Properties of Real Numbers

Section R-1Chapter R: Review

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Translating Words

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Action Operation Possible Context Clues

Combine Add Sum, Add, Total

Separate Subtract Difference, Subtract

Combine equal

groupsMultiply Product, Multiply

Separate into equal groups Divide Quotient, Divide

Quick Examples

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Write an algebraic expression to represent each situation.

A. the number of apples in a basket of 12 after n more are added

B. the number of days it will take to walk 100 miles if you walk M miles per day

Add n to 12.

Divide 100 by M.

12 + n

Quick Examples

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Write an algebraic expression to represent each situation.

C. the difference of a number less 2 equals 7.

n – 2 = 7

D. Write out: 21 ÷ 7 = 3

The quotient of 21 and 7 is 3.

Order of Operations

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To evaluate operations, one way to remember the order of operations is by using the mnemonic PEMDAS.

REMEMBER: Multiplication and Addition doesn’t always go first before Division and Subtraction

Order of Operations1. Parentheses and grouping symbols.2. Exponents.3. Multiply and Divide from left to right.4. Add and Subtract from left to right.

6 4 3

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PEMDASPEMDAS

parenthesis – combine these first

PEMDAS

exponents – apply the exponent now

PEMDAS

complete multiplication and division, left to right

PEMDAS

complete addition and subtraction, left to right

5

Example 1

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22 5 3 3 2 4

PEMDASPEMDAS

parenthesis – combine these first

22 2 3 2 4

PEMDAS

exponents – apply the exponent now

42342

PEMDAS

complete multiplication and division, left to right

468

PEMDAS

complete addition and subtraction, left to right

10

22 5 3 3 2 4

Example 2

2 [4 2 (10 6)]

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2 [4 2 (10 6)]

38

Example 3

PEMDASPEMDASPEPEMDMDASASPEMDPEMDASASPPEMDASEMDAS

2 + [4 + 2 · 16]2 + [4 + 32]2 + 36

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2 [8 3(4 2)] 3

11

Your Turn

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2 5 4 6 3 4

12

Example 4

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5 3

9 10

1

6

Example 5

5 3

9 10

3

1

2

1

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21 100

25 3

28

Your Turn

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Warm_Up #21. Solve

2. Write the equation of “The product of 5 and x is the product of 2 and 10.”

4 2[3 (6 7)] 8

04/19/23 17:45 13R-1: Properties of Real Numbers

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Add/Subtract fractions1.List the factors of the bottom number to find

the “Least Common Denominator”

2.Multiply the LCD to the top number

3.Evaluate by add or subtracting across BUT keeping the bottom number

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4 1

3 2

11

6

Example 6

4 1

3 2

6

3

6

83: 3,6,9,12,15...

2 : 2,4,6,8,10...

What are the MULTIPLES of the denominator:

What is the SMALLEST SAME MULTIPLE

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4 1

5 2

3

10

Example 7

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2 8

15 9

46

45

Your Turn

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AssignmentPg 16

27-65 odd, OMIT 43