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© Teacher Created Materials Today’s Lesson Adding and Subtracting Rational Numbers

© Teacher Created Materials Today’s Lesson Adding and Subtracting Rational Numbers

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© Teacher Created Materials

Today’s Lesson

Adding and Subtracting

Rational Numbers

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Let’s warm up today by practicing adding and subtracting money.

Warm-up Activity

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Look at the following dollar amounts:

$2.45

$5.82

$4.24

$3.00

$0.50

$6.89

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If we add them together, what do we get?$2.45

$5.82

$4.24

$3.00

$0.50

$6.89+$22.90

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If we switch the order of the numbers and then add them, do we still get the same answer?

$5.82

$0.50

$3.00

$6.89

$4.24

$2.45+$22.90 YES!

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The fact that you can arrive at the same answer, even after switching around the numbers, is called the commutative property of addition.

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Write subtraction problems using the dollar amounts from the previous activity. Does the commutative property rule still apply?

NO!

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Today, you will be adding and subtracting decimals, fractions, and negative numbers.

Whole-Class Skills Lesson

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We can represent one-half by using the counters below.

One-half of the counters is white.

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We know this because there are two counters in the set

(denominator).

One of the counters is white (numerator).

12

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How could we represent four-fifths with the counters?

Four-fifths of the counters are red.

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Like with one-half, there are five counters in the set (denominator).

Four of the counters in the set are red (numerator).

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Look at the counters below, what fraction of them are white?

Two-fourths are white.

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Look at the counters below, what fraction of them are white?

Three-sixths are white.

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Look at the counters below, what fraction of them are white?

Four-eighths are white.

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Notice, even though we added counters each time, each of these sets shows

one-half of the counters white.

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So,

= = =

1

2

2

4

3

6

4

8

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Let’s add fractions now. Look at the counters below.

+

First, let’s convert these to fractions.

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+

are white

We have the same denominator, so we can add.

6

8

5

8are white

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6

8

5

8

11

8+ =

Notice, the denominator stayed the same.

We add the numerators.

Same denominator, so we’re ready to add.

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Another example …

this can also be written as …

0.6 + 0.5 = 1.1 (one and one-tenth)

+ =

6

10

5

10

11

10= 1

1

10

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Try these problems.

0.9 + 0.1 =

1.6 + 0.8 =

6.2 + 5.2 =

7.9 – 4.6 =

3.5 – 2.5 =

1.0

2.4

11.4

5.3

1.0

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To subtract from a negative, move further down the negative number line.

– 9 – 5 =

–9–10–11–12–13–14–15

Start at –9.Move five units in the

negative direction (left).

Your answer is –14.

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Try these examples.

3.6 + 6.7 =

9.2 – 4.9 =

–5.1 + 3.2 =

0.5 – 1.6 =

–4.7 – 2.1 =

10.3

4.3

–1.9

–1.1

–6.8

=

=

+ =

6

8

7

8 813

185

+– =

3

9

7

9 9

4

+ =

2

6

1

3 6

4

3

2

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Complete these rule statements:

• To add two positive numbers, _____________.

• To add two negative numbers, ____________.

• To add two numbers of different signs, _____.

• To subtract two numbers, ________________.