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.

Work it a second time to see if you get the same answer. Or work the problem backwards: start with your answer and work backwards to see if you finish where you started. (For example, if you divided 2 1/2 by 1 3/4 and got 1 3/7 for an answer, start with 1 3/7, multiply it by 1 3/4 to see if you get 2 1/2, the number you started with. If you do, you know your answer is correct.)

When you divide by a number less than 1 (such as 7/8), the quotient will be larger than the dividend. 9 3/4 ÷ 7/8 = 39/4 ÷ 7/8 = (39/4)(8/7) = 312/28 = 11 4/28 = 11 1/7.

Assuming you're trying to reduce the fraction, there's no factor in common. This is irreducible and in simplest form.

You can simplify if the numerator and denominator have a common factor between them.

If you want the fraction in lowest terms, then you have to divide by the greatest common factor between the two numbers.

That’s the same as 32/3 / 16/9, which is equal to 32/3 x 9/16 = 288/48, which is equal to 6. Your answer is just 6.

Because you'll get the wrong answer if you flip the first fraction instead of the second.

It would be the same thing as if both the dividend and divisor were mixed numbers. You'd do the same steps. For example, 9 3/4 ÷ 7 = 39/4 ÷ 7 = 39 / [(4)(7)] = 39/28. Another example: 12 ÷ 5 3/4 = 12 ÷ (23/4) = (12)(4/23) = 48/23 = 2 2/23.

(6 1/2)(3 3/4) = (13/2)(15/4) = 195/8 = 24 3/8.

Dividing by 1/2 is the same thing as multiplying by 2. So first change 3 1/4 to 13/4, then multiply by 2: that's 26/4, which reduces to 13/2 = 6 1/2.

As a fraction 212% is 212/100 or 53/25. As a mixed number, it's 2 3/25.

Assuming no warpage, the height is (1 1/8)(43) = (9/8)(43) = 387/8 = 48 3/8 inches.

That's normal. Dividing any odd number by 2 will yield a decimal (or a fraction).

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.