Opposites and Zero Pairs

Mastering Integers

Learn how to work with positive and negative integers to solve mathematical problems.

Standard: 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram​.

​EQ: What ​are the steps to adding integers?

Adding Integers

Zero Pair

A positve number paired with a negative number results in zero when added together.

​Example: -45 + 45 = 0

​

​ What is another name for zero pairs?

​

Opposites

• What are opposites?

  • Two integers that are the same distance from zero on the number line but are on opposite sides of zero.

  ​

• Two integers that are opposites are also called additive inverses.The sum of any number and its additive inverse or opposite is zero.

• What are some situations that would be considered additive inverses?

Adding integers with same sign

The sum of two negative integers is always negative.

​

Ex. -5 + -10 = -15​

Two negative integers

The sum of two positive integers is always positive.​

​

Ex. 4 + 15 = 19​

Two positive integers

​Adding Integers with different signs

​To add integers with different signs, subtract their absolute values and take the sign of the larger number.

​

Example: -65 + 25 = -40

​

Solve: -3 + 4 14 + -25 -94 + 36 18 + -75 -13 + 91​

​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

When adding a positive and a negative integer, it will result in a ...

• positive number.

• negative number.

• zero.

• it depends on the value of the integers.

Multiple Choice

Simplify the expression

-3 + ( -2)

• 5

• 6

• -6

• -5

Song to remember adding integers:

(Sung to the tune of row row row your boat)​

​“Same sign, add and keep,

Different sign subtract.

Take the sign of the higher number,

Then you’ll be exact.”

Some text here about the topic of discussion

Multiple Choice

Solve:

25 + -63

• 88

• -88

• 38

• -38

Multiple Choice

positive x positive = ?

• positive

• negative

Multiple Choice

positive x negative = ?

• positive

• negative

Multiple Choice

negative x positive = ?

• positive

• negative

MULTIPLYING & DIVIDING INTEGERS

Multiplying or dividing numbers with the same sign will give you a positive answer.

Multiplying or dividing numbers with different signs will give you a negative answer.

Multiple Select

Which expression(s) results in a negative calculation?

• -12 ÷ -3

• -12(-3)

• -12 + (-3)

• -12 - (-3)

Mastering Integers

Understanding positive and negative integers is crucial in real-life applications. They represent opposite directions, temperatures, and financial gains/losses. Use positive integers for gains and negative integers for losses. Add and subtract integers by considering their signs. Multiply and divide integers by following specific rules. Practice and master these concepts to excel in real-life scenarios.

Multiple Choice

A submarine at -32 feet dives down 18 feet. After the dive, what will be the submarines elevation?

• 14

• -14

• 50

• -50

Multiple Choice

John had a balance of $22 in his bank account.  He wrote a check for $38.  What is his new balance?

• $16
• -$16
• $60
• -$60

Multiple Choice

The football team gained 9 yards on their first play.  On the next play they lost 17 yards.  By how many yards did their position change? 

• -8
• 8
• 26
• -26

Multiple Choice

Which addition expression is equivalent to 7 - (-3)?

• -3 + 7
• -7 + 3
• 7 + 3
• 3 + (-7)

Multiple Choice

Reduce 18/32 to lowest terms

• 1/2
• 2/15
• 9/16
• 1/3

Multiple Choice

Simplify  4/16  to lowest terms.

• 4/16
• 2/8
• 1/4
• 4

Multiple Choice

Which expression matches $$\frac{3}{5}$$ ? 

• $$5\div3$$  

• $$3\div3$$  

• $$5\div5$$  

• $$3\div5$$  

Multiple Choice

Simplify the following:  
-8 + (15 - 3) ÷ 4

• -5
• 1
• -11
• 11