Transcription of Multiplying and Dividing Fractions
1 Multiplying and Dividing FractionsImportant Ideas product of two or more Fractions is the product of the numerators over the product ofthe factorization will allow us to reduce Fractions before Multiplying so that the finalfraction will always be in lowest problems are always rewritten as equivalent multiplication by a number and Multiplying by the reciprocal of a number are the same reciprocal of a number is that number "inverted" or "turned upside down".The reciprocal of 23is 32 The reciprocal of 38is 83 The reciprocal of 15is 51 or 5 The reciprocal of 6 is 16To multiply two or more Fractions the product of the numerators over the product of the the prime factorization of the numerators and the prime factorization of common prime the remaining will now work through several examples following these steps.
2 This instructional aid was prepared by the Tallahassee Community College Learning 1: Multiply: 15 2416 25 We will write the product of the numerators over the product of the denominators and find the prime factorization of the numerators and the denominators. 15 243 5 2 2 2 316 252 2 2 2 5 5 = The next step is to cancel any prime factors which are common to both the numerator and the denominator and multiply any remaining factors. 11111111352223 9222255 10 = The fraction 910 is in lowest terms. Example 2: Multiply: 45 991210 We will write the product of the numerators over the product of the denominators, find the prime factorization of the numerators and the denominators, and multiply any remaining factors.
3 45922533191210 3322325 6// / //==// / / /Note that all of the prime factors in the numerator cancelled leaving a product of 1. Example 3: Multiply: 85227917 We will write the product of the numerators over the product of the denominators, find the prime factorization of the numerators and the denominators, cancel prime factors common to both the numerator and the denominator, and multiply any remaining factors. This instructional aid was prepared by the Tallahassee Community College Learning 2225211 8807 9 177 3 3 171071 == Note that there were no common prime factors in the numerator and denominator so there was no canceling to be done.
4 The fraction 8801071 is in lowest divide Fractions each division as multiplication by the Keep the first number the sameb. Change the division to multiplicationc. Change the second number (the one you are Dividing by) to its the steps for 4: Divide: 36155 Rewrite the division problem as an equivalent multiplication problem by changing division to multiplication and changing the second number to its reciprocal. 36 3515 515 6 = Follow the steps for Multiplying . 1111353 5115 63 5 3 26 == The fraction 16 is in lowest terms. This instructional aid was prepared by the Tallahassee Community College Learning 5: Divide: 5101449 We will rewrite the division as an equivalent multiplication problem.
5 510 549144914 10 = Follow the steps for Multiplying Fractions . 11115495 77714 107 2 5 24 == The fraction 74 is in lowest terms. Example 6: Divide: 17324 We will rewrite the division problems as an equivalent multiplication problem. Change division to multiplication and change the second number to its reciprocal. 1717317 132424 124 3 = = Note that the whole number 3 is the same as the fraction31. Follow the steps for Multiplying Fractions . 17 117 11724 32 2 2 3 372 == Note that there were no common factors that could be cancelled. The fraction 1772 is in lowest terms. This instructional aid was prepared by the Tallahassee Community College Learning Exercises Multiply or divide the following problems.
6 624 57 14 33 3915 22 5 9 10. 51197 This instructional aid was prepared by the Tallahassee Community College Learning to Practice Problems instructional aid was prepared by the Tallahassee Community College Learning Commons.
