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Unit 1: Multiplying and Dividing Fractions and Decimals 6.2E ! Extend representations for division to include fraction notation such as represents the same number ! as π ÷ π where π β 0. βA fraction is really a DIVISION PROBLEM!β β Mrs. Atkinson To turn a fraction into a long division problem, remember βtop in, bottom outβ. ! ! = π ÷ π = π) π = 3 ÷ 4 = 4 ) 3 ! ! 6.3A Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values. Reciprocal: what to multiply a number by to get one, or with a fraction just FLIP the fraction! For example: ! ! The reciprocal of is . ! ! All fraction division problems can be rewritten as a fraction multiplication problem. For example: ! ! ! ! ÷ = × ! ! ! ! When dividing by a fraction, the problem can be made simpler by multiplying by the reciprocal. For example: ! ! ! 4 ÷ can be written as 4×2 because the reciprocal of is or 2. ! ! ! βDividing by one-βhalf is the same as multiplying by 2.β βMrs. Atkinson 6.3B Determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one. Multiplying any quantity by a fraction SMALLER THAN ONE will cause the original quantity to DECREASE. For example: ! 10× = 5 ! Multiplying any quantity by a fraction BIGGER THAN ONE will cause the original quantity to INCREASE. For example: ! 10× = 15 ! 6.3E Multiply and divide positive rational numbers fluently. When talking about RATIONAL NUMBERS in 6th grade math, we mean fractions and decimals. MULTIPLYING FRACTIONS: β’ Multiply straight across; numerator times numerator, denominator times denominator; and then simplify ! ! ! ! β’ Example: × = = ! ! !" ! DIVIDING FRACTIONS: β’ KFC-β Keep the first fraction, Flip the second fraction, Change division to multiplication; then multiply normally ! ! ! ! ! ! β’ Example: ÷ = × = = ! ! ! ! ! ! MULTIPLYING DECIMALS: β’ Multiply normally, ignoring the decimal points. Then put the decimal point in the answer-β it will have as many decimal places as the original numbers combined. β’ Example: 0.03×1.1 Multiply without decimal points-β 3×11 = 33 0.03 has 2 decimal places, 1.1 has 1 decimal place so the answer has 3 decimal places, 0.033 DIVIDING DECIMALS: β’ Change the number we are dividing by, the divisor, into a whole number by moving the decimal point to the right. Then, move the decimal point in the number we are dividing, the dividend, the SAME number of places and the SAME direction. Now divide!
