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### 6th Grade Review

Whole Number Operations

Addition

1. 4137

+ 739

2. 567

+139

3. 5602

+8835

4. 65391

+ 87

5. 941372

+ 128343

- 4,876
- 706
- 14,437
- 65,478
- 1,069,715

Whole Number Operations

Subtraction

Right or Wrong?

Can you find the mistake?

- 345
- - 278
- 57

2. 9864

- 671

9193

3. 149856

- 51743

97113

- 4. 7548362
- 969457
- 6678905

Whole Number Operations

Multiplication

Learning Partners

- Create 3 multiplication problems (do not use more than 3 digits)
- Switch with a neighbor
- Check your partner’s work

Whole Number Operations

Division

RACE!

- 9954 ÷ 63
- 87 ÷ 3
- 48026 ÷ 37
- 73080 ÷ 20
- 850 ÷ 5

6. 210 ÷ 7

7. 54 ÷ 6

8. 2571 ÷ 3

9. 2992 ÷ 4

10. 63 ÷ 9

1. 1582. 293. 12984. 36545. 1706. 307. 98. 8579. 74810. 7

Solutions

- Draw a real world example of an event that must be done in a certain order

Order is

important!

E - exponents

M - multiply

D - divide

A – add

S - subtract

Vocabulary

PEMDASEXAMPLE

11 – 14 ÷ 2 + 6

Order of Operations

– the rules we follow when simplifying a numerical expression

Example 1

Simplify the expression.

3 + 15 ÷ 5

Divide.

3 + 15 ÷ 5

3 + 3

Add.

6

Example 2

Simplify the expression.

44 – 14 ÷ 2 · 4 + 6

44 –14 ÷ 2 · 4 + 6

Divide and multiply from

left to right.

44 –7 · 4 + 6

44 – 28 + 6

Subtract and add from

left to right.

16 + 6

22

Example 3

Simplify the expression.

3 + 23 · 5

Evaluate the power.

3 + 23 · 5

Multiply.

3 + 8 · 5

3 + 40

Add.

43

Example 4

Simplify the expression.

28 – 21 ÷ 3 · 4 + 5

28 –21 ÷ 3 · 4 + 5

Divide and multiply from

left to right.

28 –7 · 4 + 5

Subtract and add from

left to right.

28 – 28 + 5

0 + 5

5

When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set.

Grouping Symbols

[ ]

( )

{ }

Using the Order of Operations with Grouping Symbols

Example 5

Simplify the expression.

42 – (3 · 4) ÷ 6

Perform the operation inside the parentheses.

42 –(3 · 4) ÷ 6

42 –12 ÷ 6

Divide.

42 – 2

Subtract.

40

Using the Order of Operations with Grouping Symbols

Example 6

Simplify the expression.

A. 24 – (4 · 5) ÷ 4

Perform the operation inside the parentheses.

24 – (4 · 5) ÷ 4

24 –20 ÷ 4

Divide.

24 – 5

Subtract.

19

Using the Order of Operations with Grouping Symbols

Example 7

Simplify the expression.

[(26 – 4 · 5) + 6]2

The parentheses are

inside the brackets, so

perform the operations

inside the parentheses

first.

[(26 –4 · 5) + 6]2

[(26 –20) + 6]2

[6 + 6]2

122

144

Using the Order of Operations with Grouping Symbols

Example 8

Simplify the expression.

[(32 – 4 · 4) + 2]2

The parentheses are

inside the brackets, so

perform the operations

inside the parentheses

first.

[(32 –4 · 4) + 2]2

[(32 –16) + 2]2

[16 + 2]2

182

324

Try this one on your own!

Example 9

3 + 6 x (5+4) ÷ 3 - 7

Step 1: Parentheses

3 + 6 x (5+4) ÷ 3 – 7

Step 2: Multiply and Divide in order from left to right

3 + 6 x9 ÷ 3 – 7

3 + 54÷ 3 – 7

Step 3: Add and Subtract in order from left to right

3 + 18 - 7

Solution: 14

Try another!

Example 10

150 ÷ (6 +3 x 8) - 5

Step 1: Parentheses

150 ÷ (6 +3 x 8) – 5

Step 2: Division

150 ÷30 – 5

Step 3: Subtraction

5– 5

Solution: 0

Classify each statement as true or false. If the statement is false, insert parentheses to make it true.

(

)

false

1. 4 5 + 6 = 44

2. 24 – 4 2 = 40

(

)

false

true

3. 25÷ 5 + 6 3 = 23

4. 14 – 22 ÷ 2 = 12

true

Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month.

