Addition, Subtraction, Multiplication, and 
Division of Integers

Important Vocabulary Integers: A number with no fractional part. A real number greater than zero. Positive number: Negative number: A real number that is less than zero. Sum: The result of adding two numbers.

Important Vocabulary Difference: The result of subtracting two numbers. Absolute Value: The distance of a number from zero; the positive value of a number. Product: The result of two numbers multiplied together. Quotient: The answer to a division problem.

-2 + 6 = 4 Adding to a Negative Integer Start here End here 1 2 3 4 5 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

6 + (-2) = 4 Adding a Negative Integer to a Positive Integer End here Start 
here 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

-4 - 3 = -7 Subtracting from Negative Integers End here Start here 1 2 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

4 - (-3) = 7 Subtracting from Negative Integers Start here End here 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Try some on your own. 6 + (-8) = 2 + (-7) = -4 + 6 = -9 + 3 = -5 + 2 = 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 6 + (-8) = 2 + (-7) = -4 + 6 = -9 + 3 = -5 + 2 =

- - + + + + Rules for Multiplying Integers: Use the eraser to reveal the results. Multiplying two integers with the same signs:  
  Positive x positive = positive + + + x = Negative x negative = positive - - + x =

- - + + - - Rules for Multiplying Integers: Use the eraser to reveal the results. Multiplying two integers with the different signs:  
  Positive x negative = negative + - - x = Negative x positive = negative - - + x =

Try some. - - 5 x (-4) = - 5 x 4 = 6 x (-7) = + Negative Positive Find the products - move the positive and negative to 
remind you of the rule. + - 5 x (-4) = Positive - Negative - 5 x 4 = 6 x (-7) =

- - - + + + ÷ ÷ ÷ ÷ Rules for Dividing Integers: Use the eraser to reveal the results. Dividing two integers with the same signs:  
  ÷ Positive positive = positive + + + ÷ = ÷ Negative negative = negative - - - ÷ =

- - - - + + ÷ ÷ ÷ ÷ Rules for Dividing Integers: Use the eraser to reveal the results. Dividing two integers with different signs:  
  ÷ Positive negative = negative - - + ÷ = ÷ Negative positive = negative - - + ÷ =

- Try some. + -48 ÷ 6= 24 ÷ -6= -63 ÷ -9= Negative Positive Find the quotients - move the positive and negative to 
remind you of the rule! -48 ÷ 6= 24 ÷ -6= -63 ÷ -9= + Positive - Negative

Practice with Word Problems Introduction: Practice with Word Problems Figuring an offensive team’s total yardage gained is not just a case of 
adding up the numbers. Players make positive plays, such as yards gained rushing and yards 
gained passing. They also make negative plays, such as yards lost rushing or yard lost 
on a quarterback sack. There are also penalties; they work both ways. Examine the following game situations and figure the total yards 
gained by the team.

The Washington Redskins gained 256 rushing yards in a game. They also lost 4 yards on one play. The quarterback threw for 154 
yards, but he was sacked seven times. He lost a total of 53 yards on 
the sacks. How many total yards did the Redskins gain?

In one game the San Diego Chargers gained 187 yards rushing 
and 458 passing. But they had 211 yards of penalties against the offense. How many total yards did they gain that night?

The New England Patriots are a passing team The New England Patriots are a passing team. They ran for only 47 
yards last night, but they passed for 398. They lost 38 yards on sacks, 
and they had three offensive penalties against them for a total of 25 yards. How many total yards did they gain last night?

The Oakland Raiders only gained 75 yards passing and 62 yards 
rushing, but their opponent had 165 yards in defensive penalties. When you count all of their yards and all of the penalty yards, how 
many yards did the Raiders gain?

The following page(s) contains the answers to the tasks in 
the lesson activity.

Try some. - - - - - - + + + - 5 x (-4) = 20 - 5 x 4 = -20

Try some. -48 ÷ 6= -8 - - + 24 ÷ -6= -4 - - + -63 ÷ -9= 7 - - +

Try some on your own. 6 + (-8) = -2 -5 + 2 = -3 -9 + 3 = -6 -4 + 6 = 2 -5 + 2 = -3 -4 + 6 = 2 2 + (-7) = -5

The Washington Redskins gained 256 rushing yards in a game. They also lost 4 yards on one play. The quarterback threw for 154 
yards, but he was sacked seven times. He lost a total of 53 yards on 
the sacks. How many total yards did the Redskins gain? 353 total yards

How many total yards did they gain that night? In one game the San Diego Chargers gained 187 yards rushing 
and 458 passing. But they had 211 yards of penalties against the offense. How many total yards did they gain that night? 434 total yards

The New England Patriots are a passing team The New England Patriots are a passing team. They ran for only 47 
yards last night, but they passed for 398. They lost 38 yards on sacks, 
and they had three offensive penalties against them for a total of 25 yards. How many total yards did they gain last night? 382 total yards

The Oakland Raiders only gained 75 yards passing and 62 yards 
rushing, but their opponent had 165 yards in defensive penalties. When you count all of their yards and all of the penalty yards, how 
many yards did the Raiders gain? 302 total yards