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Subtracting Positive and Negative Integers

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WARM-UP:

1.) (-5) + (-26) =

2.) (-18) + 7 =

3.) Write a variable expression for: r less than 12

4.) -40 + 9 =

5.) 4 + (-36) =

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Let's review what we learned in the last lesson.

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TODAY we will be studying 2 methods to learn how to subtract integers.

METHOD 1 - Zero Pairs

Remember that the red chips are NEGATIVE.

The grey chips are POSITIVE.

+

+

+-

--

--

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Let's subtract 6 - 2 =

We begin with 6 POSITIVE (grey) chips.

+

+

++

+ +

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Let's subtract 6 - 2 =

+

+

++

+ +

Then we take away (or Subtract) 2 POSITIVE chips.

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++

+ +

We are left with 4 POSITIVE (Grey) chips.

So..... 6 - 2 = 4

Let's subtract 6 - 2 =

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Now, let's subtract (-5) - (-4) =

We begin with 5 NEGATIVE (or red) chips.

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- -

-

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Now, let's subtract (-5) - (-4) =

- -

-

--

Then, we take away (or Subtract) 4 NEGATIVE chips.

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Now, let's subtract (-5) - (-4) =

-

And we are left with 1 NEGATIVE (red) chip.

Therefore, (-5) - (-4) = -1

Do you have any questions so far?

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SOMETIMES we need to add Zero Pairs in order to subtract or take away chips.

For example, let's subtract 5 - (-3) =

We begin with 5 POSITIVE (grey) chips.

+ + + + +

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5 - (-3) =

We begin with 5 POSITIVE (grey) chips.++

+ +

Now, we need to take away (or Subtract) 3 NEGATIVE (red) chips but we don't have any!!

So we must ADD 3 Zero Pairs...............

- - -

+++

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+

+

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++++ +

- - -

+++Now, we can take away (or Subtract) the 3 NEGATIVE (red) chips.

And we are left with 8 POSITIVE (grey) chips.

Therefore, 5 - (-3) = 8

5 - (-3) =

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You try this one…

(-4) - 1 =

Use your pen to draw the red and grey circles.

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Try 4 - (-2) =

Use your pen to draw the red and grey circles.

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METHOD 2 - Rule for Subtracting Integers

When we subtract an integer, we add its opposite.

For example, (-10) - 7 =

(-10) + (-7) = (-17)

we add its opposite

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Of course, if we are going to ADD its opposite, we must remember the rules for ADDING INTEGERS.

Adding Different Signs -

1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.

Adding the Same Sign -

The sum of 2 positive numbers is POSITIVE.The sum of 2 negative numbers is NEGATIVE.

LET'S REVIEW

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Let's try a few more subtraction problems. Remember the RULE -

When we subtract an integer, we add its opposite.

9 - (-6) =

9 + 6 = 15

we add its opposite

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You try a few.

(-4) - (-4) = (-2) - 8 = 12 - (-3) =

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1.) Can you find the missing numbers?

-32 + = 65

47 - = 80

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2.)Anne is 8 years older than Jane and 3 yearsolder than Mary. The sum of their ages is 67.How old is each person?

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3.) Use these digits (4, 7, 9) to make as many 3 digit numbers as possible. You may only use each digit only one time in each number.

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Let's see how well you understood the lesson today.

Find each difference.

1.) -13 - 13 =

2.) 9 - (-8) =

3.) 28 - 16 =

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4.) 12 - 15 =

5.) 0 - (-47) =

6.) -190 - 82 =

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7.) (-12) - (-26) =

8.) 4 - (-60) =

9.) 22 - 38 =

10.) (-109) - 10 =

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Let's review what we learned today.

We looked at 2 different methods for SUBTRACTING integers.

METHOD 1 - Using Zero Pairs

+

-

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SOMETIMES we need to add Zero Pairs in order to subtract or take away chips.

3 - (-1) =

Begin with 3 POSITIVE chips

Add 1 ZERO PAIR

Now we can take away 1 NEGATIVE chip

And you're left with 4 POSITIVE chips

3 - (-1) = 4

+

+

++

-

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Great job today!

Remember to practice what you learned!