Comparing and Ordering Rational Numbers

Use the Number Line To compare rational numbers, plot points on The numbers farther to the right are larger. The numbers farther to the left are smaller. 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Place the number tiles in the correct places on the number line.

Now, can you see: Which integer is largest? Which is smallest?

Where do rational numbers go on the number line? Go to the screen and show where the following numbers go:

Put these numbers on the number line. Which number is the largest? The smallest?

Comparing Positive Numbers Numbers can be equal to; less than; or more than another number. The symbols that we use are: Equals "=" Less than "<" Greater than ">" For example: 4 = 4 4 < 6 4 > 2 When using < or >, remember that the smaller side points at the smaller number.

Inqualities: Less than or equal to: Greater than or equal to:

22 10.5 is ______ 15.2. A = B < C > Answer: B

23 7.5 is ______ 7.5 A = B < C > Answer: A

24 3.2 is ______ 5.7 A = B < C > Answer: B

Comparing Negative Numbers The larger the absolute value of a negative number, the smaller the number. That's because it is farther from zero, but in the negative direction. For example: -4 = -4 -4 > -6 -4 < -2 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Remember, the number farther to the right on a number line is larger.

Comparing Negative Numbers One way to think of this is in terms of money. You'd rather have $20 than $10. But you'd rather owe someone $10 than $20. Owing money can be thought of as having a negative amount of money, since you need to get that much money back just to get to zero. So owing $10 can be thought of as -$10.

25 -4.75 ______ -4.75 A = B < C > Answer: A

26 -4 ______ -5 A = B < C > 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -4 ______ -5 A = B < C > 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Answer: C

27 A = B < C > Answer: B

28 -14.75 is ______ -6.2 A = B < C > Answer: B

29 -14.2 is ______ -14.3 A = B < C > Answer: C

Comparing All Numbers Any positive number is greater than zero or any negative number. 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Any negative number is less than zero or any positive number.

< < < < < < < < < < < < < < Drag the appropriate inequality symbol between the following pairs of numbers: < < < < < < < < < < < < < < < < < < < < < < > > > > > > > > > > > > > > > > > > > > 1) -3.2 5.8 3) 63 36 5) -6.7 -3.9 7) -24 -17 9) -8.75 -8.25 2) -237 -259 4) -10.2 -15.4 6) 127 172 8) 10) -10 -7

30 A = B < C > Answer: B

31 A = B < C > Answer: B

32 A = B < C > Answer: C

33 A = B < C > Answer: C

34 A = B < C > Answer: C

35 A = B < C > Answer: B

A thermometer can be thought of as a vertical number line A thermometer can be thought of as a vertical number line. Positive numbers are above zero and negative numbers are below zero.

36 If the temperature reading on a thermometer is 10℃, what will the new reading be if the temperature: falls 3 degrees? Answer: 7°C

37 If the temperature reading on a thermometer is 10℃, what will the new reading be if the temperature: rises 5 degrees? Answer: 15°C

38 If the temperature reading on a thermometer is 10℃, what will the new reading be if the temperature: falls 12 degrees? Answer: -2°C

If the temperature reading on a thermometer is 39 If the temperature reading on a thermometer is -3℃, what will the new reading be if the temperature: falls 3 degrees? Answer: -6°C

If the temperature reading on a thermometer is 40 If the temperature reading on a thermometer is -3℃, what will the new reading be if the temperature: rises 5 degrees? Answer: 2°C

If the temperature reading on a thermometer is 41 If the temperature reading on a thermometer is -3℃, what will the new reading be if the temperature: falls 12 degrees? Answer: -15°C

Adding and Subtracting All Rational Numbers

Calculate the sum or difference. -6 – 2 59 Calculate the sum or difference. -6 – 2 Answer: -8

Calculate the sum or difference. 5 + (-5) 60 Calculate the sum or difference. 5 + (-5) Answer: 0

Calculate the sum or difference. -10.5 + 6.2 61 Calculate the sum or difference. -10.5 + 6.2 Answer: -4.3

Calculate the sum or difference. 7.3 – (-4) 62 Calculate the sum or difference. 7.3 – (-4) Answer: 11.3

Calculate the sum or difference. 63 Calculate the sum or difference. Answer: -3 1/6

Calculate the sum or difference. 9.27 + (-8.38) 64 Calculate the sum or difference. 9.27 + (-8.38) Answer: 0.89

Calculate the sum or difference. -4.2 + (-5.9) 65 Calculate the sum or difference. -4.2 + (-5.9) Answer: -10.1

Calculate the sum or difference. -2 – (-3.95) 66 Calculate the sum or difference. -2 – (-3.95) Answer: 1.95

Calculate the sum or difference. 5 - 6 + (-7) 67 Calculate the sum or difference. 5 - 6 + (-7) Answer: -8

Calculate the sum or difference. 19 + (-12) - 11 68 Calculate the sum or difference. 19 + (-12) - 11 Answer: -4

Calculate the sum or difference. -2.3 + 4.1 + (-12.7) 69 Calculate the sum or difference. -2.3 + 4.1 + (-12.7) Answer: -10.9

Calculate the sum or difference. -8.3 - (-3.7) + 5.2 70 Calculate the sum or difference. -8.3 - (-3.7) + 5.2 Answer: -6.8

Calculate the sum or difference. 71 Calculate the sum or difference. Answer: 4 1/10