Transcript Basic Math Review PP 1

Basic Math Review
Ms. Ryan
Medical Math
MCATC
2015-2016
Addition & Subtraction
• Keep all the numbers in aligned when adding
• Line up the decimals
• Touch math
Multiplication
• Times tables fact sheet-Memorize
• Easier to do vertical than horizontal
22 instead of 22 X 2 =
X 2
• Keep the numbers lined up
• Do not have to line up decimals
• Count decimal places after the problem is
solved
Division
• Opposite of multiplication
• Easier to set the problem up using the
“house”
instead of the ÷
• When dealing with decimals remember
– If it’s in the house raise it to the roof
– If it’s to the side slide
• 100 ÷ 50 means 100 inside the house and 50
outside the house
Rounding
• To the nearest whole number
– 8.51796 = 9
• To the nearest tenth
– 8.51796 = 8.52
• To the nearest hundredth
– 8.51796 = 8.518
Fractions
• The numerator is the
top number of the
fraction
• The denominator is the
bottom number of the
fraction
• Improper fractions are
usually converted to
“mixed numbers”
• Proper fractions mean
the numerator is
smaller than the
denominator
• ½, ¾ are proper
fractions
• Improper fractions
mean the denominator
is larger than the
numerator such as 6/5
Adding Fractions
• When the denominators are the same you add straight
across:
• 1/4 + 2/4 = ¾
• The numerator changes and denominator stays the same
• When the denominators are different you must find the
least common denominator:
• ¼ + 1/8 = ?
• What is the LCD of 4 & 8? It is 8 (because 8 is a multiple
of 4 and 8).
• What do you have to do to make ¼ have 8 as
denominator?
ADDING FRACTIONS CONT.
• Multiply the numerator and denominator by
the same number: 1 x 2 = 2
2x4=8
• Now you can add the fractions straight across:
1/8 + 2/8 = 3/8
Subtracting
Fractions
• Basically the same as
addition
• 3/5 – 1/5 = 2/5
• If denominators are
different find least
common denominator
• 2/3 – ¼ = ?
• LCD is 12
• Must multiply numerator
and denominator of each
fraction to get LCD
•
•
2𝑥4
8
=
3 𝑥 4 12
1𝑥3
3
=
4𝑥3
12
• Now the problem says:
• 8/12 – 3/12 = 5/12
Reducing Fractions or
Putting in Simplest Form
• To get a common
(proper) fraction into
lowest terms divide the
numerator and
denominator by the
same number
• 12/15 =
12 ÷3
15 ÷3
=4/5
• To change an improper
fraction to lowest terms
you must change to a
mixed number
• 6/5 = 6÷ 5 = 1
• 7/5 = 7÷ 5 = 1
1
5
2
5
Multiplication & Division of Fractions
• Multiply the
numerator straight
across
• Multiply the
denominator straight
across
•
3
5
3
4
x =
3𝑥3
5𝑥4
=
9
20
•
3
5
3
÷
4
• Invert the second
3
4
fraction from to
4
3
• Then set the problem
up for multiplication
•
3
5
4
3
x =
12
15
• Reduce to simplest form
•
12 ÷3
15 ÷3
=
4
5
Multiplication of Mixed Numbers
• Common fractions can
be multiplied straight
across but mixed
numbers can not
• 7 1/3 x 5/8 = ?
• First change the mixed
number to a fraction
• 7 1/3 =
3 𝑥 7 +1
3
= 22/3
• Now you can multiply
22 𝑥 5
22/3 x 5/8 =
=
3𝑥8
110/24
• Now you must reduce the
number
• 110 ÷ 24 = 4
14
24
=4
7
12
Division of Mixed Numbers
• 7
•
•
1
3
5
÷
8
=?
1
22
Change 7 to
3
3
5
8
Invert to
8
5
• Set up the problem for
multiplication
•
22
3
x
8 176
=
5 15
= 11
11
15
Decimals
• A decimal is actually a
fraction in which only
the numerator is
written
• The placement of the
decimal point is used to
indicate the multiple of
10 in the denominator
• 0.1
0.33
+0.017
0.447
Decimals
• To perform math operations terms
must be in the same system
• Decimal = common fraction 0.0011
11
=
10,000
5
• Common fraction = decimal = 5 ÷
8
8 = 0.625
• Divide the numerator by the
denominator
• When adding or subtracting
decimals line the decimal points up
•
0.70
-0.56
0.14
• 0.849 Count the number
x 0.62 of places to right of
0.52638 the decimal for each
multiplier and mark off in
answer starting at the right
• When dividing use long division.
If divisor has decimal point move
all the way to the right. Then
move the decimal point of
dividend the same number of
places to right.
16.8 ÷ 0.12 = 140
Percents
• The symbol % means per hundred
• To convert percent to a decimal move the decimal point 2
place to the left and drop the percent sign
• 50% = 0.50 or 0.5
• 12.5% = 0.125
• To convert decimal to percent move decimal point 2 places
to the right and add the percent sign
• 0.5 = 50%
• 0.125 = 12.5%
• To convert a percent to a fraction use the number given in
% as numerator and 100 as the denominator
• 50% =
50
100
Percents
• To convert a percent with a decimal in it to a
proper fraction first convert to an equivalent non
decimal fraction by multiplying the numerator
and denominator by 10
12.5
100
12.5 𝑥 10
100 𝑥 10
125
1000
• 12.5% =
=
=
• Then reduce to simplest form
125
125 ÷125
=
1000 1000 ÷125
1
8
•
=
• For a proper fraction to a % covert the fraction to
a decimal, then convert the decimal to a %
•
1
4
= 1 ÷ 4 = 0.25 move decimal 2 places to the
right to change to % so it becomes 25%