Multiplication and Division of Decimals Chapter 2 Multiplication and Division of Decimals

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

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

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

Multiplication of Decimals e.g., problem requires addition of zeros to achieve three decimal points to the left Answer = 0.090 = 0.09

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

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

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

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

Examples of Eliminating Decimal Points becomes

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

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

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

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

Examples of Reducing Numbers then reduce by

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

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

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

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

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

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., 0.777 = 0.78, 0.373 = 0.37

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