female hippopotamus weighs.

  • How much does the female hippopotamus weigh?

Does the female hippopotamus weigh more or less than the male?

Prepare a Presentation

Work Time

Prepare a Presentation

Choose one of the problems you solved. Prepare a solution that you can share with your classmates. Include a drawing and an explanation of what you did to solve the problem.

Challenge Problem

Write two word problems.

  • Write one word problem that uses multiplication and the numbers 423 and 13.
  • Write a second word problem that uses division and the numbers 423 and 13.
  • Solve both problems.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes on your classmates’ approaches to solving and writing fraction word problems.

As your classmates present, ask questions such as:

  • How are the quantities in the problem related?
  • What is the unknown quantity in the problem?
  • How does your equation represent the problem situation?
  • Is your answer reasonable? How do you know?
  • Where are the known and unknown quantities in the problem you wrote?
  • How do you know that your problem is a multiplication or a division situation?

Reciprocals and Dividing by Fractions

Formative Assessment

Summary of the Math: Reciprocals and Dividing by Fractions

Read and Discuss

  • The fractions ab and ba, with numerators and denominators inverted, are called reciprocals of each other.
  • The key property of reciprocals is that their product is always 1.

    ab×ba=a×bb×a=1
  • Reciprocals are also called multiplicative inverses. This name refers to the fact that if you multiply a fraction by a number, and then multiply the result by the reciprocal of the fraction, the result is “undone.” For example:

    34×5=154
    154×43=153=5
  • You can use the properties of reciprocals to help you divide by fractions. The general rule is: To divide by a fraction, multiply by the reciprocal of the fraction. Algebraically, the rule looks like this: ab÷cd=ab×dc=adbc

Can you:

  • Solve a problem that involves dividing a fraction by a fraction?
  • Determine which operation is needed to solve a word problem?
  • Explain what reciprocals are and how to use them to help you solve division problems involving fractions?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

An example of an everyday situation that involves fraction division is …