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Published bySara Garrison Modified over 7 years ago

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**Multiplying Rational Numbers (Multiplying Fractions)**

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**DART statement: I can multiply fractions (rational numbers).**

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Rational Numbers The term Rational Numbers refers to any number that can be written as a fraction. This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers. An integer, like 4, can be written as a fraction by putting the number 1 under it.

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**Multiplying Fractions**

When multiplying fractions, they do NOT need to have a common denominator. To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator. If the answer can be simplified, then simplify it. Example:

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**Simplifying Diagonally**

When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end. From the last slide: An alternative: 1 You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.

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Mixed Numbers To multiply mixed numbers, convert them to improper fractions first. 1

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**Mixed Numbers Convert to improper fractions. Simplify.**

Multiply straight across.

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Mixed Numbers Try these on your own.

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**Sign Rules Remember, when multiplying signed numbers...**

Positive * Positive = Positive. Negative * Negative = Positive. Positive * Negative = Negative.

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Try These: Multiply Multiply the following fractions and mixed numbers:

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Solutions: Multiply

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**Solutions (alternative): Multiply**

Note: Problems 1, 2 and 4 could have been simplified before multiplying. 1 2 2 1 1 2 1 3 1 3

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