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how do you multiply fractions?

I would like to know how to multiply / divide, and add / subtract fractions please

3 Answers by Expert Tutors

Erik S. | Math is the best subject in which I have ever tutoredMath is the best subject in which I have...
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How to add or subtract fractions:

1.  Look at the denominators.  Are they the same or are they different?

2.  If they are different, then that means each fraction is divided into different numbers of equal parts -- so different that you won't know how many equal parts you will end up with when you add or subtract.  That's why the denominators have to be the same.

3.  To make the denominators the same, you must determine the least common denominator of the two fractions.

4.  Then you divide it by the denominator of one fraction to determine by which number to multiply both the numerator and the denominator of that fraction and thereby change it without affecting the value.  For example, when you multiply 1/2 by 2/2 (i.e. 1/2 * 2/2), you will get 2/4.  However, you will not have a different value because you will have multiplied 1/2 by a fraction that's equivalent to 1 when the numerator is the same as the denominator.

5.  Repeat step 4 with the other fraction.

6.  Now that the denominators of both fractions are the same, you finally know how many equal parts you will end up with when you add or subtract.  So you can perform either one of those operations with the new numerators of both fractions, but you keep the denominator since that denotes the number of equal parts.

How to multiply fractions:

1.  You multiply both the numerators and the denominators.  If you don't understand how this works, I will explain in further steps with an example.

2.  Here's what fraction multiplication looks like: (2/3)*(4/5).

3.  2 is the numerator of the first fraction, and 3 is the denominator of that fraction.  The denominator means into how many equal parts the whole is divided, and the numerator means how many of those equal parts are visible.  Therefore, 2 out of all 3 equal parts are visible.

4.  Now, you can divide the whole into further equal parts by multiplying both the numerator and the denominator by any number you want.  That is to say, you can divide each of 3 equal parts into 5 equal parts so that the final number of equal parts of the entire whole will be 3*5=15 to make the final denominator of the fraction product.

5.  Now, since only 2 equal parts out of 3 were visible, and each of those 3 equal parts was divided into 5, each of those 2 visible equal parts had to be divided into 5 so that we can take a certain number out of each of the 2 groups of 5 equal parts, and that is 4 according to the numerator of the second fraction.  This is how you multiply the numerators of the fractions, so 4*2=8 to make the final numerator of the fraction product.

6.  So now the fraction product is 8/15, and in conclusion, you can take a fraction of a fraction.

Another way to explain fraction multiplication is this:

You can multiply both the numerator and denominator of the first fraction by the denominator of the second fraction (e.g. you can multiply both the 2 and 3 in 2/3 by 5, the denominator of the other fraction and get 10/15).  Then you can multiply both the numerator and denominator of the other fraction by the numerator of the first fraction (e.g. you can multiply both the 4 and 5 in 4/5 by 2, the numerator of the first fraction and get 8/10).  Now, when you multiply (2/3)*(4/5), you can change it to (10/15)*(8/10) without affecting the fractions' values.  Now that you have 10/15, you can take 8 out of those 10/15, and your final answer will be 8/15.

How to divide fractions:

1.  You keep the first fraction but multiply by the reciprocal of the other fraction.  If you don't understand how this works, I will explain with an example in further steps:

2.  Here's an example: (1/2) / (3/4).

3.  This can mean what fraction of 3/4 is 1/2?

4.  It would be a lot easier to see if the divisor were 1 because any number divided by 1 is that number.

5.  Let's imagine the fraction divisor, 3/4, as 1 by converting it to that number.  First, you take the reciprocal by swapping positions of both the numerator and denominator.  So the reciprocal of 3/4 is 4/3.  Then you multiply the fraction by its reciprocal to get a product of 1.

6.  Now that you have multiplied the fraction divisor by its reciprocal to get 1, you use the latter by which to multiply the fraction dividend as well because all fractions must be multiplied by anything equivalent to 1.  That's how you end up multiplying the fraction dividend by the reciprocal of the fraction divisor.

Monika J. | Monika is my name and Science is my game!Monika is my name and Science is my game...
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Fractions:

1.You need the least common denominator (commonly referred to as LCD). This means that you want the smallest possible number in the denominator, in which both of the original denominators will divide into.

2. Set your equation up so that you see the LCD on the bottom and simply add the two numerators.

Ex: 2/3 + 8/12  --> 8/12 + 8/12= 16/12 or 1 1/3 (unless the directions say not to, always simplify your answer)

Subtraction:

1. Again, find your least common denominator.  Really, any common denominator is acceptable but the LCD helps when you simplify the answer later.

2. Write you equation horizontally and not vertically( like a normal  subtraction problem), with the common denominator on bottom and the converted numerators on top.

3.  Perform the subtraction accross the top and place the common denominator on bottom.

4. Simplify if possible.

Ex: 4/5 - 1/3 --> 12/15 - 5/15 = 7/15

Multiplication:

1. Don't waste your time with common denominators.  Just multiply the numerators together and place the result in the numerator position on the other side of the = sign.

2. Multiply your denominators together and place the result in the denominator position on the other side of the = sign.

3. Simplify if possible.

Ex: 5/12 x 2/3 = 10/36 or 5/18

Division:

1. Always express your work. This will help you keep track of what  you did and show that you know what you are talking about.

2. Write you equation horizontally.

3. Take one fraction and invert it. (ex. 4/5 --> 5/4)

4. Then multiply your equations using the same method as above.

Ex:  (4/5)/(1/3) = x   --> (5/4) * (1/3) = 5/12

That fraction division in that example above was not right. You actually invert only the 2nd fraction and multiply it by the first.
Josh B. | Mechanical Engineer Tutoring MathematicsMechanical Engineer Tutoring Mathematics
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Well if you are adding or subtracting fractions, you want to first get common denomenators (or bottom number of fraction) before you can do so.

Example: 5/4 + 7/8.

We know that in order to make 4 in the first denomenator equal to the 8 in the other denomenator, we have to multiply it by 2.  However, the only way to do so without changing the value of the fraction is to do it in a form that equals one. For instance: 2/2 equals 1.  So in essence, if I multiply 5/4 by 2/2 I am actually just multiplying it by 1.  I am not changing the value of the fraction, I am just making it to where I can add it to 7/8.

So, if I multiply 5/4 by 2/2, what I am doing is saying (2*5)/(2*4).  This equals 10/8.

If I know add 10/8 to 7/8 that is saying (10+7)/8.  This equals 17/8.

Since we also covered multiplication in the previous example I will skip to division:

When you divide a fraction by another fraction, you are multiplying by its reciprical.

Ex:

(4/5)/(3/2) is the same as saying (4/5)*(2/3).  Which would be (4*2)/(5*3) = 8/15