To change a mixed number to an improper fraction, you multiply the whole number by the denominator, and then add that number to the numerator. That number is the numerator of the improper fraction. The denominator stays the same.
Ex.: 4 2/3
to find the improper fraction, you first multiply 4 x 3= 12. Then you add the numerator to that.
12 + 2= 14. 14 is the new numerator!! So the improper fraction is 14/3.
To change an improper fraction to a mixed number, you have to figure out how many times the denominator goes into the numerator. The answer to that is the whole number. Anything left over in the numerator that the denominator couldn't go into is the the numerator of the fraction part. Once again, the denominator stays the same.
Ex.: 12/5. 5 goes into 12 two times. The two is the whole number. 5 x 2= 10, and since 12-10 is 2, two is the numerator of the fraction part. The denominator stay the same, so the mixed number is 2 2/5
Thursday, January 27, 2011
Subtracting Fractions
To subtract fractions you put the two fractions one over the other. If you have two mixed numbers you subtract the fraction part first then the whole number. If the two fractions have different denomenators you have to find the LCD (SEE VOCAB POST), of each fraction then subtract them. If the fraction on the bottom is bigger than the fraction on the top you have to borrow, by taking one whole from the whole number part of the mixed number. That whole number is the same two numbers as the numerator and the denominator. (the denominator is the same as the fraction part of the mixed number). You add that whole fraction to the current fraction to get the number that you can subtract. You then do the problem, and get your answer. You can also go into negatives, if the top fraction is greater than the lower. All you have to do is subtract the two fractions and get your negative number, then you subtract your two whole numbers. You take the negative number and subtract it from the answer you got from subtracting the two whole numbers and you get your answer.
Ex.: 4 3/7 - 3 6/7 if you borrow you take 1 (7/7) from the 4 and add it to 3/7 now your question is 3 10/7 - 3 6/7 you do 10/7 - 6/7 and get 4/7 then 3 - 3 which is 0 so your answer is 4/7
Ex.: 4 3/7 - 3 6/7 if you go into negatives you have to do 3/7 - 6/7 which is -3/7 then 4 - 3 is 1 so you subtract 3/7 from 1 (7/7) and get 4/7
Ex.: 4 3/7 - 3 6/7 if you borrow you take 1 (7/7) from the 4 and add it to 3/7 now your question is 3 10/7 - 3 6/7 you do 10/7 - 6/7 and get 4/7 then 3 - 3 which is 0 so your answer is 4/7
Ex.: 4 3/7 - 3 6/7 if you go into negatives you have to do 3/7 - 6/7 which is -3/7 then 4 - 3 is 1 so you subtract 3/7 from 1 (7/7) and get 4/7
Adding Fractions
To add fractions you find the LCD of the two fractions and then you add the numerator, remember DON'T ADD THE DENOMINATORS!!!! Then you simplify the fraction and put it in simplest form.
Ex.: To find the sum of 3/4 + 7/12 you find the LCD,
4's multiples: 4, 8, 12, 16, 20, 24
12's multiples: 12, 24, 36, 48
The LCD of 3/4 and 2/12 is 12 so 4 x 3 is 12 so you have to do the same thing with the numerator and 3 x 3 is 9 so 3/4 becomes 9/12 and 2/ 12 stays the same because 12 x 1 is 12 and 2 x 1 is 2 and you addition problem becomes 9/12 + 2/12. To add it you only add the numerators and you keep the denominators the same. So you add the numerators, 9 + 2 = 11 and the denominators stay the same so the answer is 11/12.
Ex.: To find the sum of 3/4 + 7/12 you find the LCD,
4's multiples: 4, 8, 12, 16, 20, 24
12's multiples: 12, 24, 36, 48
The LCD of 3/4 and 2/12 is 12 so 4 x 3 is 12 so you have to do the same thing with the numerator and 3 x 3 is 9 so 3/4 becomes 9/12 and 2/ 12 stays the same because 12 x 1 is 12 and 2 x 1 is 2 and you addition problem becomes 9/12 + 2/12. To add it you only add the numerators and you keep the denominators the same. So you add the numerators, 9 + 2 = 11 and the denominators stay the same so the answer is 11/12.
