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# Fraction Word Problems Study Guide (page 2)

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Updated on Oct 3, 2011

## Changing Improper Fractions and Mixed Numbers

### Changing Improper Fractions to Mixed Numbers

To change an improper fraction into a mixed number, divide the numerator by the denominator. Then, place the remainder, if there is one, over the same denominator. For example, to change to a mixed number, divide 12 by 7. The result is 1, with a remainder of 5. The mixed number is .

### Changing Mixed Numbers to Improper Fractions

To change a mixed number into an improper fraction, multiply the whole number part by the denominator. Then, add this product to the numerator. This value is the new numerator, and the denominator remains the same. For example, to change the mixed number to an improper fraction, multiply 4 by 3 to get 12. Then, add 12 + 1 = 13 to get the new numerator. Because the denominator remains the same, the improper fraction is .

To add or subtract fractions, you must ﬁrst have a common denominator. Then, add or subtract the numerators and keep the denominators. For example, in order to add , add the numerators and keep the denominator of 7. The result is .

On the other hand, to subtract , use the least common multiple of the denominators to ﬁnd the least common denominator. The least common multiple of 4 and 2 is 4, so change the second fraction to also have a denominator of 4. To do this, multiply the numerator and denominator by 2:. Now that there is a common denominator, subtract the numerators and keep the denominator..

When you are adding or subtracting mixed numbers, add or subtract the fraction parts and add or subtract the whole number parts. For example, to add , the fraction part adds to and the whole number parts add to 2 + 1 = 3. The answer is .

#### Tip:

Use the greatest common factor (GCF) to simplify fractions, and use the least common multiple (LCM) to find a common denominator.

## Multiplying Fractions

To multiply fractions, multiply across the numerators and denominators. Then, simplify the product if necessary. For example, . Since 12 and 45 share a greatest common factor of 3, divide each by 3 to simplify the fraction. The simpliﬁed fraction is .

#### Tip:

If the numerator of a fraction has a common factor with the denominator of a fraction in a multiplication problem, you may cross cancel the common factors. For example, when multiplying , 3 and 9 share a common factor of 3. By canceling out this factor, the problem becomes . The fraction is in simplest form.

To multiply mixed numbers, ﬁrst change to improper fraction form, and then follow the same steps as before. For example, .

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