Q&A for How to Divide and Multiply Fractions

Yes, and it will make things easier if you do, especially if you're working with really big numbers.

Step 1 says to multiply the numerators--that means multiply the top number in both fractions. For example, if you want to multiply 2/3 (two thirds) and 1/2 (one half), I would start by multiplying 2 and 1 together.

The same way you would positive fractions. If both fractions have the same sign your answer will be positive regardless of whether they are both negative or both positive. But if your fractions have different signs, you will get a negative answer.

Same as with positive fractions, except the sign of the answer may be affected. If one of the fractions is negative, the answer will be negative. If both of the fractions are negative, the answer will be positive.

Multiply the numerator by the other numerator, and multiply the same number with each of the denominators. You then can divide to the smallest whole values for each.

Reduce whenever you can exactly divide a whole number into both the numerator and denominator. It's easiest to recognize when you can divide a small integer (like 2, 3 or 5) into both the numerator and denominator.

First change each mixed fraction into an improper fraction. For example, change 1 1/2 to 3/2. Then follow the steps given to multiply the improper fractions.

First, make the denominator of the fractions equivalent. Then add the numerators or subtract them.

Ignore signs while multiplying/dividing. Once you have the final number, count the negative signs among the original fractions. If there is an odd number of negative signs, the answer has a negative sign. If there is zero or an even number of negative signs, the answer has a positive sign.

In word problems, the word "of" typically indicates multiplication. Three-fifths of two hundred women means (3/5)x200 or 120 women.

It's just like normal multiplication and division. You see what the value you would get from multiplying the numbers, or from dividing them.

You need to convert the mixed number into an improper fraction and then divide the fractions normally.

It's not required, but it is customary to do so.

There are two ways to do this: (1) Divide the numerator by the whole number if it will divide evenly. (2) Multiply the denominator by the whole number, then reduce the fraction if possible.

39 divided by 13 = 3. 195 divided by 13 = 15. Therefore, the answer is 3/15 or simplified: 1/5

No, you need to take the greatest common factor (GCF) to simplify it. To multiply, you multiply them regularly: the top first, and then the bottom. To divide, you flip one of the fractions and divide it that way, and then you can simplify it by the (GCF).

9/4 x 11/10 = 99/40. this is already in its simplest form, so just convert it to a mixed number or leave it this way.

To multiply mixed numbers, you need to turn your mixed number into an improper fraction. Then, you can multiply that to get your answer. wikiHow's article on multiplying mixed numbers might be helpful to you too.

Add a 1 to the whole number as a denominator. Then, multiply your number by your fraction.

Change the mixed fraction into a improper fraction. Then do the step as shown. For example, if you had 3 4/5, change it to 19/5. Then do the steps.

You can't divide three fractions. The process of division involves dividing one number (or fraction) into another.

The question is: how many one-thirds (1/3) are there in 8 1/3? To find out, divide 8 1/3 by 1/3. 8 1/3 is 25/3. 25/3 ÷ 1/3 = (25/3)(3/1) = 75/3 = 25. There are 25 servings in the bag.

Look for the largest number that will divide exactly into both the numerator and the denominator. Perform those divisions to reduce the fraction as far as possible. For example, to reduce 28/189, we must recognize that 28 is exactly divisible by 2, 4 and 7, and 189 is exactly divisible by 3, 7 and 9. So the largest integer that is exactly divisible into both the numerator and the denominator is 7. Perform those two divisions, and we're left with 4/27, the fully reduced fraction.

It's a way of making multiplication of fractions a little easier. It involves cancelling a number (or a factor) in one numerator and the same number (or factor) in another denominator. Here's an example: An easy way to multiply 4/7 by 21/44 is first to factor the numerators and denominators where possible. 4/7 is (2)(2) / 7, and 21/44 is (3)(7) / (2)(2)(11). Now cancel both 2's in the first numerator and both 2's in the second denominator, and cancel the 7 in the first denominator and the 7 in the second numerator. The cancellations leave these fractions to be multiplied: (1/1)(3/11), with an easy product of 3/11.

The GCF, or Greatest Common factor, is the largest number that two numbers can both be divided by.

Are you thinking of dividing numerators and dividing denominators analogous to the multiplication rule? Like (3/10) / (1/5) = (3/1) / (10/5) = 3/2. That's also a perfectly valid technique (you can check that it equals (3/10)*(5/1)). The only reason it isn't usually taught is that, unless the numbers work out as nicely as in this example, you'll get a fraction of fractions. You'll then be expected to simplify that in which case you won't save any time over the usual method. So it's a good trick when it works out nicely, but the advantage of converting to a multiplication problem is that it limits how messy the simplification can get.

2¾ / 2/3 = 11/4 / 2/3 = (11/4)(3/2) = 33/8 = 4 1/8.

Multiply them the way you multiply any fractions: numerator times numerator, and denominator times denominator. The product will be an improper fraction, which you should reduce and then, if you prefer, change to a mixed number.

Regardless of what the denominators are, the method is the same. Just multiply the two denominators to get your new one.

Work left to right: first divide4/3 by 20/3. Then multiply that quotient by 11/9.