1. Copyright © 2015 Cengage Learning® Chapter 2 Multiplication and Division of Decimals

2. Copyright © 2015 Cengage Learning® Place product’s decimal point same number of places to the left as total numbers after decimal point in fractions multiplied. (continues) 2-2 Multiplication of Decimals If you multiply 0.02 × 3.4, you will get 68 and need to place the decimals. Since there are three numbers total after the decimal in the numbers being multiplied, you will have that many digits after the decimal in your answer. So, start at the left and count back 3 spaces for the answer. 0.068

3. Copyright © 2015 Cengage Learning® Multiplication of Decimals (cont’d) Example: Problem requires product’s decimal point to be placed three places to the left: Answer = 0.175 Remember, if there is no number before the decimal, put a “0” before it to emphasize the decimal. (continues) 2-3

4. Copyright © 2015 Cengage Learning® Multiplication of Decimals (cont’d) If product contains insufficient numbers for correct placement of decimal point, add as many zeros as necessary to the left, including one before the decimal. (continues) 2-4

5. Copyright © 2015 Cengage Learning® Multiplication of Decimals (cont’d) Example: Problem requires addition of zeros to achieve three decimal points to the left: Answer = 0.090 2-5

6. Copyright © 2015 Cengage Learning® Review of Terminology Numerator –Top number –In example, 0.25 Denominator –Bottom number –Think “d” for “down” –In example, 0.125 2-6

7. Copyright © 2015 Cengage Learning® Division of Decimal Fractions A calculator may be used for all division of decimal fractions. –However, if solving problem manually, following the three precalculator/precalculation steps makes final division easier. 2-7

8. Copyright © 2015 Cengage Learning® Precalculator/Precalculation Steps 1.Elimination of decimal points 2.Reduction of fractions 3.Reduction of numbers ending in zero 2-8

9. Copyright © 2015 Cengage Learning® Step 1. Eliminate Decimal Points Move decimal points same number of places to the right in numerator and denominator until eliminated from both. –May have to add zeros Eliminating the decimal points from a decimal fraction does not alter the value of the fraction, or the answer obtained in the final division. 2-9

10. Copyright © 2015 Cengage Learning® Examples of Eliminating Decimal Points becomes 2-10

11. Copyright © 2015 Cengage Learning® Step 2. Reduce Fractions Divide both numbers by their greatest common denominator/divisor. –Largest number that divides into both numerator and denominator. 2-11

12. Copyright © 2015 Cengage Learning® Notes on Reducing Fractions Greatest common denominator usually 2, 3, 4, or 5: –Or multiples of these numbers For example, 6, 8, 25, etc. If greatest common denominator is difficult to determine, reduce several times by using small common denominators. One way to do this is to keep dividing both numbers by 2 if they are both even numbers. 2-12

13. Copyright © 2015 Cengage Learning® Examples of Reducing Fractions Greatest common denominator is five: Greatest common denominator is 25: (If you didn’t see they were divisible by 25, you would divide by 5 twice.) 2-13

14. Copyright © 2015 Cengage Learning® Step 3. Reduce Numbers Ending in Zero Numerator and denominator end in zero(s). Cross off same number of zero(s) in both numerator and denominator. These numbers have to be at the end of each of the numbers to be able to cross them off. 2-14

15. Copyright © 2015 Cengage Learning® Examples of Reducing Numbers then reduce by 2-15

16. Copyright © 2015 Cengage Learning® Calculator Use Personal calculator required if frequent calculations necessary – Practice using until proficient Running totals should be disregarded. – Can cause confusion All calculator entries and answers must be double-checked. (continues) 2-16

17. Copyright © 2015 Cengage Learning® Calculator Use (cont’d) Calculators add zero when there is no whole number. Calculators eliminate excess zeros at end of answer. If calculating manually, must add aforementioned zeros. 2-17

18. Copyright © 2015 Cengage Learning® Expressing to the Nearest Tenth Increase answer by one if number representing hundredths is five or greater. Drop number representing hundredths if less than five. For example, 0.35 = 0.4, 0.61 = 0.6 2-18

19. Copyright © 2015 Cengage Learning® Expressing to the Nearest Hundredth Increase answer by one if number representing thousandths is five or greater. Drop number representing thousandths if less than five. For example, 0.777 = 0.78, 0.373 = 0.37 2-19

20. Copyright © 2015 Cengage Learning® Practice, Practice, Practice More practice means: –Increased proficiency –Decreased risk of errors 2-20