Perform the operations in parentheses first.

(5 + 3 · 3) · 4

(5 + 9) · 4

Add.

Multiply.

14 · 4

56

Sandy ran 56 miles last month.

Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate how many words will she know at the end of seven weeks.

Perform the operations in parentheses first.

(3 · 4 · 7) + 30

(12 · 7) + 30

Multiply.

Add.

84 + 30

Jill will know 114 words at the end of 7 weeks.

114

Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Write an expression and simplify to find how much Denzel paid for a month with 8 calls beyond the basic plan.

$51

Simplify each expression.

1. 27 + 56 ÷ 7

2. 9 · 7 – 5

3. (28 – 8) ÷ 4

4. 136 – 102 ÷ 5

5. (9 – 5)3 · (7 + 1)2 ÷ 4

35

58

5

116

1,024

EQ: How can I perform operations with fractions?

Adding Fractions

With Different Denominators!

1. 2/3 + 1/5

2. 1/15 + 4/21

3. 2/9 + 3/12

- Steps:
- Find the LCD
- Rename the fractions to have the same LCD
- Add the numerators
- Simplify the fraction

Subtracting Fractions

With Different Denominators!

1. 2/3 – 4/12

2. 4/6 – 1/15

3. 2/12 – 1/8

- Steps:
- Find the LCD
- Rename the fractions to have the same LCD
- Subtract the numerators
- Simplify the fraction

Multiplying Fractions

1. 2/9 x 3/12

2. ½ x 4/8

3. 1/6 x 5/8

- Steps:
- Multiply the numerators
- Multiply the denominators
- Simplify the fraction

Dividing Fractions

- Steps:
- Keep it, change it, flip it!
- Multiply the numerators
- Multiply the denominators
- Simplify the fraction

1. 2/10 ÷ 2/12

2. 1/8 ÷ 2/10

3. 1/6 ÷ 3/15

Keep it, Change it, Flip it!

More with fractions

Changing Improper Fractions to Mixed Numbers

- Steps:
- Divide
- Remember…First come, first serve

1. 55/9

2. 39/4

3. 77/12

Divide!

Changing Mixed Numbers to Improper Fractions

- Steps:
- Multiply the whole number by the denominator
- Add the result to the numerator (that will be your new numerator)
- The denominator stays the same

1.

2.

3.

Check Mark Method

Operations with Mixed Numbers

1.

2.

- Steps:
- Convert both mixed numbers to an improper fraction
- Follow the necessary steps for the given operation
- Simplify

- True
- True
- False

Homework: handout

EQ: How do I perform operations with decimals?

Decimals

Math Dictionary

- A way to represent fractions
- EX:

- Look at the last decimal place…that place value is the denominator of the fraction
- 2. The numbers to the right of the decimal are the numerator

Place Value Game

FunBrain - Place Value Puzzler

Ordering

- Order from least to greatest
3.84, 4.4, 4.83, 3.48, 4.38

5.71, 5.8, 5.68, 5.79, 5.6

Rounding

- Round to the nearest one
17.6

- Nearest thousandth
12.5503

- Nearest hundredth
2.2959

- Nearest thousandth

Decimal Operation Chant

Do you know your decimals?

Do you know your decimals?

Add or Subtract, line it up, line it up!

Add or Subtract, line it up, line it up!

Multiply, Count it out, count it out!

Multiply, Count it out, count it out!

Division, step it out!

Division, step it out!

Now you know your decimals!

Now you know your decimals!

Adding and Subtracting Decimals

- Just make sure to line up the decimal points so that all the decimal points are on a vertical line

Draw a line through the points!

HINT:

Multiplying Decimals

- Multiply the numbers like normal
- Move the decimal to the right the exact number of place values in the numbers being multiplied

Try One!

45.68 x 3.5=

Dividing Decimals

- Stranger Story
- The stranger moves toward the door, so you move the same amount back
- The stranger gets to the door!
- GET AWAY! Go to the ROOF!

Dividing Decimals

- Then, divide like normal

EQ: How are percents, ratios, and proportions related?

Percent:

Math Dictionary

- A ratio that compares a number to 100
- Out of 100
- Part/whole

25%

30%

95%

73%

Ratio:

Math Dictionary

- A comparison of two numbers
- Part
Part

What is the ratio of pink circles to white circles?

Expression --

Math Dictionary

- A collection of numbers, variables, and symbols
- NO equal sign!!

Example

10 (x+3) + 2

Find the variable, replace it

Simplify the expression

Now your all done

Just remember to…

PLUG IT IN! PLUG IT IN!

Handout

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