


FractionsOperations with Mixed NumbersAddition  Subtraction  Multiplication  Division 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. AdditionThe steps for adding mixed numbers are
ExamplesAt 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
ExerciseTry 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. SubtractionThe steps for subtracting mixed numbers are very similar to adding
ExamplesSometimes 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
ExerciseTry 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. MultiplicationThe steps for multiplying mixed numbers are
ExamplesExerciseTry 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.
DivisionRecall 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
ExamplesOccasionally the answer is obvious, so you can write it straight away. ExampleExerciseAnd 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.
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