Q&A for How to Divide Fractions by Fractions

Change the mixed number to an improper fraction: 2½ becomes 5/2. Then invert ½ to become 2/1. Multiply 5/2 by 2/1, and reduce or simplify if possible. (5/2)(2/1) = 10/2 = 5.

Invert 3/5 to 5/3, and multiply by ¾: (3/4) x (5/3) = 15/12 = 5/4 or 1¼.

The reciprocal is a fraction whose numerator is 1 and whose denominator is the whole number. For example, if the whole number is 5, think of it as 5/1, then invert that fraction to 1/5.

5 3/4 shared with 4 people means 5 3/4 divided by 4. To do this, you need to turn the 4 into a fraction (4/1). Then you will need to flip the 2nd fraction(reciprocal) and turn the division sign into a multiplication sign (1/4). Next, you will need to turn the 5 3/4 into an improper fraction (23/4), that is, 5 x 4 + 3. Then, you multiply fractions as usual; the numerators together and the denominators together to get 23/16. You will need to simplify your answer and turn it into a mixed number fraction. The answer is equal to 1 7/16 meaning each person receives that much. = 5 3/4 divided by 4/1 = 5 3/4 x 1/4 = 23/4 x 1/4 = 23/16 = 1 7/16

Multiply the denominator by the whole number, and reduce the resulting fraction if possible.

2 1/3 as an improper fraction is 7/3. 7/3 divided by 4/5 = (7/3)(5/4) = 35/12, or 2 11/12.

11/12 ÷ 24/5 = (11/12) x (5/24) = 55/288.

32 ÷ 26 = 16/13.

That's 5/2 divided by 2, which is 5/4 or 1¼.

The whole number 8 can be written as 8/1. Its reciprocal is 1/8.

First invert the fraction. Then multiply the whole number by the new numerator. Leave the new denominator unchanged. For example, to divide 4 by 3/5, invert the fraction to 5/3. Then multiply 4 by 5 to make a new numerator of 20. Retain the new denominator, so that the quotient is 20/3. You can express that as 6 2/3.

First find the lowest common denominator among the fractions, and convert each to an equivalent fraction having that denominator. Then add and subtract the new numerators. Reduce the answer if possible. The LCD is (5)(4)(3) = 60. The fractions convert to 324/60, 495/60, and 380/60, respectively. Then the numerators: 324 + 495 - 380 = 439. The answer is 439/60 (which won't reduce).

You should get 1 no matter what method you use. If you flip 1/2, you get 2. 1/2 times 2 = 2/2 which simplifies to 1. You may be flipping both numbers (only flip one) or not simplifying.

Invert ¼ to 4/1, then multiply by 7/8: (4/1)(7/8) = 28/8 = 7/2 = 3½.

1/4 multiplied by 1/2 is 1/8. 1/4 divided by 1/2 is 1/2. Dividing by 1/2 is the same as multiplying by 2.

A whole number is always placed over one in that situation (e.g,. 1=1/1, 2=2/1, 3=3/1), so in a situation where you needed to multiply, say, 3 by 5/7, you would write it as (3/1)*(5/7) and then multiply the two fractions as you normally would.

Divide 12 by 2. This is basic knowledge gained from memorizing the times tables, as you cannot do long division here. If you have memorized the tables, you will know that the only number that can be multiplied by 2 to get 12 is 6. So the answer is 6.

Take the example 0.285. The numerator of the fraction is the same as the digits following the decimal point in the decimal. So here the numerator is 285. The denominator is a "1" followed by the same number of zeroes as the number of digits that follow the decimal point in the decimal. Here the denominator is 1000, because there are three digits in 285. Thus, the fraction is 285/1000. If the decimal had been 1.285, the fraction (mixed number in this case) would be 1 285/1000.

Divide by a number greater than 1.

Change them to improper so they have common denominators, then carry on with the usual procedure.

Yes. Let's say we have (5/8) / (-7/4). The reciprocal of -7/4 is 4/-7 or -4/7. Now we have (5/8)(-4/7). So we have (5 * -4) / (8 * 7) = -20/56 = -5/14. However, if both the numerator and denominator are negative, then the fraction is positive.

Divide the numerator by the denominator. For example: 8/9=0.88.

Change 4 1/5 to 21/5. Change 1 2/3 to 5/3. Invert 5/3 to 3/5. Multiply 21/5 by 3/5, which equals 63/25, or 2 13/25.

Assuming you're looking for the other fraction, if you're given the dividend and the quotient, divide the dividend by the quotient to find the divisor. If you're given the divisor and the quotient, multiply the quotient by the divisor to find the dividend.

Multiply the numerators together to get the new numerator. Multiply the denominators together to get the new denominator. Reduce if possible.

There are two ways to do it: (1) If the numerator will divide evenly by the whole number, do that, and leave the denominator unchanged; (2) Multiply the denominator by the whole number, and leave the numerator unchanged. In either case, reduce if possible.

That doesn't change anything except that the answer will be negative. For example, to divide (-¾) by 2/5, invert the 2/5 to become 5/2, then multiply (-¾) by 5/2. That equals (-15/8), or -1 7/8. If the dividend is positive and the divisor is negative, the quotient will be negative.

Invert only the second fraction (the divisor), and then multiply the inverted fraction by the first fraction (the dividend). Reduce the resulting fraction if possible.

Usually yes, but not when the divisor (the second number) is a fraction less than 1. Here's a simple example: Say you want to divide 4 by ½. Invert the divisor: ½ becomes 2/1 or 2. Multiply that 2 by the original number, 4: (2)(4) = 8. That's your answer. That means that eight ½'s will fit into 4.

First change the two mixed numbers to improper fractions: 1-2/5 becomes 7/5, and 3-2/5 becomes 17/5. Now work left to right: (7/5) ÷ (3/4) = (7/5)(4/3) = (28/15). (28/15)(17/5) = 476/75 (which won't simplify).