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Technical Mathematics, Sixth Edition by Michael A. Calter Ph.D., Paul A. Calter

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11.6. Multiplying and Dividing Fractions

Now we will do the four basic operations with fractions: adding, subtracting, multiplying and dividing. We will start with multiplication and division.

11.6.1. Multiplying Fractions

We multiply a fraction by another fraction as follows:

NOTE

The product of two or more fractions is a fraction whose numerator is the product of the numerators of the original fractions and whose denominator is the product of the denominators of the original fractions.

Example 42:

These examples show the multiplication of fractions. Note that in (b) we have canceled out the common factors 2 and 3 from the numerator and denominator after multiplying, and in (c) we have converted the mixed numbers to improper fractions before multiplying.

NOTE

When multiplying mixed numbers, students sometimes try to multiply the whole parts and the fractional parts separately.

The correct way is to write each mixed number as an improper fraction and to multiply as shown.

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