Integers Comparing and Ordering EQ How do we

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Integers: Comparing and Ordering

Integers: Comparing and Ordering

EQ • How do we compare and order rational numbers?

EQ • How do we compare and order rational numbers?

Rational Numbers Integers Whole Numbers (Positive Integers) Fractions/Decimals Negative Integers

Rational Numbers Integers Whole Numbers (Positive Integers) Fractions/Decimals Negative Integers

Rational numbers • Numbers that can be written as a fraction. Example: 2 =

Rational numbers • Numbers that can be written as a fraction. Example: 2 = 2 ÷ 1 = 2 1

Whole Numbers • Positive numbers that are not fractions or decimals. 1 2 3

Whole Numbers • Positive numbers that are not fractions or decimals. 1 2 3 4 5 6

Integers • The set of whole numbers and their opposites. -7 -6 -5 -4

Integers • The set of whole numbers and their opposites. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Positive Integers • Integers greater than zero. 0 1 2 3 4 5 6

Positive Integers • Integers greater than zero. 0 1 2 3 4 5 6

Negative Integers • Integers less than zero. -6 -5 -4 -3 -2 -1 0

Negative Integers • Integers less than zero. -6 -5 -4 -3 -2 -1 0

Comparing Integers • The further a number is to the right on the number

Comparing Integers • The further a number is to the right on the number line, the greater it’s value. < -1 Ex: -3 ___ -5 -4 -3 -2 -1 . . 0 1 2 3 4 5 -1 is on the right of -3, so it is the greatest.

Comparing Integers • The farther a number is to the right on the number

Comparing Integers • The farther a number is to the right on the number line, the greater it’s value. > -5 Ex: 2 ___ -5 -4 -3 -2 -1 . 0 1 2 . 3 4 5 2 is on the right of -5, so it is the greatest.

Comparing Integers • The farther a number is to the right on the number

Comparing Integers • The farther a number is to the right on the number line, the greater it’s value. > -2 Ex: 0 ___ -5 -4 -3 -2 -1 . 0 . 1 2 3 4 5 0 is on the right of -2, so it is the greatest.

Ordering Integers When ordering integers from least to greatest follow the order on the

Ordering Integers When ordering integers from least to greatest follow the order on the number line from left to right. Ex: 4, -5, 0, 2 -5 -4 -3 -2 -1 . 0 . 1 2 . 3 Least to greatest: -5, 0, 2, 4 4 . 5

Ordering Integers When ordering integers from greatest to least follow the order on the

Ordering Integers When ordering integers from greatest to least follow the order on the number line from right to left. Ex: -4, 3, 0, -1 -5 -4 -3 -2 -1 . 0 . . 1 2 3 . Greatest to least: 3, 0, -1, -4 4 5

Try This: < 4 a. -13 ___ b. -4 ___ -7 < < 32

Try This: < 4 a. -13 ___ b. -4 ___ -7 < < 32 c. -156 ___ d. Order from least to greatest: -9, -3, 5, 15 15, -9, -3, 5 ________ e. Order from greatest to least: 2, -7, -8, -16, -7, -8, 2 ________

EQ • How do we find the absolute value of a number?

EQ • How do we find the absolute value of a number?

Absolute Value • The distance a number is from zero on the number line.

Absolute Value • The distance a number is from zero on the number line. Symbols: |2| = the absolute value of 2 Start at 0, count the jumps to 2. -5 -4 -3 -2 -1 0 1 2 It takes two jumps from 0 to 2. |2| = 2 3 4 5

Absolute Value • The distance a number is from zero on the number line.

Absolute Value • The distance a number is from zero on the number line. Ex: |-4| = Start at 0, count the jumps to -4. -5 -4 -3 -2 -1 0 1 2 3 It takes four jumps from 0 to -4. |-4| = 4 4 5

Solving Problems with Absolute Value When there is an operation inside the absolute value

Solving Problems with Absolute Value When there is an operation inside the absolute value symbols; solve the problem first, then take the absolute value of the answer. Ex: |3+4| =|7| = 7 Ex: |3|- 2 = 3 -2 = 1 Hint: They are kind of like parentheses – do them first!

Compare the following: 7 _____ I -7 I 8 _____ -15 -12 _____ -8

Compare the following: 7 _____ I -7 I 8 _____ -15 -12 _____ -8 List in order least to greatest -9, 0, -11, 3, -1, 8 8, -2, 4, -8, 3 Answer the following: What is the opposite of 8? What is the opposite of 0? True or False. A negative whole number is not considered an integer.

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