1. Multiplication and Division of Decimals
Chapter 2
Multiplication and Division of Decimals

2. Multiplication of Decimals
Decimal point in product of decimal fractions placed same number of places to the left in product as total of numbers following decimal points in fractions multiplied

3. Multiplication of Decimals
e.g., problem requires product’s decimal point to be placed three places to the left
Answer = 0.175

4. Multiplication of Decimals
If product contains insufficient numbers for correct placement of decimal point, correct by adding as many zeros as necessary to the left

5. Multiplication of Decimals
e.g., problem requires addition of zeros to achieve three decimal points to the left
Answer = = 0.09

6. Division of Decimal Fractions
Calculator may be used for all division of complex decimal fractions
However, if solving problem manually, following the three precalculator/precalculation steps makes final division easier

7. Review of Terminology Numerator Denominator Top number
In example, 0.25
Denominator
Bottom number
Think “d” for “down”
In example, 0.125

8. Precalculator/Precalculation Steps
Elimination of decimal points
Reduction of fractions
Reduction of numbers ending in zero

9. 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

10. Eliminating Decimal Points
Eliminating decimal points from decimal fraction before final division does not alter value of fraction nor answer obtained during final division

11. Examples of Eliminating Decimal Points
becomes

12. Step 2. Reduce Fractions
Divide both numbers by their greatest common denominator/divisor
Largest number that divides into both numerator and denominator

13. Notes on Reducing Fractions
Greatest common denominator usually 2, 3, 4, or 5
Or multiples of these numbers
e.g., 6, 8, 25, etc.
If greatest common denominator difficult to determine, reduce several times by using small common denominators

14. Examples of Reducing Fractions
Greatest common denominator is 5 Greatest common denominator is 25

15. 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

16. Examples of Reducing Numbers
then reduce by

17. Calculator Use Calculator entry errors tend to be repetitive
All calculator entries and answers must be double-checked
Personal calculator required if frequent calculations necessary
Practice using until proficient

18. Calculator Use Running totals should be disregarded
Can cause confusion
Calculators add zero when no whole number present
If calculating manually, must add these zeros
Calculators eliminate excess zeros at end of answer

19. Expressing to the Nearest Tenth
Express answer to nearest tenth by carrying division to hundredths
Then round off number representing hundredths to the tenths place

20. Expressing to the Nearest Tenth
Increase answer by 1 if number representing hundredths is 5 or greater
Drop number representing hundredths if less than 5
e.g., 0.35 = 0.4, 0.61 = 0.6

21. Expressing to the Nearest Hundredth
Express answer to nearest hundredth by carrying division to thousandths
Then round off number representing hundredths

22. Expressing to the Nearest Hundredth
Increase answer by 1 if number representing thousandths is 5 or greater
Drop number representing thousandths if less than 5
e.g., = 0.78, = 0.37

23. Practice, Practice, Practice
More practice means:
Increased proficiency
Decreased risk of errors