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Mastering Fraction Multiplication and Cancellation Techniques

This guide provides comprehensive insights into multiplying fractions, including proper techniques for handling whole and mixed numbers. Learn how to multiply fractions by following straightforward steps: multiply the numerators and denominators, then simplify your answers. Discover the importance of converting mixed numbers into improper fractions before multiplication. Additionally, we explore the concept of cancellation to reduce fractions prior to multiplication, making calculations simpler and quicker. This resource is perfect for students and educators looking to enhance their understanding of fraction multiplication.

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Mastering Fraction Multiplication and Cancellation Techniques

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  1. Fraction Multiplication And Cancelation

  2. Fraction Multiplication • Here are some fraction multiplication problems • Can you tell how to multiply fraction from these examples?

  3. 14 14 14 14 34 __ __ __ __ __ Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. = + + 3 • = = + +

  4. There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. So 3 = . 3 __ 1 3 3 • 1 1 __ ______ __ 1 1 • 4 4 Notice that when you multiply a proper fraction and a number greater than 1, the product is between the factors. Multiply numerators 3 __ • = = Multiply denominators 4

  5. 1 1 __ __ 4 3 1 1 __ __ 4 3 1 1 1 __ __ __ 4 3 12 One way to find of is to make a model. Find of . = •

  6. Multiplying Fractions

  7. Multiplication • Multiply numerator by numerator • And denominator by denominator

  8. Try some. • Multiply the following:

  9. Answers • Multiply the following:

  10. Mixed Numbers • Because of the order of operations, • Mixed numbers cannot be multiplied as is • Change mixed numbers to improper fractions, then multiply.

  11. Try some • Change any whole or mixed numbers to improper. • Multiply straight across. • Simplify answers

  12. Answers • Change any whole or mixed numbers to improper. • Multiply straight across. • Simplify answers

  13. Cancelling Reduce before you multiply

  14. Canceling • Reducing before multiplying is called canceling. • ICK! Instead think the following in your head.

  15. Try one • Say “--- goes into ____ this many times.” • As you cross each number out and write what is left after canceling above the number.

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