Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 1 Arithmetic Needed for Dosage

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Adding Fractions: Same Denominator Add two numerators and write the sum over the denominator Example: 1/6 + 4/6 = 5/6

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Adding Fractions: Different Denominators Convert each fraction, multiplying both numbers by lowest common denominator Add two numerators together and reduce Example: 2/6 + ¼ = –2/6 (× 2/× 2)= 4/12 –¼ (× 3/× 3) = 3/12 –4/12 + 3/12 = 7/12

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Subtracting Fractions: Same Denominator Subtract numerators and write the difference over denominator Example: 14/24 – 9/24 = 5/24

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Subtracting Fractions: Different Denominators Convert each fraction using lowest common denominator Subtract the numerators and reduce Example: 2/6 - ¼ = –2/6 (× 2/× 2)= 4/12 –¼ (× 3/×3) = 3/12 –4/12 - 3/12 = 1/12

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Multiplying Fractions Multiply numerators across Multiply denominators across Reduce lowest terms Example: 1/8 × 2/4 = 2/32 = 1/16

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Multiplying Fractions: Mixed Numbers Change into improper fraction –Multiply whole number by denominator and then add total to the numerator –Example: 2½ × 1/3 = 5/2 × 1/3 = 5/6

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Fraction to Decimal Divide numerator by the denominator Fraction numerator = dividend Fraction denominator = divisor Answer = quotient Example: 2/3 = 0.666

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Reading Decimals 0.2 is read as two tenths (2/10) 0.02 is read as two hundredths (2/100) is read as two thousandths (2/1000)

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Rounding off Decimals Round off decimal, drop the final number –Example: becomes 4.62 Exception: If final number is 5 or above, drop it and then increase adjacent number by 1 –Example: 2.36 becomes 2.4

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Question A neonate weighs 8¼ pounds. How would this weight be reported as a decimal to the nearest hundredth? A B C D. 8.32

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer C First change 8¼ into an improper fraction by multiplying whole number by denominator and then add total to the numerator. Answer: 8 x 4 = = 33/4 Divide numerator by the denominator. Answer: 33/4 = 8.25 pounds

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Adding Decimals Stack vertically, making sure all the decimal points line up Add each vertical column of numbers Example:

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Subtracting Decimals Stack vertically, making sure all the decimal points line up Subtract each vertical column of numbers Example:

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Multiplying Decimals Line up numbers on the right and do not align decimal points Multiple each top number by each bottom number Place the decimal point in the answer by starting at the right and moving the point the same number of places equal to the sum of the decimal points in the numbers multiplied Example: 1.4 x 3.02 = 4.228

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dividing Decimals REMINDER Numerator = dividend Denominator = divisor Answer = quotient Write dividend and place a decimal point immediately after it. Then place another decimal point above it on quotient line. Example: 12/16 = 0.75

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Question What is to the nearest hundredths? A. 6.3 B C D

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer C –0.3 is to tenths –0.33 is to hundredths –0.326 is to thousandths place Round off decimal, drop the final number. Exception: If final number is 5 or above, drop it and then increase adjacent number by 1 –Example: becomes 6.33

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Percentage Parts per hundred Fraction with variable numerator and a denominator that’s always 100

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Fraction Converted to Percentage Denominator 100, write numerator as a percent –Example: 15/100 = 15% Denominator not 100, convert fraction using 100 as common denominator –Example: 9/20 = 45/100 = 45%

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Ratios Converted to Percentage Second number in ratio is 100, write first number as percent –Example: 4:100 = 4% Second number in ratio not 100, convert ratio using 100 as common number –Example: 2:20 = 10:100 = 20%

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Decimals Converted to Percent Move decimal point two places to right and write percent sign –Example: 0.06 = 6%

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Ratio and Proportion Fraction shows part (numerator) relates to whole (denominator) Ratio relationship between two numbers Ratios written as two numbers separated by a colon –Example 2:10 Proportion relationship between two ratios or two fractions

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Solving Ratio and Proportion Cross multiply Clear x Reduce –Example: 7/70 = 11/x 7x = 70 x × 11 / 7 x = 110

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Ratio and Proportion in Dosage Order: 1.5 mg of medication Supply: 0.75 mg per 4 mL 1.5/0.75 = x/4 6 = 0.75 x x = 6/0.75 x = 8

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Question A client is to receive 150 mg of a medication. The medication is supplied in 75 mg per 2 mL. Use ratio and proportion formula to solve the problem. How many mL should be administered? A. 1½ B. 2 C. 3.5 D. 4

Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer D. 4 Order: 150 mg of medication Supply: 75 mg per 2 mL 150/75 = x/2 300 = 75x x = 300/75 x = 4