Q&A for How to Divide Mixed Fractions

Change both mixed numbers to improper fractions. Invert the second improper fraction, then multiply it by the first fraction to get the answer. Reduce it if possible, and convert it to a mixed number if desired.

Flip both the second and third fractions.

Any fraction multiplied by its reciprocal is equal to 1. For example, 5/10 x 10/5 = 50/50 = 1. When you divide by a fraction, you want to cancel the second fraction by changing it to a 1. So, to do this, you have to multiply it by its reciprocal (or flip it). But, if you're going to multiply the second fraction by its reciprocal, you also have to multiply the other number by its reciprocal. So when you "flip and multiply" you are really cancelling out the second fraction, which leaves you with just multiplying the first fraction by the second fraction's reciprocal.

First, change the mixed number to an improper fraction. Next, multiply the divisor and simplify if needed. Then, put your answer in the lowest term. Make sure to check your work.

Set up a proportion: 12 is to 3 3/4 as 18 is to x, where x is the number of pounds needed. Change the 3 3/4 to 15/4, then multiply both the 12 and the 15/4 by four to clear the fraction. The proportion is now 48 is to 15 as 18 is to x. Cross-multiply to solve for x.

Not always. It depends on the greatest common factor of the numerator and denominator. If the fraction was 3/9, you would divide by 3 because that is the greatest common factor.

Multiply the numerators together to get the new numerator. Multiply the denominators together to get the new denominator.

Three plus three is six and two thirds plus two thirds equals one and a third feet of thread. six plus one and a third equals seven and one third, so yes, that is right.

The easiest way to do this is to convert the mixed number into an improper fraction: 2 1/4 equals 9/4. Then do the division: since we're dividing by a whole number, just divide the numerator by the whole number, and leave the denominator alone: 9/4 ÷ 3 = 3/4, your final answer. If the divisor had been a mixed number instead of a whole number, you would convert both mixed numbers to improper fractions, invert the second improper fraction, and multiply it by the first improper fraction to get your answer. Reduce if possible. (You could do the above example this way, too, if you wanted: convert the whole number 3 to an improper fraction, 3/1. Invert it to 1/3. Multiply it by 9/4: (9/4)(1/3) = 9/12 = 3/4.)

You would first follow the steps above to divide 34 by 5 1/2: 5 x 2 = 10 10 + 1 =11 So, 5 1/2 as an improper fraction is 11/2. 32 is a whole number, so converting it to a fraction, you get 32/1. So, your problem is now 32/1 divided by 11/2. Take the reciprocal of 11/2, then multiply the fractions. 32/1 x 11/2 = 352/2 Now you need to multiply 352/2 x 21/8 = 7392/16 Next you need to simplify. 7392 and 16 are both divisible by 16, so 7392/16 = 462/1, which simplifies to just 462.

Change all three mixed numbers into improper fractions. Change all the division signs to multiplication signs, and flip the second and third number (reciprocals) for a three number equation. Multiply normally.

The distributive property is really not applicable to division of mixed numbers. To divide 3 2/3 by 4½, you first convert both mixed numbers to improper fractions, invert the divisor (the second fraction), then multiply the inverted fraction by the first fraction, and reduce if possible: (3 2/3) ÷ 4½ = (11/3) ÷ (9/2) = (11/3)(2/9) = 22/27 (which is not reducible). (If the final result is greater than 1, you can convert it back to a mixed number if desired.)

(4 1/8) / (2 2/11) = (33/8) / (24/11) = (33/8)(11/24) = 363/192 = 121/64 1 = 1 57/64.

It doesn't matter whether the fractions are proper or improper. The process is exactly the same: invert the second fraction (the divisor) and then multiply the first fraction (the dividend) by the inverted fraction. Say you wanted to divide (a/b) by ( c/d). You invert the second fraction and multiply it by the first fraction: (a/b)(d/c) = ad / bc. Again, it doesn't matter whether the denominators are smaller, larger or the same as the numerators. The operation remains the same.

Dividing by any number is the same as multiplying by that number's reciprocal. So dividing by -5 is the same as multiplying by (1/-5). So (5/2) / (-5) = (5/2)(1/-5) = 5 / -10 = -5/10 = -1/2.

It can't be done. A "mixed fraction" (or mixed number) is a combination of a whole number and a proper fraction and is the equivalent of an improper fraction with a numerator greater than its denominator. A proper fraction is one whose numerator is smaller than its denominator. Therefore, a proper fraction cannot be converted into a mixed fraction. (A fraction whose numerator equals its denominator is also considered an improper fraction.)

1 1/2 ÷ 1 1/6 = 3/2 ÷ 7/6 = (3/2)(6/7) = 18/14 = 9/7 = 1 2/7.

It's because multiplying is (in the case of fractions) easier than dividing, and multiplication is the reciprocal (the "flip") of division.

Assuming you mean (5/4) / (15/5), remember 15/5 = 3. So that would be (5/4) / 3 = (5/4)(1/3) = 5/12.

First convert each mixed number to an improper fraction: 2 4/5 = 14/5, and 2 1/3 = 7/3. Now invert the second fraction: 3/7. Then multiply the first fraction by the inverted fraction: (14/5)(3/7) = 42 / 35 = 6/5 = 1 1/5, your final answer.

Yes, but you need to covert the mixed number to a simple fraction and then flip it. For instance, if I were to find the reciprocal of 1 3/5, I would change it to 8/5 first and then flip it to 5/8. 5/8 is the reciprocal of 1 3/5.

Multiply the whole number by the denominator, then add the numerator. Put your product above the original denominator.

The size of the mixed number does not matter. Divide any mixed number into another one by using the techniques shown in the article above.

It is always appropriate to simplify an answer if it consists of a reducible fraction -- that is, when both numerator and denominator can be evenly divided by the same integer (whole number) other than 1.

Divide the numerator by the denominator. For example, to convert ¾ to a decimal, divide 3 by 4. 3 ÷ 4 = 0.75.

If you're asking about multiplying one fraction by another, multiplying by a fraction means finding that fraction of another number. As a simple example to illustrate the concept, multiply ½ by ½. Multiplying the numerators yields 1. Multiplying the denominators yields 4. So the answer is ¼. That makes sense because half of a half is a quarter.

Anything divided by 1 is itself, so you can ignore that part. Start by multiplying 2x1/5 : just multiply 2 times the numerator. Think of 2 as 2/1, and multiply the numerators together and the denominators together. Then multiply the 2nd 1/5 by that. You should end up with 2/25.