Warm Up Lesson 1-1 Word Problems

1-2 Adding and Subtracting Real Numbers

Warm Up

Lesson 1-1 Word Problems


Add real numbers; Subtract real numbers

Lesson ObjectivesLesson Objectives

2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.


real numbers The set of all numbers that can be represented on a number line are called. The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|.

Opposites numbers which are the same distance from zero on the number line, but on opposite sides

Additive inverse the opposite of a number, used when subtracting numbers.




Subtracting Real Numbers


Additional Example 1A: Adding and Subtracting Numbers on a Number Line

Add or subtract using a number line.

Start at 0. Move left to –4.

11 10 9 8 7 6 5 4 3 2 1 0

+ (–7)

–4 + (–7) = –11

To add –7, move left 7 units.

–4

–4 + (–7)


Additional Example 1B: Adding and Subtracting Numbers on a Number Line


Start at 0. Move right to 3.

To subtract –6, move right 6 units.

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

+ 3

3 – (–6) = 9

3 – (–6)

–(–6)



–3 + 7

Check It Out! Example 1a

Start at 0. Move left to –3.

To add 7, move right 7 units.

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

–3

+7

–3 + 7 = 4


Check It Out! Example 1b


–3 – 7 Start at 0. Move left to –3.

To subtract 7, move left 7 units.

–3–7

11 10 9 8 7 6 5 4 3 2 1 0

–3 – 7 = –10


Check It Out! Example 1c


–5 – (–6.5) Start at 0. Move left to –5.To subtract –6.5, move right 6.5 units.

8 7 6 5 4 3 2 1 0

–5

–5 – (–6.5) = 1.5

1 2

– (–6.5)


Additional Example 2: Adding Real NumbersAdd.

Use the sign of the number with the greater absolute value.

Different signs: subtract the absolute values.

A.

B. –6 + (–2)

(6 + 2 = 8)

–8 Both numbers are negative, so the sum is negative.

Same signs: add the absolute values.


Add.

–5 + (–7)

Check It Out! Example 2

–12 Both numbers are negative, so the sum is negative.


a.

(5 + 7 = 12)

–13.5 + (–22.3)b.

(13.5 + 22.3 = 35.8)

–35.8 Both numbers are negative, so the sum is negative.




c. 52 + (–68)

(68 – 52 = 16)

–16 Use the sign of the number with the greater absolute value.

Different signs: subtract the absolute values.

Add.


Subtract.

–6.7 – 4.1

–6.7 – 4.1 = –6.7 + (–4.1) To subtract 4.1, add –4.1.

Same signs: add absolute values.

–10.8 Both numbers are negative, so the sum is negative.

Additional Example 3A: Subtracting Real Numbers

(6.7 + 4.1 = 10.8)


Subtract.

5 – (–4)

5 − (–4) = 5 + 4

9

To subtract –4, add 4.

Additional Example 3B: Subtracting Real Numbers

Same signs: add absolute values.(5 + 4 = 9)

Both numbers are positive, so the sum is positive.


Additional Example 3C: Subtracting Real Numbers

Rewrite with a denominator of 10.

Same signs: add absolute values .

Subtract.

Both numbers are negative, so the sum is negative.–5.3

To subtract , add .

,


Subtract.

13 – 21

Check It Out! Example 3a

13 – 21 To subtract 21, add –21.

Different signs: subtract absolute values.


–8

= 13 + (–21)

(21 – 13 = 8)


Check It Out! Example 3b

Subtract.

Both numbers are positive, so the sum is positive.

To subtract , add .–3 12

3 12

Same signs: add absolute values.

4


–14 – (–12)


Subtract.

–14 – (–12) = –14 + 12

(14 – 12 = 2)

To subtract –12, add 12.


–2

Different signs: subtract absolute values.


Additional Example 4: Oceanography ApplicationAn iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg?Find the difference in the elevations of the top of the iceberg andthe bottom of the iceberg.

elevation at top of iceberg

minus elevation at bottom

of iceberg

75 – (–247)

75 – (–247) = 75 + 247

= 322

To subtract –247, add 247.Same signs: add the

absolute values.

–75 –247


Additional Example 4 ContinuedAn iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg?The height of the iceberg is 322 feet.


Check It Out! Example 4

What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the ocean's surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet?

elevation at top of iceberg

minus elevation of the

Titanic

–

550 – (–12,468)

550 – (–12,468) = 550 + 12,468 To subtract –12,468, add 12,468.Same signs: add the

absolute values.= 13,018

550 –12,468


Check It Out! Example 4 Continued

What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the ocean's surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet?

Distance from the top of the iceberg to the Titanic is 13,018 feet.

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Warm Up Lesson 1-1 Word Problems