Buksis-1.1 Revisi Akhir

1.1

What are you going to learn?

Positive and Negative Numbers In a weather forecast, it is predicted that it will rain in

À To use negative numbers

the city P with a minimum temperature of 1 ºC below

À To draw integers in a number line

zero and a maximum temperature of 6 ºC. It will be

À To compare integers À To put integers in a sequence

Key Terms: • •

• •

integers positive integers negative integers number line

sunny in the city Q with a temperature of 6 ºC and cloudy in the city R with a temperature of 10 ºC. Can whole numbers 0, 1, 2, 3, ... represent the situation above?

A bird is perching on the top of the mast of a fisherman’s boat with a height of 3 metres. Meanwhile, the fisherman is diving 5 meters under the sea level.

-

Look at the picture of a thermometer on the right. What numbers are on the

+5

picture? You may write the temperature of 5 degrees above zero

0

as 5 ºC, and write the temperature of 5 degrees below zero as -5 ºC. The number 5 is read as positive 5 while the number –5 is read as negative 5. The numbers 5 and -5

-5

can be drawn on a vertical or a horizontal line as follows.

Vertical number line

-5

0

+5

Horizontal number line

Mathematics for Junior High School - Year 7 / 1

A set of integers; ..., −3, −2, −1, 0, 1, 2, 3, ... , can be

symbolized as I. The three dots (...) on the right and the left mean that the numbers continue without ending to both directions. The complete number line of integers can be drawn as follows. z

z

z

z

z

z

z

z

-6 -5 -4 -3 -2 -1

z

z

z

z

z

0

1

2

3

4

5

6

Negative integers

Positive integers

0 is neither positive nor negative

Example 1

a. Determine all integers between −5 and 4. Solution: −4, −3, −2, −1, 0, 1, 2, 3 b. Write all even integers between −6 and 11. Solution: The even integers between −6 and 11 are −4, −2, 0, 2, 4, 6, 8, and 1 Use the number line above, answer the following: • What is the number on the left of 0 with the same distance as the distance from 0 to 2? The number is called the inverse of 2. • What is the number on the right of 0 with the same distance as the distance from 0 to -4? The number is called the inverse of -4. • What is the sum of -4 and its inverse? • What is the inverse of 6? • What is the inverse of -5? • Without using a number line, find the inverse of 12. • Without using a number line, find the inverse of −15. • Does every integer have an inverse? • What is the sum of an integer and its inverse?

2 / Student’s Book – Integers

Comparing and Ordering Integers Suppose 5 and -5 are on a number line. How many units are there from 0 to 5? How many units are there from 0 to -5? Two numbers are said inverse to each other if they have the same distance from 0 on the number line, but different direction. What are other numbers that inverse to each other?

Let 5 and 3 be on a number line. Which number has a longer distance from 0? Which number has a shorter distance from 0? What other numbers have a shorter distance than 5? What other numbers have a longer distance from 0 than 3?

Remember = is read equal to < is read less than > is read greater than 3 < 5 is read three is less than five 5 > 3 is read five is greater than three

On a horizontal number line, the numbers located on the left side of another number are always less than those on the right side. For instance, since 3 is on the left side of 5, 3 is less than 5, written as 3 < 5. Since 5 is on right side of 3, 5 is greater than 3 or 5 > 3. -8 -7

-6

-5

-4

-3

-2

-1

0

decrease

1

2

3

4

5

4

5

6

6

increase

What if we use a vertical number line?

Example 2

Change the sign † to <, >, or = on −4 † −7

Solution: -8 -7

-6

-5

-4

-3

-2

-1

0

1

2

3

The number −4 is located on the right side of −7.

Mathematics for Junior High School - Year 7 / 3

Therefore, −4 > −7.

Problem 1

Arrange the following numbers from the least to the greatest. a. 5, −3, 6, −6, 2, 4, −1 b. 9, −5, 6, −12, 17, 8, −14

Problem 2

In a mathematics test, the score for the right answer is 4, for the wrong answer is -1, and 0 for failing to answer. Complete the table below (use a spreadsheet, if possible) and then sort the students based on their scores from the highest to the lowest. Number of Correct Answers

Number of Wrong Answers

Number of Unanswered Questions

Abdullah

5

3

2

Aminah

6

4

0

Galuh Erna

5

2

3

Zainul

8

2

0

Nabila

8

1

1

Zaty

8

0

2

Hamidah

7

1

2

Yusuf

7

3

0

Students’ Names

4 / Student’s Book – Integers

Total Score

1. Draw a number line.

Put each of the following

numbers on your number line. a. –1

b. 4

c. –7 d. –9

e. 2

f. 8

2. Write an integer expressing a temperature of 14 degrees Celsius below zero. 3. Write the inverses of the following integers. a. 13

b. –8

c. 150

d. −212

4. Write three opposing pairs of situations. For example, stepping up two steps and stepping down two steps on a staircase. 5. Change the sign † to <, >, or =. a. 0 † −8

b. 1 †−7 c. −12 †−5

e. −66 †5

f. 76 †−239 g. −999 † −99 h. −45

d. –3 †−7

†−45 6. Write the following integers from the least to the greatest. a. –2, 3, 4, −1

b. 3, −2, 0, −7

c. 4, −5, −2, 3, −1

d. –12, 0, −3, 9, 98, −10, 54 e. –1, 0, −11, −101, −111, 101, 11 7. Write the following integers from the least to the greatest. a. –10, 8, 0, −6, 5

b. 56, −56, −40

c. 0, −12, −3, −5, −64

d. 75, −3, −4, 12, 0, 9, −10

8. Write an integer which is between the integers below.

Mathematics for Junior High School - Year 7 / 5

a. –7 and 3 9. Critical

b. 0 and −6 c. –5 and −13

Thinking.

Why is any negative

integer less than any positive integer? Explain. 10. Critical Thinking. Write down the steps to determine whether an integer is greater or less than another integer.

6 / Student’s Book – Integers