Download eighth grade you should know 2014

EIGHTH GRADE “YOU SHOULD KNOW”
Study Guide and Practice
Sets of Numbers:
1) Natural or Counting Numbers: 1, 2, 3, 4…
2) Whole Numbers: 0, 1, 2, 3, 4…
3) Integers: …-3, -2, -1, 0, 1, 2, 3, …
4) Rational: Terminating decimals (4.56), Repeating decimals
(.333333…), fractions, perfect square roots
5) Irrational: non-terminating decimals (3.14157…), nonperfect square roots
6) Real numbers: all the sets
→
↑
RATIONAL
↑
INTEGERS
↑
WHOLE
↑
NATURAL
REAL
←
↑
IRRATIONAL
Identify the set(s) of numbers that each belongs to:
1) 9.43243…_____________________________________
2) -4 __________________________________________
3) 0___________________________________________
4) 5.12 _________________________________________
5)
16
________________________________________
Properties:
1) Commutative Property – when adding or multiplying, the numbers can
be switched around and you still get the same answer.
EX: 2 + 4 = 4 + 2
(5)(2) = (2)(5)
2) Associative property – when adding or multiplying numbers that are
in and out of parenthesis, you can switch the numbers around.
EX: 5 + (2 + 3) = 3 + (2 + 5)
8(9 × 7) = 9(8 × 7)
3) Distributive Property – when multiplying a number by a sum or
difference, you can distribute the number through the parenthesis by
multiplying.
EX: 3(5 + 2) = 3 × 5 + 3 × 2 or 15 + 6
7(x – 5) = 7x – 35
4) Additive Identity: add zero to any number to obtain the original
number.
EX: 7 + 0 = 7
0 = identity element of addition
5) Multiplicative Identity: multiply one by any number to obtain the
original number.
EX: 8 × 1 = 8
1 = identity element of multiplication
6) Additive Inverse: the opposite of a number
7+-7=0
7) Multiplicative Inverse: reciprocal or “flip” of a fraction
2×½=1
Identify the property:
1) 8 + 0 = 8 ______________________________________
2) 5(x – 6) = 5x – 30 _______________________________
3) 18 + (-18) = 0 __________________________________
4) 9 + (4 + 5) = 5 + (4 + 9) ___________________________
5) What is the additive inverse of 8 ___________
6) What is the multiplicative inverse of 2
5
______________
7
Basic Operations with Decimals and Fractions:
Decimal:
1) When ADDING and SUBTRACTING decimals, you must line up the decimal
points and bring the decimal straight down into your sum or difference.
18.2 - 6.008 =
4,785 + 9 + 2.307
18.200
- 6.008
12.192
4,785
9
+
2 .307
4,796.307
2) When MULTIPLYING with decimals, the decimal points are irrelevant
until the very end. Multiply the numbers like normal and count the number
of digits that are behind the decimal point in each number. This is how
many places you move the decimal point in the product beginning at the end
of the number.
.2 × 6.03 = 1.206
3) When DIVIDING with decimals, move the decimal point to the end of the
divisor (the outside number) and move the decimal point the same number of
places in the dividend (the inside number). Divide like normal and bring the
decimal point straight up in the quotient.
Fractions
1) When ADDING and SUBTRACTING fractions, you must find a common
denominator and make equivalent fractions to the ones given.
Example with Borrowing:
2) When MULTIPLYING fractions, change all mixed numbers into improper
fractions, cross-cancel if possible, and then multiply straight across.
3) When DIVIDING fractions, KEEP it, CHANGE it, FLIP it.
3 2
3 5 15
÷
= × =
4 5
4 2
8
=
7
8
Converting Fractions ↔ Decimals
Fraction to Decimal – divide numerator by denominator
Change 5/8 into a decimal:
Decimal to Fraction – put the decimal number over the ending place value
Change .8 to a fraction in lowest terms.
Read it: .8 (eight tenths)
Write it: 8/10
Reduce it: 4/5
Change .09 to a fraction in lowest terms.
Read it: .09 (nine hundredths)
Write it: 9/100
***Any Repeating Decimal must be placed over 9!!***
Practice: On your Own!!
1) 5.36 + 9.1 =
2) 5
2
1
+3 =
5
4
3) 98.01 – 16.482 =
4) 9
1
2
– 6 =
8
3
5) 4.1 (2.3) =
6) 7
1
1
× 1 =
2
4
7) 62.4 ÷ 0.04 =
8) 12 ÷ 4 ½ =
Change each fraction into a decimal or each decimal into a fraction:
9)
5
=
8
11) 1.12 =
10) 9
8
=
9
12) 0.034 =
Ratios:
Ratio: a comparison of two numbers
Example:
6 boys and 8 girls
The ratio of boys to girls = 6:8 or 3:4
Rate: a comparison of different units
Ex: 150 miles in 3 hours
Unit Rate: when changing a rate into a unit rate, just divide!!
Ex: 15 inches per 5 hours = 3 inches per hour
Proportion: two ratios that are set equal to each other.
Practice: On your Own!!
Reduce each ratio (remember to have the same units):
1) 9 boys to 12 girls
2) 300 cars to 500 trucks
3) 8 inches to 3 feet
4) 1 pound to 20 ounces
Convert each to a UNIT RATE:
5) $81 for 3 shirts
6) 500 people in 4 rooms
7) 672 miles in 10 hours
Solve each proportion:
8)
3
x
=
8 12
9)
9 10
=
x 12
INTEGER RULES
 Adding with Same Signs –
add and keep the sign
 Adding with Different
Signs– subtract and keep
the sign of largest number
 Subtraction – Keep,
 Multiply or Divide with
Same Signs = Positive
 Multiply or Divide with
Different Signs = Negative
 Absolute Value – distance
from zero (always positive)
Change, Change (make it an
addition problems and
follow the addition rules)
Practice: Perform the operation
1) - 4 + 3 = ____
9) 300 ÷ (-100) = _______
2) -16 – (-8) = ______
10) |-2 × 4 - 3| = ______
3) 5 – (-2) = ______
11) -32 = ________
4) 16 + (-4) = ______
12) (-3)2 = ______
5) |-6| - |10| = ______
13) 4│-2 + 4│ = _____
6) -3 × -2 = _____
14) -2 × 3 – 6 = ____
7) 16 × (-2) = ______
8) -14 ÷ (-2) = ______