# Dividing Mixed Numbers

## Dividing Mixed Numbers - How it Works - Video

### Example 1

Example 1:

In dividing mixed numbers, we must convert the mixed numbers into improper fractions first. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 2 and 1/3 becomes 7/3 because 3 x 2 + 1 = 6 + 1 = 7. And 1 and 3/5 becomes 8/5. Now, we have the fractions 7/3 and 8/5. Now we flip the operation from division to multiplication so that we can flip the second improper fraction from 8/5 to 5/8. So now we have 7/3 times 5/8. Now we can multiply the top numbers, 7 x 5 = 35, and bottom numbers, 3 x 8 = 24. After using long division on the fraction, 35/24, we get 1 and 11/24,

### Example 2

Example 2:

In dividing mixed numbers, we must convert the mixed numbers into improper fractions first. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 1 and 3/4 becomes 7/4 because 4 x 1 + 3 = 4 + 3 = 7. And 3 and 2/3 becomes 11/3. Now, we have the fractions 7/4 and 11/3. Now we flip the operation from division to multiplication so that we can flip the second improper fraction from 11/3 to 3/11. So now we have 7/4 times 11/3. Now we can multiply the top numbers, 7 x 3 = 21, and bottom numbers, 4 x 11 = 44. Since we have a proper fraction, we can't covert it to a mixed number, so our answer is 21/44.

### Example 3a

Example 3a:

In dividing mixed numbers, we must convert the mixed numbers into improper fractions first. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 3 and 3/4 becomes 15/4 because 4 x 3 + 3 = 12 + 3 = 15. And 2 and 1/6 becomes 13/6. Now, we have the fractions 15/4 and 13/6. Now we flip the operation from division to multiplication so that we flip the second improper fraction from 13/6 to 6/13. So now we have 15/4 times 6/13. Now we can multiply the top numbers, 15 x 6 = 90, and bottom numbers, 4 x 13 = 52. After using long division on the fraction, 90/52, we get 1 and 38/52, Since 38 and 52 are both multiples of 2, we must reduce. We divide 38 ÷ 2 = 19 and 52 ÷ 2 = 26. So our final answer is 1 and 19/26.

### Example 3b

Example 3b:

In dividing mixed numbers, we must convert the mixed numbers into improper fractions first. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 3 and 3/4 becomes 15/4 because 4 x 3 + 3 = 12 + 3 = 15. And 2 and 1/6 becomes 13/6. Now, we have the fractions 15/4 and 13/6. Now we flip the operation from division to multiplication so that we flip the second improper fraction from 13/6 to 6/13. So now we have 15/4 times 6/13. This time instead of multiplying the numbers we are going to reduce the numbers so we can have smaller numbers. We look at the numbers and see that 6 and 4 are both multiples of 2. So we divide 6 ÷ 2 = 3 and 4 ÷ 2 = 2. Now we have 15 times 3 on top and 2 times 13 on bottom, which is 45/26. After dividing, 45 by 26, we get 1 remainder 19, and our mixed number is 1 and 19/26.

### Example 4

Example 4:

In dividing mixed numbers, we must convert the mixed numbers into improper fractions first. So we need to multiply the denominator and the whole number and add the numerator and keep the denominator. So 3 and 3/4 becomes 15/4 because 4 x 3 + 3 = 12 + 3 = 15. And 2 and 5/8 becomes 21/8. Now, we have the fractions 15/4 and 21/8. Now we flip the operation from division to multiplication so that we flip the second improper fraction from 21/8 to 8/21. So now we have 15/4 times 8/21. This time instead of multiplying the numbers we are going to reduce the numbers so we can have smaller numbers. We look at the numbers and see that 15 and 21 are both multiples of 3. So we divide 15 ÷ 3 = 5 and 21 ÷ 3 = 7. We also see that 4 and 8 are both multiples of 4. So we divide 8 ÷ 4 = 2 and 4 ÷ 4 = 1. Now we have 5 times 2 on top and 1 times 7 on the bottom, which is 10/7. After dividing, 10 by 7, we get 1 remainder 3, and our mixed number is 1 and 3/7.

## Live Worksheet

Here is the link if you prefer.