Math Tips
Reducing a Fraction
When working with fractions, make sure your answer is expressed in its
lowest terms. That is, both the numerator and the denominator are reduced
to the lowest number possible. This means that there is no number, except
1, that can be divided evenly into both the numerator and the denominator.
For example, if you have the fraction 6/12, you can reduce it by dividing
both the numerator and denominator by 3. Then, 6/12 = 2/4. However
you always need to check and see if you can reduce the fraction even
further. In this case, you could further reduce the fraction by dividing by 2.
Then, 2/4 = ½. Now the fraction is in its lowest terms. If possible, try to
pick the largest number to divide by to reduce the number of steps to a
minimum. In our example of 6/12, if you recognize that the highest number
you could divide both parts of the fraction by is 6, you can immediately end
up with the final answer 6/12 = ½.
Adding and Subtracting Fractions
To add or subtract fractions, each fraction must have the same denominator
(i.e. the same number in the bottom of the fraction.) If they are the same,
you then simply add or subtract the top numbers (the numerators).
3/7 + 2/7 = 5/7
8/9 – 1/9 = 7/9
If the denominators are different, you must find the lowest common
denominator (LCD.) The LCD is the smallest number that is divisible by the
denominator of each fraction. Once you determine the LCD, you multiply the
top and the bottom by the number that will make the denominator of the
fraction equal to the LCD. For an addition problem, you then add the two
numerators (i.e. numbers in the top) and put that sum over the LCD.
Example: 2/3 + 1/4 = ?
These fractions have different denominators (3 and 4.) The smallest number
that 3 and 4 can evenly divide into is 12, so the LCD is 12. To make the
denominator of the first fraction equal to 12, multiply the bottom of the
fraction by 4. You also have to multiply the top number by 4.
So 2/3 = 8/12
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Now convert the second fraction. To make the denominator of the second
fraction equal to 12, multiply the top and the bottom of the fraction by 3:
¼ = 3/12
Now just add the top numbers together. 8/12 + 3/12 = 11/12
Here is an example of subtracting fractions
The smallest number both 2 and 15 can
divide into is 30. So 30 is the LCD
To make the denominator of the first fraction equal to 30, multiply the top
and bottom of the fraction by 15.
½ = 15/30
So
Now convert the second fraction. To make the denominator of the second
fraction equal to 30, multiply the top and the bottom of the fraction by 2.
So 2/15 = 4/30.
Now just subtract the top numbers.
15/30 – 4/30 = 11/30
Bottom Line: To add or subtract fractions, the denominators must be the
same. Also, remember to reduce the answer to its lowest terms
Multiplying and Dividing Fractions
To multiply fractions, simply multiply across the top and across the bottom
of the fractions.
To divide fractions, take the reciprocal of the second fraction (i.e. “flip” the
second fraction) and multiply it by the first.
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Convert a Mixed Number to a Fraction
A mixed number contains a whole number and a fraction e.g. 2 ¾.
To convert a mixed number to a fraction, follow these steps:
•Multiply the whole number part by the fraction's denominator. e.g. for
2 ¾, multiple 2 times 4 = 8
• Add that number to the numerator (in our example add 8 to 3 = 11)
•Then write the result on top of the denominator. (in our example, it is
11/4). So 2 ¾ = 11/4
Converting an Improper Fraction to a Mixed Number.
An improper fraction is a fraction whose numerator is larger than the
denominator e.g. 11/4.
To convert the fraction to a mixed number:
•Divide the numerator by the denominator (in the example 11/4, divide 11
by 4).
•Write down the whole number answer (in our example, 2)
•Then write down any remainder above the denominator. (in our example,
we have a remainder of 3, so we get ¾)
So 11/4 becomes 2 ¾
Multiplying Decimal Numbers
Multiply the numbers, ignoring the decimal points. For example, assume the
problem is .03 x 1.1. Ignore the decimal point so you have 3 x 11 = 33.
In the answer, you now reinsert the decimal point. You will need as many
decimal places as the two original numbers combined. In the example .03 x
1.1, there are three decimal places. Therefore, in the answer 33, you insert
3 decimal places, which makes the answer .033
Dividing a Decimal Number by a Whole Number
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To divide a decimal number by a whole number, you first divide normally,
ignoring the decimal point. For example, 4.08 ÷ 8
8
51
4.08
Next you insert the decimal point directly above the decimal point in the
problem. In the example, the answer then is .51
Dividing a Decimal Number by a Decimal Number
The first step is to move the decimal point so that you are dividing by a
whole number. For example, 8.14 ÷ .2
In this problem, you would
change .2 to 2
Once you move the decimal point in the divisor, you must also move the
decimal point in the number you are dividing. Move the decimal point the
same number of positions. In our example of 8.14 ÷ .2, we moved the
decimal point one position to change .2 to 2. So we now have to move the
decimal point in 8.14 one position so the number is now 81.4.
Next you divide normally, ignore the decimal point.
407
2 81.4
The final step is to insert the decimal point in the answer directly above the
decimal point in the problem. In the example, the answer then becomes
40.7
Converting a Percent to a Decimal
Move the decimal point two places to the left and remove the “%” sign.
Examples:
21% = .21
123% = 1.23
.53% = .0053
Convert a Decimal to a Percent
Move the decimal point two positions to the right and add the % sign.
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Examples:
.35 = 35%
7.5 = 750%
.0082 = .82%
Converting a Fraction to a Decimal
Divide the numerator (the top number) by the denominator (the bottom
number)
Example: 2/5 = 2 divided by 5 = .4
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