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## Operations with Mixed Numbers

To the already established methods for adding, subtracting, multiplying and dividing fractions, we need only add one more step at the beginning and one at the end.

At the beginning the mixed numbers are converted to improper fractions.

Sometimes the usual methods give an improper fraction answer, so the last step is to convert the improper fraction to a mixed number.

The steps for adding mixed numbers are

1. Convert each mixed number to an improper fraction.
2. Multiply the numerator and denominator of each improper fraction by a factor to obtain the lowest possible common denominator for the two fractions.
4. Reduce the answer fraction if possible .
5. If the answer is an improper fraction convert it to a mixed number.

### Examples  At times, the numbers to be added will have an obvious answer in which case you can go straight to an answer, but failing that, the above method will always work.

### Example ### Exercise

Try adding two mixed numbers. Enter as much working as you wish. If the answer is obvious, just enter it. If not, change the mixed numbers to improper fractions and add as usual. If the answer is an improper fraction, change it to a mixed number reducing the fractional part if possible.

 Improper fractions Fractions with lowest common denominator + = + = + Enter your working above.Enter answer here = =

## Subtraction

The steps for subtracting mixed numbers are very similar to adding

1. Convert each mixed number to an improper fraction.
2. Multiply the numerator and denominator of each improper fraction by a factor to obtain the lowest possible common denominator for the two fractions.
3. Subtract the numerators
4. Reduce the answer fraction if possible .
5. If the answer is an improper fraction convert it to a mixed number.

### Examples  Sometimes the numbers to be subtracted will have an obvious answer so you can go straight to an answer, but failing that, the above method will always work.

### Example ### Exercise

Try subtracting two mixed numbers. Enter as much working as you wish. If the answer is obvious, just enter it. If not, change the mixed numbers to improper fractions and subtract as usual. If the answer is an improper fraction, change it to a mixed number reducing the fractional part if possible.

 Improper fractions Fractions with lowest common denominator − = − = − Enter your working above.Enter answer here = =

## Multiplication

The steps for multiplying mixed numbers are

1. Convert each mixed number to an improper fraction.
2. Multiply the numerators and multiply the denominators of the two fractions.
3. Reduce the answer fraction if possible .
4. If the answer is an improper fraction convert it to a mixed number.

### Examples  ### Exercise

Try multiplying two mixed numbers. Enter as much working as you wish. If the answer is obvious, just enter it. If not, change the mixed numbers to improper fractions and multiply as usual. If the answer is an improper fraction, change it to a mixed number reducing the fractional part if possible.

 Improper fractions × = × Enter your working above.Enter answer here = =

## Division

Recall that in a division the number to divide by is the divisor. For example, 3 is the divisor in the division 2 ÷ 3.

The steps for dividing mixed numbers are

1. Convert each mixed number to an improper fraction.
2. Change the division to a multiplication by the receprocal of the divisor.
3. Multiply the numerators and multiply the denominators of the two fractions.
4. Reduce the answer fraction if possible .
5. If the answer is an improper fraction convert it to a mixed number.

### Examples  Occasionally the answer is obvious, so you can write it straight away.

### Example ### Exercise

And now some practice dividing two mixed numbers. Enter as much working as you wish. If the answer is obvious, just enter it. If not, change the mixed numbers to improper fractions and change the division to multiplication by the reciprocal then multiply as usual. If the answer is an improper fraction, change it to a mixed number reducing the fractional part if possible.

 Improper fractions Working space ÷ = ÷ = × Enter your working above.Enter answer here = =