Multiplying fractions
To multiply fractions, you do NOT need to find a common denominator (LCD- see vocab), but you must change any mixed number to an improper fractions (see post about this topic). To start, cross factor if possible (see post below), then multiply the denominators to get the BOTTOM number of the product, then multiply the numerators to get the TOP number of the product. Then simplify, and if you have an improper fraction (see vocab), then you change it to a mixed number (see vocab AGAIN)
Ex.: 3/7 x 4/8
first, you multiply 8 x 7 = 56,
then you multiply 3 x 4= 12.
The product is 12/56. Then simplify to get: 6/28
Ex.: 3/7 x 4/8
first, you multiply 8 x 7 = 56,
then you multiply 3 x 4= 12.
The product is 12/56. Then simplify to get: 6/28
Wednesday, January 26, 2011
Cross Factoring
When you are going to multiply or divide two fractions, if the numerator of one and the denominator of the other have a common factor, then you change those numbers to the number of times the factor goes into that part of the fraction (numerator or denominator.) Make sure to change both common numbers!
Ex.: in the problem 5/8 x 4/10 the numerator of 5/8 (5) and the denominator of 4/10 (10) have a common factor (5) and vice-versa so you can change the 5 in 5/8 to a 1 because 5 goes into 5 once and the 10 in 4/10 has to become a 2 because 5 goes into 10 twice.Your problem then becomes 1/8 x 4/2 you can do the same things with the 8 from 1/8 (it becomes a 2) and the 4 in 4/2 (it becomes a 1) your problem becomes 1/2 x 1/2 which equals 1/4 . If you hadn't cross factored you would have had to do 5/8 x 4/10 which equals 20/80 which eventually simplifies to 1/4 but it would take a lot longer!!!
Dividing Fractions
To divide fractions, you have to keep the first fraction, change the division sign to a multiplication sign, and use the last fraction's reciprocal (flip) (SEE VOCAB POST), cross factor if possible (SEE POST ABOVE) then do the easy, multiplication problem. Be sure to simplify the product.
EASY TRICK: KCF (keep, change, flip). see above...
Ex.: 5/7 divided by 2/6
is the same as:
5/7 x 6/2= 30/14 = 2 2/14 = 2 1/7 (to learn to change improper fraction to a mixed number or vise versa see a post above)
EASY TRICK: KCF (keep, change, flip). see above...
Ex.: 5/7 divided by 2/6
is the same as:
5/7 x 6/2= 30/14 = 2 2/14 = 2 1/7 (to learn to change improper fraction to a mixed number or vise versa see a post above)
Vocab
reciprocal- the fraction's flipped value. Ex.: 2/3's reciprocal is 3/2
value- how much the number is, or represents.
numerator- number on TOP of the fraction. Ex.: in the fraction 2/3, 2 is the numerator
denominator- number on the BOTTOM of a fraction. Ex.: in 2/3, 3 is the denominator
LCD (least common denominator)- when you are adding or subtracting fractions, you must
change the two denominators to match, so you find the smallest
common multiple between those denominators to use in the place
of the numbers. Remember to change the numerators, too, in the
same way as you changed the denominators.
improper fractions- a fraction where the top number is bigger than the bottom. In other words,
its a whole number, or more, changed into a fraction. Ex.: 4/3
mixed numbers- a whole number and a fraction, put together side by side. Ex.: 4 2/3
simplify- to keep the value of a fraction, but changing it to smaller numbers.
simplest form- to simplify a fraction so it's as small as possible.
equivalent - two fractions that are equal but have different numbers.
value- how much the number is, or represents.
numerator- number on TOP of the fraction. Ex.: in the fraction 2/3, 2 is the numerator
denominator- number on the BOTTOM of a fraction. Ex.: in 2/3, 3 is the denominator
LCD (least common denominator)- when you are adding or subtracting fractions, you must
change the two denominators to match, so you find the smallest
common multiple between those denominators to use in the place
of the numbers. Remember to change the numerators, too, in the
same way as you changed the denominators.
improper fractions- a fraction where the top number is bigger than the bottom. In other words,
its a whole number, or more, changed into a fraction. Ex.: 4/3
mixed numbers- a whole number and a fraction, put together side by side. Ex.: 4 2/3
simplify- to keep the value of a fraction, but changing it to smaller numbers.
simplest form- to simplify a fraction so it's as small as possible.
equivalent - two fractions that are equal but have different numbers.
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