Ch.2+Lectures


 * Chapter 2 Lectures**

__Part 1: Multiplying and Dividing Fractions__

Multiplying and dividing fractions is very different from adding and subtracting. One of the major differences is that when multiplying and dividing fractions there is no need to find a common denominator. Another difference is that the denominator will not remain the same, as it does when adding and subtracting fractions.

Example 1: Multiplying Fractions. Watch the following video:

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As you can see, there is no need for a common denominator. You simply multiply the numerators and multiply across the denominator. In the example, it was not possible to simplify the answer, but in other cases it may be possible. Remember to simplify! Following is an example where you would need to simplify.

Example 2: Multiplying Fractions and Simplifying. Watch the video:

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Guided Practice: Multiply the following fractions and simplify. 1.(3/4)(2/3) 2.(1/2)(3/4) 3.(3/8)(1/10)

Check your answers here.

Finally, we are at dividing fractions. __Make sure that you do not divide the numerator and then divide the denominators. This is wrong__. When dividing fractions, you actually multiply the first fraction by the reciprocal of the second fraction. Remember that the reciprocal is when you switch the numerator and denominators of a fraction. The reciprocal of 2/3 is 3/2. The reciprocal of 6 is 1/6 because 6 is really 6/1.

Guided Practice: Find the reciprocal of the following fractions: 4. 3/4 5. 1/7

Example 3: Divide fractions. Watch the video:

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 * Remember that to divide fractions, you must multiply by first fraction the reciprocal of the second fraction. Then simplify the fraction if possible.

Guided Practice: Divide the fractions 6. 3/2 ÷ 5/6 7.6/7 ÷ 1/2 Check your answers here.

You have completed the lecture. Return to the unit 2 page.

__Part II: Multiplying and Dividing Mixed Numbers__

Remember that multiplying fractions is simply multiplying the numerators and multiplying the denominators. However, mixed numbers require a bit more work. If you are multiplying mixed numbers, you must first convert them to improper fractions and then multiply.

Example 4: Multiply Mixed Numbers. Watch the video:

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Guided Practice: Multiply the mixed numbers 8. (1 2/3)(5 1/2) 9. 3 (1/2)(2 4/5) Check your answers here.

Dividing mixed numbers is similar. First, you need to convert the mixed numbers into improper fractions and then you multiply the first fraction by the reciprocal of the second fraction (like you do when dividing fractions).

Example 5: Dividing Mixed Numbers. Watch the video:

media type="youtube" key="sTGeck8KyhY" height="315" width="420" align="center"

Guided Practice: Divide the following mixed numbers 10. 1 1/2 ÷ 2 1/3 11. 3 1/2 ÷ 5 1/4 Check your answers here.

Now we have completed addition, subtraction, multiplication, and division. Examine the following charts to better understand the differences between the four processes with fractions and mixed numbers:


 * = **Fractions** ||= Need a common denominator? ||= Process ||
 * = Addition ||= Yes ||= Add numerator, keep denominator ||
 * = Subtraction ||= Yes ||= Subtract numerators, keep denominator ||
 * = Multiplication ||= No ||= Multiply numerators, multiply denominators ||
 * = Division ||= No ||= Multiply first fraction by the reciprocal of second fraction ||


 * = **Mixed Numbers** ||= Need a Common Denominator? ||= Process ||
 * = Addition ||= Yes ||= Add whole numbers, add fractions, simplify ||
 * = Subtraction ||= Yes ||= Convert to improper fractions, subtract, simplify ||
 * = Multiplication ||= No ||= Convert to improper fractions, multiply numerators and denominators, simplify ||
 * = Division ||= No ||= Convert to improper fractions, multiply first fraction by reciprocal of second fraction, simplify ||

You have completed the lecture. Return to the unit 2 page.