adding integers 10.2

Adding Integers

10.2

CCS: 6.NS.3. Fluently add, subtract, multiply, and divide integers using the standard algorithm for each operation.

Objectives:Students will be able to:• Use integer chips to add integers• Add integers with the same sign• Add integers with different signs

ADDING INTEGERS

We can model integer addition with tiles.

Represent -2 with the fewest number of tiles

Represent +5 with the fewest number of tiles.

ADDING INTEGERS What number is represented by combining the 2 groups of

tiles?

Write the number sentence that is illustrated. -2 + +5 = +3

+3Notice the 2 red and 2 yellow tiles will cancel out leaving 3 yellow tiles.

ADDING INTEGERS

Use your red and yellow tiles to find each sum.

-2 + -3 = ?

+ = -5 -2 + -3 = -5

ADDING INTEGERS -6 + +2 = ?

+ = - 4

+ = +1 -3 + +4 = ?

ANSWER

ANSWER

-6 + +2 = -4

-3 + +4 = +1

We can show this same idea using a number line.

-5 50 10-10

What is 5 + 4?

Move five (5) units to the right from zero.Now move four more units to the right.

The final point is at 9 on the number line.Therefore, 5 + 4 = 9.

9

-5 50 10-10

What is -5 + (-4)?

Move five (5) units to the left from zero.Now move four more units to the left.

The final point is at -9 on the number line.Therefore, -5 + (-4) = -9.

-9

To add integers with the same sign, add the absolute values of the integers. Give the answer the same sign as the integers.

Examples

1 . 15 12

Solution

27

2 . 14 33( ) 47

3 . 4 12x x( ) 16 x

What is (-7) + 7?

-5 50 10-10To show this, we can begin at zero and move seven units to the left.

Now, move seven units to the right.

Notice, we are back at zero (0).

For every positive integer on the number line, there is a corresponding negative integer. These integer pairs are opposites or additive inverses.

Additive Inverse Property – For every number a, a + (-a) = 0

When using integer tiles, the additive inverses make what is called a zero pair.For example, the following is a zero pair.

1 -1

This also represents a zero pair.

x -x

1 + (-1) = 0.

x + (-x) = 0

Add the following integers: (-4) + 7.

-5 50 10-10

Start at zero and move four units to the left.

Now move seven units to the right.

The final position is at 3.Therefore, (-4) + 7 = 3.

Add the following integers: (-4) + 7.

-5 50 10-10

Notice that seven minus four also equals three.In our example, the number with the larger absolute value was positive and our solution was positive.

Let’s try another one.

-5 50 10-10

Add (-9) + 3

Start at zero and move nine places to the left.

Now move three places to the right.

The final position is at negative six, (-6).Therefore, (-9) + 3 = -6.

-5 50 10-10

Add (-9) + 3

In this example, the number with the larger absolute value is negative. The number with the smaller absolute value is positive.We know that 9-3 = 6. However, (-9) + 3 = -6. 6 and –6 are opposites. Comparing these two examples shows us that the answer will have the same sign as the number with the larger absolute value.

To add integers with different signs determine the absolute value of the two numbers. Subtract the smaller absolute value from the larger absolute value. The solution will have the same sign as the number with the larger absolute value.

Example Subtract Solution

12 15 15 12 317 25 ( ) 25 17 8

The Rules for adding integers are as follows:

1. If the numbers have the same signs, add them and keep that sign.

2. If they have opposite signs, subtract and take the sign of the larger number.

WHAT DOES THIS MEAN???

Example 1

7 + (-6)= We have opposite signs, so we have to subtract and keep the sign of the higher number.

7 - 6 =1 Since 7 has an absolute value that is more than 6, we keep the sign of 7 (which is positive).

7 + (-6)= 1 Our answer is positive

Example 2

4 + (-9)= We have opposite signs, so we have to subtract and keep the sign of the higher number.

9 - 4 =5 Since 9 has an absolute value that is more than 4, we keep the sign of 9 (which is negative).

4 + (-9)= -5 Our answer is negative

Example 3

(-16) + (-6)= We have the same signs, so we simply add the numbers and keep the given sign

(-16)+ (-6) = -22

Our answer is negative

TRY THESE:

1.-8 + 72 =

2.16 + (-5)=

3.-51 + (-17) =

4.91 + 28 =

5.Challenge! (-2) + (-5) + 5 + (-4)=

64

11

-68

119

-6

VIDEO TIME!Watch this Video for Adding IntegersWatch this Video for Adding Integers

using a number line

ClassworkCheck out this interactive racing game for Adding Integers

Need More Practice? Try Orbit Integers to Add Integers

Homework: p. 500, 2-42 even