8th Precourse Practice.pptx

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PRECOURSE

PRACTICE

8

TH

GRADE

This is a review of concepts you should have learned

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ANSWER KEY

(AFTER YOU COMPLETE YOU WORK

CORRECT YOUR ANSWERS, THEN VIEW THE FOLLOWING SLIDES FOR ANY

PROBLEMS YOU GOT INCORRECT)

1.

4.9

2.

10.6

3.

9.5 or 9.50

4.

1

5.

$8.97

6.

33 words / 1 min

7.

yes

11.

x=12

12.

x=14.3

13.

x=45

14.

x=10

15.

x=9

16.

x=120

17.

No (commutative)

18.

Yes (distributive)

19.

Yes (distributive)

21. 12 cm2

22. A=113.04 cm2 C = 37.68 cm 23. 166 in2

24. 34%

25. 812%

26. 0.46%

27. 0.02

28. 0.14

29. 6.5 or 6.50

30. 44%

32. , 67%, 0.7

33. Mean = 3

median = 2 mode = 1 range = 5

34. Mean = 6

median = 5 mode = 3 and 6 range = 11

35. 351

36. 162

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DECIMALS #1-2

1. 5.7 – 0.8

2. 37.1 3.5

4 17

5 . 7 - 0 . 8 4 . 9

1. Align the decimals

2. Subtract from right to left

(note – you need to borrow for the 10ths place)

3. Bring the decimal straight down

0 1 0. 6

3 5 3 7 1. 0

− 0

3 7

− 3 5

2 1

− 0

2 1 0

− 2 1 0

First – Rid the divisor of decimals.

Whatever you do outside, you do

Your new problem becomes this.

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DECIMALS #3

3. 2.5(3.8) (note-parentheses mean multiply)

4

2 . 5 x 3 . 8 2 0 0

+ 7 5

_{9 . 5} ₀

1

Multiply the 1’s (25 x 8)

Multiply the 10’s (25 x 3). Don’t forget the placeholder.

Add the partial products While you multiply, pretend the decimal is

not there

1 decimal 1 decimal

2 decimals

Count the # of digits to the

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FRACTIONS #4-5

4. =

dot means multiply

5. =

1. Multiply the numerators 2. Multiply the

denominators 3. Simplify

x 2 x

3

First you need a common denominator (a multiple that works for both denominators). In this case, the multiples of 4 are4,

8, 12, 16, 20. The multiples of 6 are 6, 12, 18, 24, 30. The smallest multiple they share is 12 so use 12 to rewrite

each fraction.

Once the denominators are the same, simply add the

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FRACTIONS #6

6. To divide fractions

copy, change, flip

Copy the 1st_fraction

Change to

Flip the 2nd

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RATES # 7-8

7.

You need to buy 3 notebooks for your classes at school. Each notebook

costs $2.99. What is the total cost of 3 notebooks?

• _{$2.99 x 3 = $8.97}

8.

Write a rate as a fraction in simplest form

66 words in 2 minutes

A rate tells you how many for only 1 unit, so to solve rate problems you divide.

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PROPORTIONS #9

9.

Tell whether the ratios form a proportion

,

The first way to solve is to simplify the ratios



 _{The simplified ratios are the same, so they do form a proportion}

The 2nd_{way is to cross multiply}



A proportion shows that two ratios are equal

48

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PROPORTIONS #10

10.

Solve the proportion using cross products

3x

=

30 Now isolate

3x = 30

3 3

x = 10

Use cross products to solve proportions, then isolate the

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SOLVING EQUATIONS

#11-13

11.

x + 7 = 19

- 7 -7

x = 12

12. x - 1.5 = 12.8

+ 1.5 + 1.5

x = 14.3

13. x – 15 = 30

+ 15 +15

x = 45

To solve an equation, isolate the variable using inverse operations (opposite math).

You want to get x by itself, so get rid of the 7. Opposite math is

subtract

You want to get x by itself, so get rid of the 1.5 Opposite math is

add

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SOLVING EQUATIONS

#14-16

14. 4 + x = 14

- 4 - 4

x = 10

15. 2x = 18

x = 9

To solve an equation, isolate the variable using inverse operations (opposite math).

subtract

The 2 next to the x means multiply. The opposite of multiply

is divide

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EQUIVALENT EXPRESSIONS

#17-19

Tell whether the two expressions are equivalent. If so, tell what property makes them

equivalent.

17.

8 + 2b and -2b + 8

 _{No – The order is switched (commutative), but 2b -2b}

18.

