Math Grade 6 Negative Integers What have we

Math Grade 6

Negative Integers? What have we learned so far?

Integers less than zero are negative integers. -6 -5 -4 -3 -2 -1 Negative integers are written with a (-) sign. Integers greater than zero are positive integers. 0 1 2 3 4 5 6 Positive integers can be written with a (+) sign.

Complete the table below by Number - 42 - 3. 5 + 38 Integer Not Integer or -ve . +ve

The integers between -4 and 1 are: -3 -2 -1 and 0

Positive And Negative Numbers

Just as there are +ve and -ve integers, there also +ve and -ve decimals and fractions.

Can anyone think of examples of where you would use negative numbers? Negative Numbers?

Negative numbers are used to show debt. Dan had $40. 75 in his bank account and he withdrew $70. 8. What will his balance be now? Balance: $ -30. 05

Negative numbers are used to measure under sea level. 30. 5 m 20. 5 m 10. 5 m 0 m -10. 5 m -20. 5 m -30. 5 m -40. 5 m -50. 5 m

60 m 40 m Use positive or negative numbers to estimate the height above or below sea level of the following objects: 20 m 0 m -20 m -40 m -60 m

Positive and negative numbers can be shown on a number line. – 0. 8 – 0. 3 -1 -0. 9 -0. 8 -0. 7 -0. 6 -0. 5 -0. 4 -0. 3 -0. 2 -0. 1 Negative Numbers 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1 Positive Numbers We can use the number line to compare positive and negative numbers. For example, – 0. 3 ‘is greater than’ – 0. 8

What is an x-axis? A number line that runs horizontally (left-right) through zero is called an x-axis. It is used as a reference line so you can measure distance from its origin zero. x-axis origin

What is an abscissa? Abscissa is the location of a point on an x-axis. Consider the x-axis below. x-axis What is the abscissa of point A? The abscissa of point A is -2. 5. What is the abscissa of point B? The abscissa of point B is +2. 5. What is the abscissa of point C? The abscissa of point C is +4. 5.

Consider the x-axis below. A B C x-axis Give the abscissas of points A, B, and C. A(-2) B(+1) C(+6)

Locate the points of the following abscissas on the given x-axis. A (– 2) B(+2) C(+4) A D B D(0) C

Comparing Positive and Negative Numbers can be compared using the following symbols: • < means “less than” • • = means “equal” • • Ex: 2 < 7 “ 2 is less than 7” Ex: -3 =-3 “-3 is equal to -3” > means “greater than” • Ex: 5 > -1 “ 5 is greater than -1”

Comparing Positive and Negative Numbers How can you tell one number is less than another? • Locate them on a number line. • Compare -2 and -4. As you go to the right, numbers increase on a number line. -2 > -4 since -4 is lower on the number line.

Comparing Positive and Negative Numbers All positive numbers are greater than zero. All negative numbers are less than zero. A negative number is less than a positive number. When comparing numbers on a number line, the number that is farther to the right is greater.

Replace □ with <, >, or = to make true sentences. -9 □ 8 → -9 < 8 0 □ -84 → 0 > -84 5 □ -5 → 5 > -5 -6 □ -4 → -6 < -4 -7 □ -7 → -7 = -7 +27 □ 0 → + 27 > 0

Ordering Positive and Negative Numbers Write each set of numbers in increasing order. -162 , - 10 , - 81, 59 → - 162 < - 81 < - 10 < 59 9 , -8 , 4 , -9→ -9<-8<4<9 2 , 6 , -2, 0→ -2< 0< 2<6 7 , 5 , -1 , -5→ -5<-1<5<7

Write each set of numbers in increasing order. -0. 25 , -0. 1, -1 → -1 < - 0. 5 < -0. 25 < - 0. 1 9 , -9. 02 , -9 → -9. 2 < - 9. 02 < -9 < 9 -2. 32 , -2 , 0 → -2. 32 < -2. 2 < - 2 < 0 -5. 33 , -5. 03→ -5. 33 < -5. 3 < - 5. 03 < - 5

Absolute Value What is the absolute value of a number? It is the distance of that number from zero on the number line. What does absolute value look like? the absolute value of 7 |7| | -7 | = 7 the absolute value of – 7 |7|=7 |– 7|

What is the absolute value of a number? It is the distance of that number from zero on the number line. |7|=7 7 units -8 -7 -6 -5 -4 -3 -2 -1 0 |-7 | = 7 7 units 1 2 3 4 5 6 7 8

What is the absolute value of a number? It is only how far a number is from zero on a number line. 7 is seven units away from zero, and -7 is seven units away from zero. So, the absolute value of 7 is 7 and the absolute value of -7 is also 7. |7|=7 |-7 | = 7 7 units -8 -7 -6 -5 -4 -3 -2 -1 7 units 0 1 2 3 4 5 6 7 8

Absolute Value |-2| = 2 The absolute value of a number is its distance from zero on the number line. |3| = 3 because 3 is three units from zero on the number line. |-5| = 5 because -5 is five units from zero on the number line.

Evaluate each expression. |3| =3 | - 68 | = 68 |-9| = 9 Since distance is always positive, the absolute value of any number is always positive.

Expression How to Read Value Opposite of the absolute value of negative nine -9 -|+13| Opposite of the absolute value of thirteen -13 -|2| Opposite of the absolute value of two -2 -|-9|

Evaluate each expression. |-8| = 8 |-56|= 56 -|-201|= -201 |+17|= 17 -|-13|= -13 -|18|= -18

Evaluate each expression. |-8. 3| = 8. 3 |-56. 21|= 56. 21 -|-201. 3|= -201. 3 |+1. 07|= 1. 07 -|-1. 23|= -|8. 05|= -1. 23 -8. 05