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|| PRE-ALGEBRA ||
|| COMMON DENOMINATORS ||
FOR AGES 10 AND 11
POINTS TO REMEMBER :
You can not compare apple with orange. You can compare apple with apple or orange with orange.
If you want to compare heights of two kids standing on platforms of two different levels you may be miss guided. For correct answer, both kids have to be on the same level.
Same principle applies in addition or subtraction of fractions from fractions.
* Base, i.e denominators, of all the fractions in an addition or subtraction problem have to be the same or common.
For example:
| 1 | 3 | |
| -- | + | -- |
| 2 | 8 |
Both fractions have different bases. i.e. different denominators.
Let us make both denominators common and rewrite the equation.
| 4 | 3 | |
| -- | + | -- |
| 8 | 8 |
Now, we can add numerators of both fractions with similar base.
The answer will be 7/8.
** If a fraction has the same numerator and denominator it equals to 1.
For Example:
| 3 | ||
| -- | = | 1 |
| 3 |
*** Therefore, multiplying the fraction by another fraction having same numerator and denominator would not change the value.
For Example:
| 3 | 3 | 2 | 6 | |||
| -- | = | -- | x | -- | = | -- |
| 5 | 5 | 2 | 10 |
Example:
Problem:
| 1 | 2 | |
| -- | + | -- |
| 2 | 3 |
Solution:
First, find out the common denominator (LCD) of both the fractions. Then make both the denominators equal to this number (LCD).
The LCM of 2 and 3 is 6. To make both the denominators 6 multiply 2 by 3 and 3 by 2.
Same way you have to multiply the numerator of the first fraction by 3 and the numerator of the second fraction by 2 to keep the value of the fraction same.
Once the denominators are same you can add the fractions
| 1x3 | 2x2 | 3 | 4 | 7 | ||||
| -- | + | -- | = | -- | + | -- | = | -- |
| 2x3 | 3x2 | 6 | 6 | 6 |
The answer is 7/6. You cannot reduce this fraction.
So the final answer is 7/6.
7/6 is an improper fraction. If you want to change it into a mixed number then, the answer will be 1 and 1/6.
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