Whole Numbers
ADDITION:
SUBTRACTION:
MULTIPLICATION:
DIVISION:
PLUS
MINUS
MULTIPLY
DIVIDE DIVIDED BY
TOTAL
DECREASED BY
TIMES
DIVIDED INTO
INCREASED BY
SUBTRACTED FROM
MULTIPLIED BY
QUOTIENT
ADDED TO
DIFFERENCE
TWICE
÷
SUM OF
LESS THAN
PRODUCT OF
MORE THAN
-
X
+
Decimals
ADDITION:
Decimal is to the right of whole #
8, 3.2, 56.8
Line up the decimals
8.
3.2
+ 56.8
Add
Drop the decimals down
MULTIPLICATION:
DIVISION:
Multiply first
If dividing by a whole # …
Count total # of decimal places
Decimal point goes above decimal in problem
.
14 42.28
In answer, count right to left the # of decimal
places
68.0
SUBTRACTION:
8 15
Decimal is to the right of the whole #
69.5
- 32.6
Line up the decimals
Cannot divide by a decimal so…
.42
x .6
move decimal right in both places (inside & out)
.252
.
.6 8 .6
.
6 86.
=
36.9
Subtract
Drop the decimals down
Fractions
ADDITION:
MULTIPLY:
DIVIDE:
Put whole numbers over /1
Put whole numbers over /1
Change mixed numbers to improper fractions
Change mixed numbers to improper fraction
Cross cancel
Flip the right numbers
Multiply across the top numerators
Cross cancel
Find the common denominator
Multiply across the bottom denominators
Multiply across the top numerators
Subtract
Reduce
Multiply across the bottom denominators
Find the common denominator
Add top fraction numbers
Reduce
Add whole numbers
SUBTRACTION:
9
12
1
12
4 34
1
+ 8 12
12 10
12 56
12 =
If bottom fraction is larger…
Borrow 1 from the whole #
Make a fraction (look at
denominator)
Add the top numbers together
If there is no top fraction…
Borrow 1 from the whole #
Make a fraction (look at
denominator)
16 83 = 15 88 + 83 = 15 11
8
−9
5
8
= −9
5
8
= −9
5
8
8 × 2 14 =
28
1
×
9
4
=
18
1
Reduce
= 18
7 ÷ 4 15 =
1
14 = 13 44
− 5 34 = − 5 34
6 86 = 6 34
1 r 2
3
5
3
8 14
2
7
1
1 7
1
÷
×
21
5
5
21
3
=
=
5
3
= 1 23
PERCENTS
MEASUREMENTS AND FORMULAS
is
of
Set up the formula:
=
%
100
12 inches
3 feet
1 yard
16 ounces
12 months
52 weeks
Cross multiply.
Divide the number with the x into both sides.
exs.
1. What % of 50 is 12?
12
50
2.
3.
=
x
100
50 x = 1200
25% of what is 40?
40
25
= 100
25 x
x
= 4000
50 x
50
=
1200
50
x = 24
25 x
25
=
4000
25
x = 160
=
20
100
100 x
100
100 x = 1800
=
1800
100
D =T ×S
T = D÷S
S = D ÷T
A = L ×W
MPG = D ÷ gal
2000 lbs.
454 grams
5280 feet
2.2 lbs.
100 cm
1000 mm
=
=
=
=
=
=
1 ton
1 lb.
1 mile
1 kilogram
1m
1m
(Distance = Time x Speed)
(Time = Distance ÷ Speed)
(Speed = Distance ÷ Time)
(Area = Length x Width)
(Miles/gal = Distance ÷ gallons)
x = 18
SAMPLES:
REDUCING
1)
5 Reduce by 5.
...0
1)
15
100
=
3
20
2)
25 or 50 or 75 Reduce by 25.
100
100
100
2)
75
100
=
3
4
3) ..0 Reduce by dropping the 0 on each row.
...0
3)
30
100
= 103
4)
12
14
4)
1 foot
1 yard
36 inches
1 pound
1 year
1 year
P = Sum of all sides.
20% of 60 is what?
x
60
=
=
=
=
=
=
even on the top
Reduce by 2.
even on the bottom
=
6
7
FRACTIONS/DECIMALS/PERCENTS
Fractions into decimals:
Divide the bottom into the top.
ROUNDING
1
4
=?
.25
4 1.00
Decimals into percents:
Move the decimal right 2 places. Add a % sign.
.75 = ?
.75 = 75%
Round to tens:
Percents into decimals:
Move the decimal left 2 places. Drop the % sign.
30% = ?
Find the place value.
Look at the number to the right:
If the number is 5 or more, increase the place value by 1.
If the number is less than 5, leave the place value the same.
Fill in 0's to the right of the place value.
30% = .30
53,498
53,498
8 is more than 5, so add 1 to the 9 (tens place). Since it
increases to 10, we carry the 1.
Decimals into fractions:
Count the places after the decimal. Put the number on top and reduce.
235
47
.235 = ? .235 = 1000
= 200
tenths
hundredths
We get 53,500.
thousandths
STATISTICS
DIVISIBILITY
2
3
4
5
6
8
9
10
even
sum of digits divisible by 3
last two digits divisible by 4
ends in 5 or 0
divisible by 2 and 3
last three digits divisible by 8
sum of digits divisible by 9
ends in 0
Mean
Median
Mode
Range
Probability of an Event
Odds in Favor
Odds Against
Percent Increase/Decrease
n!
average
middle number
most often
big - small
good/total
good : bad
bad : good
(change/original)x100
n(n − 1)(n − 2) . . . 3 ⋅ 2 ⋅ 1