Download Fraction Computation Notes

Fraction Computation Notes
Addition:
1. Make sure to convert all fractions to have common denominators. Make sure to adjust all numerators by the
appropriate factor also.
2. DO NOT ADJUST THE WHOLE NUMBERS!!!!(Don’t convert mixed numbers into improper fractions!!!)
3. Add the numerators of all fractions, while keeping the common denominator. Add the whole numbers if
applicable.
4. Simplify your fraction: reduce if proper; divide if improper to get a mixed number.
5. Add the whole numbers together, if applicable
1
3
EX: 5  2
3
4
9
13
1
 5 2 7  8
4
12 12 12
12
Subtraction:
1. Make sure to convert all fractions to have common denominators. Make sure to adjust all numerators by the
appropriate factor also.
2. If you can subtract the fractions do so, along with the whole numbers.
3. If you cannot subtract the fractions, rename one whole thing into a fraction by using the common denominator
and add it to the existing fraction.
EX: 5 ¼ - 3 ¾ becomes 4 +
4
5
2
1
+ ¼; therefore the problem is now 4 - 3 ¾ which equals 1 or 1
4
4
4
2
4. If there was no existing fraction to add onto the renaming, just subtract.
EX: 5 - 3 ¾ becomes (4 +
4
4
1
) - 3 ¾ ; therefore the problem is now 4 - 3 ¾ which equals 1
4
4
4
Multiplication:
1.
2.
3.
4.
Convert all mixed numbers and whole numbers into improper fractions.
Look to simplify any numerator with any denominator before multiplying.
Multiply the remaining numerators together, as well as the existing denominators.
If the answer is an improper fraction, divide and reduce. If already proper make sure it is reduced to lowest
terms.
EX: 2
2
8 9 8 3
x 9  x  x  24
3
3 1 1 1
EX: 4
1 7 9 7 3 7 21
1
x  x  x  2
2 15 2 15 2 5 10
10
Division:
1.
2.
3.
4.
Convert all mixed numbers and whole numbers into improper fractions.
Convert the second fraction (divisor) to its reciprocal. (Flip it over!)
Multiply the remaining numerators together, as well as the existing denominators.
If the answer is an improper fraction, divide and reduce. If already proper make sure it is reduced to lowest
terms.
2
3
EX: 2  9 
8 9 8 1 8
  x 
3 1 3 9 27
1 7 9 7 9 16 9 8 72
2
   x  x 
 10
2 16 2 16 2 7 1 7
7
7
EX: 4 
Decimal Computation Rules
Addition and Subtraction:
1. Make sure each number has a decimal point (whole numbers have it following the one’s place: 5.).
2. Line up the decimal points and place zeroes (optional for addition) in place values to line up all place values.
3. Add or subtract as you would whole numbers. Place the decimal point in the answer I n line with the other
decimal points.
EX: 4 + 6.2 + .36
4.00
6.20
+ .36
10.56
EX: 23 – 4.59
23.00
4.59
18.41
Multiplication of decimals:
1. There is no need to line up decimal place values or add zeroes to any number before multiplying.
2. Multiply the number as you would whole numbers (ignore the decimal points).
3. Count how many decimal place values there are total in the factors.
4. Place that many decimal place values in the answer.
EX: .24 x 1.2 = 24 x 12 = 288, 3 total decimal place values in .24 x 1.2 so the answer becomes .288
EX: .0004 x 6 = 4 x 6 = 24, 4 total decimal place values in .0004 and none in 6, so the answer is .0024 (notice
added zeroes to hold place values).
Division of Decimals:
1. There are two types of problems encountered: dividing by a whole number or dividing by a decimal.
2. Dividing by a whole number is simple. Just divide as normal and bring the decimal point straight up in your
answer.
.62
EX: 2.48 ÷ 4 = 4 ) 2.48
3. Dividing by decimal causes us to multiply each number by the appropriate power of ten before dividing, (or
moving the decimal point to the right the same number of places in each number )so the divisor is a whole
number. Then proceed as dividing whole numbers above.
EX: 2.48 ÷ .4 causes each number to be multiplied by 10 resulting in 24.8 ÷ 4.
EX: 24.8 ÷ .004 causes each number to be multiplied by 1000 resulting in 24,800 ÷ 4.