3(k + 6) and 3d + 18 3 (k + 6)

Multiply the # outside the parentheses by each # inside

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AREA #20-21

20. This shape is a parallelogram so Area =

base x height

Remember that height always stands

straight

A = 1 x 8 = 8 in

2

21. This shape is a triangle so Area = ½ (base x

height)

A = ½ (4 x 6)

= ½ (24) = 12 cm

2

Area Formulas

Square,Recangle,Parallelogram A= base x height

Triangles A = ½ (base x height)

Circles

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AREA/CIRCUMFERENCE #22

22. Circumference = x diameter

= 3.14 x 12 =

37.68 cm

Area = x radius

2

= 3.14 x 6

2

Circumference is the distance around the edge of a circle. Use the formula

(use 3.14 for ) The radius goes ½ way

across the circle, so 6 is the radius. The diameter goes

all the way across, so the diameter would be 12

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SURFACE AREA #23

23. Find the surface area of the rectangular prism

15

Surface area is the amount of space needed to cover the flat faces of a 3d

object. To find surface area: 1. Find the area of each face

2. Total the areas

Face Formula Area

Front (blue,red) A = base x height

4 x 5 = 20

Back (blue,red) A = base x

height = 20 Left (yellow,blue) A = base x

height

7 x 5 = 35

Right

(yellow,blue) A = base x height = 35 Top (red,yellow) A = base x

height

4 x 7 = 28

Bottom

(red,yellow) A = base x height = 28

Color coding the edges helps to

find the

dimensions. Each face is a rectangle so

A= bxh

Add the

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DECIMALS TO PERCENTS

#24-26

24.

0 . 3 4

=

34%

25.

8 . 1 2

=

812%

26.

0 . 0 0 4 6 =

0.46%

1. Move the decimal 2 times right 2. Fill in any blank spots with zeros

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PERCENTS TO DECIMALS

#27-29

27.

2 %

= __ 2% =

0.02

28.

1 4 %

=

0.14

29.

6 5 0 %

=

6.5 or 6.50

1. Move the decimal 2 times left 2. Fill in any blank spots with zeros

3. Put a decimal

You do not see decimals on the original numbers, so the

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ORDERING RATIONAL #S

Order the #s from least to greatest

31.

, 40%, 0.37

 _{To change to a percent divide, then move the decimal (}  _{40% is already in percent form}

 _{0.37 = 37% (move the decimal 2 times right)}

 _{Now use the percents to compare number (, 40%, and 0.37 or 37%)}  _{Answer - 0.37, , 40%}

1. Change all numbers to the same form (in this case percents are easiest to use when comparing)

2. Order

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ORDERING RATIONAL #S

Order the numbers from least to greatest

32. 67%, , 0.7



_{67% is already in percent form}



_{To change first divide, then move the decimal (}



_{0.7 = 70% (move the decimal 2 times right)}



_{Now use the percents to compare (67%, or 0.6 or 66.6% , 0.7 or 70%)}



Answer - , 67%, 0.7

1. Change all numbers to the same form (in this case percents are easiest to use when comparing)

2. Order

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MEAN, MEDIAN, MODE,

RANGE # 33

33.

Find the mean, median, mode, & range of the following set of numbers

2, 1, 1, 5, 6

 _{Mean – 2 + 1 + 5 + 6 = 15}

15 5 = 3 (divide by 5 because there are 5 numbers in the set)

 _{Median – First put the #s in order from least to greatest, then find the middle #} 1 , 1 , 2 , 5 , 6

The median is 2

 _{Mode – The mode is the most frequently occurring #} The mode is 1 because it occurs most often  _{Range – The greatest minus the least}

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MEAN, MEDIAN, MODE,

RANGE # 34

33.

Find the mean, median, mode, & range of the following set of numbers

4 , 6 , 3 , 3 , 6 , 14

 _{Mean – 4 + 6 + 3 + 3 + 6 + 14 = 36}

36 6 = 6 (divide by 6 because there are 6 numbers in the set)

 _{Median – First put the #s in order from least to greatest, then find the middle #} 3 , 3 , 4 , 6 , 6 , 14

There are 2 middle #’s so find the average (4 + 6 = 10, then 10 2 = 5)

The median is 5

 _{Mode – The mode is the most frequently occurring #}

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COMPUTATION # 35-36

35.

27 x 13

36.

324 2

1 2

2 7 x 1 3 8 1 + 2 7 3 5 1

1

Multiply the 1’s (27 x 3). Since 7 x 3 = 21, carry the 2

Multiply the 10’s (27 x 1). Don’t forget the placeholder

Add the partial products

1 6 2

2 3 2 4

− 2

1 2

− 1 2

0 4

Long Division Steps: 1. Divide

2. Multiply 3. Subtract 4. Bring Down

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COMPUTATION # 37

37.

168 24

Note – It helps to round the divisor to help

estimate the division step. Think 25 x what is close to 168. Since 25 x 6 = 150), try 6 (24 x 6 = 144). That

might not be enough so try 7 (24 x 7 = 168).

That’s perfect

0 0 7

2 4 1 6 8

− 0

1 6

− 0

1 6 8

− 1 6 8

0

Long Division Steps: 1. Divide

2. Multiply 3. Subtract 4. Bring Down

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