EXAMPLE PROBLEMS
Section
5) Reducing Fractions : (find the biggest number that can go into both the
top and bottom number, or just start
with any number that will go into both and continue to simplify until it can’t
be reduced anymore)
Example 1: 
( divide top and bottom by
2) 
, (it can still be reduced, divide by 2)
It will continue to reduce to 
, which is the
answer.
Or we could have divided both the top and bottom by 16 to begin with since 16
goes into itself
and into 64 evenly;
Answer =
Example 2: 
(This is an improper
fraction, meaning the top #, the numerator , is greater than or equal
to the bottom #, the denominator. This will reduce into a mixed number)
(4 goes into 9 only two times equaling 8.
And 9 – 8 equals 1) 
(We are left with a remainder 1; put the 1 on the 4 = ¼)
Answer = 
Example 3: 
( Change a mixed number
to an improper fraction. Start first by multiplying
the whole number ‘3’ by the denominator ‘4’ and then add that
number to the
numerator ‘1’. So we get --- 
Answer = 
There a 3 types of fractions:
Normal =
Improper =
Mixed number (whole number and a normal fraction) =
6) Adding and subtracting fractions : (Before adding
or subtracting we must make sure the
denominators are the same )
Example 1: 
First
change denominator to be equal = 
Now just add the numerators 
Answer: 
Example 2: 
Again
first get equal denominators, both 3 and 4 can go into 12, so
multiply each fraction by the number that will make their denominators equal to
12.
and 
now
subtract
Answer: 
7) Multiplying and dividing fractions: (When multiplying, just
multiply straight across and reduce.
When dividing, flip the second fraction, change sign to a multiplication
sign, then multiply and reduce.)
Example 1: 
= multiply straight across
now reduce, =
Answer:
Example 2: 
= flip second fraction and
change sign = 
multiply =
and
reduce =
Answer:
Example 3: 
= first change the mixed
number to an improper fraction = 
now
multiply and change back to mixed number 
Answer: 
10) Decimals: (Adding, subtracting, multiplying and
dividing decimals.)
Example 1: 4.2 – 0.64
(when subtracting or adding just line up the decimals, add any zeros if
necessary , and just add or subtract)
Answer:
Example 2: 4.2 × 0.64
(Count the number of places behind the decimals, ‘3’, remember that
number, then just multiply like normal and add the decimal back in the
number of places you counted before, ‘3’)
2688 - now move the
decimal to the left ‘3’ spaces = 2.688
Answer: 2.688
Example 3: 4.2 ÷ 0.64
(We can’t divide by a decimal, so first move the decimal to the right as
many spaces as needed to get rid of the decimal for the number we’re
dividing by ‘.64’. We must then move the decimal on the other number,
‘4.2’ to the right just as many times as we moved the decimal on the
first number ‘.64’)
(We move the decimal on the .64 to the right 2 times to get rid of the
decimal. We must also move the decimal on the 4.2 to the right 2 times)
Answer: 6.5625
13) Percents: (percents can be solved a number of
different ways ; here we will just show a few)
- Tip 1: of stands for ‘multiplication’ and is stands for
‘=’
- Tip 2: Change % to decimal – move % sign twice to the left:
30% = .3
Change decimal to % - move decimal twice to the right: 1.34 = 134%
Example 1: 41% of 320 is?
(Tip 1: Write the problem out as fol lows : 41% × 320 =?
Tip 2: Change the percent to a decimal and multiply: .41 × 320 =?
- Count all spaces behind the decimal ‘2’, multiply, and move
the decimal to the left that many spaces in the final answer.
Answer: = 131.2
Example 2: 30% of what number is 45?
- rewrite the problem out: .3 × ? = 45
- divide both sides by .
--- .3s cancel out on
the left hand side, and we’re
left with: 
---- now divide
= move the decimals and divide
Answer: 150
Example 3: What percent of 60 is 15?
- rewrite the problem out: ?% × 60 = 15
- divide both sides by 60:
--- 60’s on left hand side cancel out and
that
gives us: 
--- now divide =
change decimal to a % = 25%
Answer: 25%
