Multiplication & Division To Solve Problems

Multiplication & Division To Solve Problems

Division Is Multiplying by the Inverse

Opening

Division Is Multiplying by the Inverse

You can use what you know about multiplication to find the answer to a division problem.

Consider this division problem: 12 ÷ (−3).

You know that dividing is the same as multiplying by the inverse (4 ÷ 2 is the same as 4⋅12).

  • How could you rewrite 12 ÷ (−3) as a multiplication problem using the inverse of −3?
  • What is the answer?
  • What is the answer to the original division problem?

Math Mission

Opening

Create rules for determining the sign of the answer to a division problem.

Divide Positive and Negative Numbers

Work Time

Divide Positive and Negative Numbers

Use the fact that dividing is the same as multiplying by the inverse to rewrite these problems as multiplication problems.

Then solve the multiplication problems in order to find the answer to the original division problems.

  • −10 ÷ 2
  • −8 ÷ −14

Hint:

You need to find the inverse of 2 to rewrite the first division problem as a multiplication problem. What is the inverse of 2?

Create Problems

Work Time

Create Problems

  • Use a variety of numbers, including integers, fractions, and decimals, to write three division problems. Use both positive and negative numbers.
  • Use the fact that dividing is the same as multiplying by the inverse to rewrite the problems as multiplication problems. Then solve the multiplication problems in order to find the answers to your original division problem.

Hint:

Make sure to:

  • Put positive and negative numbers in different positions in the problems.

Complete the Table

Work Time

Complete the Table

Complete this table to show what you think the rules are for dividing positive and negative numbers.

HANDOUT: Creating a Table for Rules of Operations with Integers

Hint:

Look at the division problems you worked on today. What patterns do you see in your answers that can help you determine the rules?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain your rules for dividing positive and negative numbers. Support your explanation with your table and your work.

Challenge Problem

Insert one symbol and one ÷ symbol in each to make the resulting inequality true. Try not to perform any calculations.

  1. 15[ ]3>15[ ]3
  2. 45[ ]12>45[ ]12
  3. 1.8[ ]0.3>1.8[ ]0.3
  4. 78[ ]0.12>78[ ]0.12

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ explanations and rules for dividing positive and negative numbers.

Hint:

As your classmates present, ask questions such as:

  • How did you determine the sign of the answer for problems that involve dividing a positive number by a negative number?
  • How did you determine the sign of the answer for problems that involve dividing a negative number by a positive number?
  • How did you determine the sign of the answer for problems that involve dividing a negative number by a negative number?

Positive and Negative Numbers

Work Time

Positive and Negative Numbers

Calculate:

  1. 48
  2. 0.1(0.1)
  3. (10)0.1
  4. (4)÷(8)
  5. (0.1)÷(0.1)
  6. 40÷(8)
  7. (34)÷(38)

Multiplying and Dividing

Formative Assessment

Summary of the Math: Multiplying and Dividing

Read and Discuss

  • A positive number multiplied or divided by a positive number equals a positive number.
  • A positive number multiplied or divided by a negative number equals a negative number.
  • A negative number multiplied or divided by a positive number equals a negative number.
  • A negative number multiplied or divided by a negative number equals a positive number.

Hint:

Can you:

  • Explain how to determine whether a quotient is positive or negative?

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.

Something that surprised me about multiplying and/or dividing with positive and negative numbers is …