Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a proper fraction. For example, 3 1/2 is a mixed number, where 3 is the whole number and 1/2 is the fraction.

Converting between Mixed Numbers and Improper Fractions

To convert a mixed number to an improper fraction, you can follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the result to the numerator of the fraction.
3. Write the sum over the original denominator to get the improper fraction.

For example, to convert 3 1/2 to an improper fraction:

3 * 2 + 1 = 6 + 1 = 7

So, 3 1/2 as an improper fraction is 7/2.

To convert an improper fraction to a mixed number, you can follow these steps:

1. Divide the numerator by the denominator.
2. The quotient becomes the whole number in the mixed number.
3. The remainder becomes the new numerator in the proper fraction.
4. The original denominator remains the same.

For example, to convert 7/2 to a mixed number:

7 ÷ 2 = 3 with a remainder of 1

So, 7/2 as a mixed number is 3 1/2.

Adding and Subtracting Mixed Numbers

When adding or subtracting mixed numbers, it's helpful to first convert them to improper fractions, perform the operation, and then convert the result back to a mixed number if needed.

For example, to add 2 1/4 and 3 2/3:

First convert both mixed numbers to improper fractions:

2 1/4 = 9/4

3 2/3 = 11/3

Find a common denominator (in this case, the least common multiple of 4 and 3, which is 12):

9/4 = 27/12

11/3 = 44/12

Now add the two improper fractions:

27/12 + 44/12 = 71/12

Finally, convert the result back to a mixed number:

71 ÷ 12 = 5 with a remainder of 11

So, the sum of 2 1/4 and 3 2/3 is 5 11/12.

Multiplying and Dividing Mixed Numbers

To multiply or divide mixed numbers, it's best to first convert them to improper fractions, perform the operation with the fractions, and then convert the result back to a mixed number if needed.

For example, to multiply 2 1/4 by 3 2/3:

First convert both mixed numbers to improper fractions:

2 1/4 = 9/4

3 2/3 = 11/3

Multiply the two improper fractions:

(9/4) * (11/3) = 99/12

Finally, convert the result back to a mixed number:

99 ÷ 12 = 8 with a remainder of 3

So, the product of 2 1/4 and 3 2/3 is 8 3/12, which simplifies to 8 1/4.

Practice Problems

1. Convert the mixed number 4 3/5 to an improper fraction.

2. Convert the improper fraction 17/4 to a mixed number.

3. Add 1 2/3 and 2 5/6, and express the sum as a mixed number.

4. Subtract 3 3/8 from 5 1/4, and express the difference as a mixed number.

5. Multiply 2 1/2 by 3 2/5, and express the product as a mixed number.

6. Divide 5 1/3 by 2 3/4, and express the quotient as a mixed number.