Fractions, like decimals, represent part of a whole. They have 2 parts, the numerator and the denominator. The denominator tells you how many pieces the whole has been cut into. The numerator tells you how many pieces of that whole that you have or is left. You have covered fractions in the lower grades, but just to be sure that you remember, we will go over the basics again in 7th grade.
Finding a common denominator
When adding, subtracting, or comparing fractions, you have to have a common denominator. This means finding the lowest common multiple of ALL the denominators and converting the fractions:
These two fractions do not have common denominators, so one has to be found in order to put them together. (Otherwise, its like adding apples and oranges.)
To find a common denominator, list the multiples of both current denominators and find the lowest one that matches. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 Multiples of 7: 7, 14, 21, 28, 35, 42 28 is a multiple for both 4 and 7, so we will use that as a common denominator. Remember when changing to a common denominator, you have multiply the numerator and denominator by the same number to keep the fraction equivalent. Now that you have common denominators you can add them together. (Its adding apples and apples now!) |
Converting Mixed Numbers to Fractions
One skills that you need to have in order to solve many fraction based problems is the ability to change a mixed number into a fraction. Once the mixed number has been changed into a fraction format, you can use the new fraction to perform the operation required.
Mixed numbers to fractions
1. Multiply the denominator times the whole number. 2. Add your answer from step 1 to the numerator. 3. Keep the same denominator and use the answer from step 2 as your numerator. Converting Whole Numbers to FractionsTo convert a whole number to a fraction, simply place the whole number over 1.
After that, you may convert the new fraction to any denominator you choose by simply multiplying both numerator and denominator by the same number to create an equivalent fraction. |
Adding Fractions
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When adding fractions, make sure you have a common denominator for the fractions. After that, just add the numerators and keep the denominator the same.
One thing to remember about fractions, you always have to simplify!
One thing to remember about fractions, you always have to simplify!
Subtracting Fractions
![Picture](/uploads/2/0/1/1/20114429/4399090.jpg)
Subtracting fractions works much in the same way that adding fractions work. You must have a common denominator for both fractions. After that, simply subtract the numerators and keep the denominator the same.
Again, when working with fractions, always remember to simplify!
Again, when working with fractions, always remember to simplify!
Multiplying Fractions
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Multiplying fractions is fairly easy. Simply multiply the numerators together and the denominators together to get your new numerator and denominator, like below:
When working with fractions, always remember to SIMPLIFY!!!
Dividing Fractions
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Dividing fractions means cutting a part of a whole into pieces. While it can look kind of complicated, once you know the rules, it is fairly simple. When dividing fractions, you can choose the much easier option of multiplying by a reciprocal. A reciprocal basically means the opposite of a number. In the case of a fraction, you flip the fraction upside down. So what was 2/5 becomes 5/2. Then you have a much easier multiplication problem that looks like:
Now we can simply apply the rules for multiplying fractions that we talked about above.
And, as always when working with fractions, remember to SIMPLIFY!!!