Can someone plz explain adding,subtracting fractions to me?

Question

like what r some of the rules. and what is the way to chang and mixed number into a improper fraction?

Answer 1

The rule is first change the fractions to have a common denominator, then just add (or subtract) the numerators.
Example: 3/4 + 1/8 = 6/8 + 1/8 = 7/8

To change a mixed numeral to a fraction, multiply the whole number part by the fractional part's denominator, then add the numerator to this. This will be the top of the improper fraction; the bottom stays the same as it was in the mixed numeral.
Example: 3 1/5 = (15 + 1)/5 = 16/5

Answer 2

I suggest be more aware of the 'invisible' things in mathematics expressions. To ease writings and for intuitive readings, we leave out many seemingly redundant items. However, when working with mathematics expression, if you really think that whatever you don't see are not there, many methods look like magic, or mere pattern transformation, and thus some will find it hard to remember or learn it by design their own non-mathematical rules but only to find many contradictions as they are expose to more mathematics rules.

Here, in a mixed number, e.g. 2 3/5, it looks like a single number, or single term. Actually, it is not, it is just a simplified way of writing 2 + 3/5. So, we don't 'change' 2 3/5 into an improper fraction, but we work out the answer of the expression '2 + 3/5' that involves two terms into a single term. My advice: forget about magical terms such as 'change' when learning maths, we re-express.

The term 3/5 can also be perceived as 3 x 1/5, while 2 as 2 x 1. 1/5 and 1 are two different quantities, or different objects, just as apple and orange. We can't answer the question of 3 apples + 2 oranges as 3+2=5 apples or 5 oranges. Similarly, we cannot add the numbers 2 and 3 because it is 2 ones and 3 1-fifths. Luckily, it is simpler in maths as we can re-expressed 2 ones in terms of a number of 1-fifths or 3 1-fifths in terms of a number of ones.

Using the first way, you will end up with an improper fraction, while the second way, hmmm... back to the mixed number or as a decimal expression.

So, since 2 = 2/1 = 2 x 1/1 = 2 x 5/5 = 10 / 5 = 10 1-fiths, 2 + 3/5 = 10 1-fifths + 3 1-fifths = 13 1-fifths = 13/5. (Notice the invisible division by 1, or multiply by 1 that is quite stupid to be written but be aware of their existence.)

Thus, slightly more complicated, or more general, is the case when none the denominator is a factor of another (in the above case, 1 is a factor of 5), e.g. 7/6 + 3/10. This is where you need to find a third number that has both 6 and 10 as factors. The most straightforward way is to multiply 6 and 10 to get 60, which will work and I prefer this method. However, a more ancient method, from the era without cheap calculators, people try to get a smallest of such numbers, and in this case, it is 30.

Using 60, we have 7/6 = (7x10)/(6x10) = 70 x (1/60), and 3/10 = (3x6)/(10x6) = 18 x (1/60), and the sum is (70+18) x (1/60) = 78 x (1/60) = 88/60 = 22/15

Using 30, we have 7/6 = (7x5)/(6x5) = 35 x (1/30), and 3/10 = (3x3)/(10x3) = 9 x (1/30), and the sum is (35 + 9) x (1/30) = 44 x (1/30) = 44/30 = 22/15

Thus, in the second method, you spent extra time to look for the smallest number having 6 and 10 as factors or usually called lowest common multiple aka LCM.

Answer 3

To change a mixed number into an improper fraction multiply the whole number by the denominator (bottom) and add it to the numerator (top).
The main rule is you can only add and subtract if the denominators (bottom) are the same. To do that multiply the fractions by some form of 1 (1/1,2/2...) until the denominators are the same.

Answer 4

Think of a dollar bill.

If you changed a one dollar bill into quarters, you would have 4 quarters. Each one of those quarters is 1/4 of the dollar bill. The 1 comes from 1 dollar and the 4 comes from dividing the dollar by 4. 100 divided by 4 equals 25.

If you changed a one dollar bill into dimes, you would have 10 dimes. Each one of those dimes is 1/10 of the dollar bill. The 1 comes from 1 dollar and the 10 comes from dividing the dollar by 10. If you had 5 dimes you would have 5/10 or 1/2 because 5 divides into 10 twice. You also know that 5 dimes equals 50 cents which is half of a dollar. You could also write it this way .50

Let's take the one dollar again and change it into nickels. A nickel is 5 cents and a dollar is 100 cents. Divide 100 cents by 5 cents and the answer is 20. So 1/5 of a dollar is 20 or written another way .20

Fractions are just a way of showing a piece of something. If your brother came home and chowed down half of the pie that was for dessert that night, you could write that he ate 1/2 of the pie. Or 50/100 because 50 divides into 100 twice so it would still be 1/2 which is called reducing a fraction.

Answer 5

To change a mixed number, you have to multiply the denominator and the integer, then add the numerator. Your new number will be what you get by doing that as the numerator and keep your denominator.
Only rule I can think to tell you is to always have like denominators and whatever you do to the denominator, be sure to do it to the numerator in order to keep it equal. Fractions are fun to work with.

Answer 6

let the fraction be a/b and c/d
addition a/b +c/d
first multiply the denominator ...becomes bd
multiply both fractions by bd/bd
then a/b becomes ad/bd
c/d becomes cb/bd
now you can add them (ad+cb)/bd ..eqn 1
if subtraction (ad-cb)/bd..eqn 2
let us now take a numeical example 2/3 and 1/4 i.e a=2, b=3, c=1, d=4
addition..eqn1..(2*4+1*3)/(3*4) = (8+3)/12 =11/12
subtraction...eqn 2..(2*4-1*3)/(3*4) = (8-3)/12 = 5/12