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# Multiplying - Rational Numbers Class 8 Notes | EduRev

## Class 8 : Multiplying - Rational Numbers Class 8 Notes | EduRev

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Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Seventh Grade Mathematics  Unit 1

MATHEMATICS ? GRADE 7 ? UNIT 1: Operations with Rational Numbers
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012 ? Page 70 of 105
All Rights Reserved

Learning Task: Multiplying Rational Numbers

You have recently practiced multiplying positive and negative integers on a number line. It is
now your turn to model how to multiply. Below are “hints” to help you get started.

The rules for moving along the number line are as follows:
Moving to the left or west means moving in a negative direction.
Moving to the right or east means moving in positive direction.
Time in the future is represented by a positive value.
Time in the past is represented by a negative value.

Multiplying Using the Number Line Model

Try these problems on your own.

In the city of Mathematica, there is a town center which attracts many visitors to the city. From
the town center, a train takes visitors to different popular locations. The map shows a few
favorite destinations that people like to visit. Answer the following problems about traveling
around the city.

1. The train leaves Town Center traveling east at the speed of 2 blocks per minute. How
many blocks will you be in 4 minutes? Where will you be in 4 minutes?

2. The train leaves the Town Center going west at 2 blocks per minute.  What popular
location will you arrive at in 6 minutes?  How many blocks away from the Town Center
will you be?

3. The train passes through the Town Center going east at 2 blocks per minute.  Where was
that train 3 minutes ago?

Page 2

Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Seventh Grade Mathematics  Unit 1

MATHEMATICS ? GRADE 7 ? UNIT 1: Operations with Rational Numbers
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012 ? Page 70 of 105
All Rights Reserved

Learning Task: Multiplying Rational Numbers

You have recently practiced multiplying positive and negative integers on a number line. It is
now your turn to model how to multiply. Below are “hints” to help you get started.

The rules for moving along the number line are as follows:
Moving to the left or west means moving in a negative direction.
Moving to the right or east means moving in positive direction.
Time in the future is represented by a positive value.
Time in the past is represented by a negative value.

Multiplying Using the Number Line Model

Try these problems on your own.

In the city of Mathematica, there is a town center which attracts many visitors to the city. From
the town center, a train takes visitors to different popular locations. The map shows a few
favorite destinations that people like to visit. Answer the following problems about traveling
around the city.

1. The train leaves Town Center traveling east at the speed of 2 blocks per minute. How
many blocks will you be in 4 minutes? Where will you be in 4 minutes?

2. The train leaves the Town Center going west at 2 blocks per minute.  What popular
location will you arrive at in 6 minutes?  How many blocks away from the Town Center
will you be?

3. The train passes through the Town Center going east at 2 blocks per minute.  Where was
that train 3 minutes ago?

Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Seventh Grade Mathematics  Unit 1

MATHEMATICS ? GRADE 7 ? UNIT 1: Operations with Rational Numbers
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012 ? Page 71 of 105
All Rights Reserved
4. You would like to take the train to the Zoo from the Town Center. How many minutes
will this take if the train travels 2 blocks per minute? Write a math sentence to represent
this scenario.

5. You waited 4 minutes for the train to arrive. The train was traveling west at 2 blocks per
minute. Where was the train?

Let’s look to see if there are any patterns.

1. When you moved east (right) and it was time in the future, two positive numbers
represented the situation.  What was the result on the number line when moving east and
moving in the future occurred? Was the result of multiplying positive or negative? Is this
always true?

2. When you moved east (right) and it was time in the past, a positive number and a
negative number represented the situation.  What was the result on the number line when
moving east and moving in the past occurred? Was the result of multiplying positive or
negative? Is this always true?

3. When you moved west (left) and it was time in the future, a negative number and a
positive numbers represented the situation.  What was the result on the number line when
moving west and moving in the future occurred? Was the result of multiplying positive or
negative? Is this always true?

4. When you moved west (left) and it was time in the past, two negative numbers
represented the situation.  What was the result on the number line when moving west and
moving in the past occurred? Was the result of multiplying positive or negative? Is this
always true?

5. What multiplication patterns can you see from each situation? Fill in the chart below
according to the signs of the factors and products.

Factor Factor Product
+ number     + number
(-) number (-) number
+ number  (-) number
(-) number + number

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