Medical Dosage Calculations A Dimensional Analysis Approach Eleventh Edition Chapter 1 Review of Arithmetic for Dosage Calculations

Learning Objectives (1 of 2) 1.1 Reduce and build fractions into equivalent forms. 1.2 Add, subtract, multiply, and divide fractions. 1.3 Simplify complex fractions. 1.4 Convert between decimal numbers and fractions. 1.5 Add, subtract, multiply, and divide decimal numbers. Slide 2 is list of textbook LO numbers and statements

Learning Objectives (2 of 2) 1.6 Calculate doses based on body weight. 1.7 Write percentages as decimal numbers and fractions. 1.8 Find the percent of a number and the percent of change. 1.9 Estimate answers. 1.10 Use a calculator to verify answers. Slide 3 is list of textbook LO numbers and statements

Decimal Numbers (1 of 2)

Decimal Numbers (2 of 2) A decimal number represents a fraction with a denominator of 10, 100, 1000, and so on. Each decimal number has three parts: the whole number part, the decimal point, and the fraction part.

Changing Decimal Numbers to Fractions (1 of 4) Reading a decimal number will help you to write it as a fraction:

Changing Decimal Numbers to Fractions (2 of 4) A number can be written in many different forms. For example, the decimal number 0.5 is read as five tenths. In fraction form, it is:

Changing Decimal Numbers to Fractions (3 of 4) A decimal number greater than 1, such as 3.5 is read as three and five tenths, and can also be written as a mixed number which combines a whole number and a proper fraction,

Changing Decimal Numbers to Fractions (4 of 4) Write 2.25 as an improper fraction. The number 2.25 is read as two and twenty-five hundredths and written

Ratios A ratio is a comparison of two numbers. 5 to 10 can be expressed at 5:10 or 5/10.

Changing Fractions to Decimal Numbers (1 of 6) To change a fraction to a decimal number, think of the fraction as a division problem.

Changing Fractions to Decimal Numbers (2 of 6) Here are the steps for this division: Step One: Replace 2 with 2.0 and then place a decimal point directly above the decimal point in 2.0

Changing Fractions to Decimal Numbers (3 of 6) Step Two: Perform the division 2.

Changing Fractions to Decimal Numbers (4 of 6)

Changing Fractions to Decimal Numbers (5 of 6)

Changing Fractions to Decimal Numbers (6 of 6)

Rounding Decimal Numbers (1 of 5) Rounding off may either increase or decrease the number. For example, round off 1.267 to the nearest tenth (one decimal place) Answer: 1.3 Rounding down a number will not increase the number. In particular, to round 1.267 down to the tenths place (one decimal place) Answer: 1.2

Rounding Decimal Numbers (2 of 5) (a) Round off 4.8075 to the nearest hundredth, tenth, and whole number. 4.8075 rounded off to the nearest: hundredth = 4.81 tenth = 4.8 whole number = 5

Rounding Decimal Numbers (3 of 5) (b) Round down 3.726 to the nearest hundredth, tenth, and whole number. 3.726 rounded down to the nearest: hundredth = 3.72 tenth = 3.7 whole number = 3

Rounding Decimal Numbers (4 of 5) For small liquid volumes: amounts less than 1 mL will be rounded to hundredths, while amounts greater than 1 mL will be rounded to tenths. For example, 0.345 mL ≈ 0.35 mL and 1.345 mL ≈ 1.3 mL

Rounding Decimal Numbers (5 of 5) Because the danger of an overdose must always be guarded against (particularly with pediatric meds and high-alert drugs), the amount of medication to be administered is sometimes rounded down instead of rounded off

Adding Decimal Numbers Keep the decimal points aligned

Subtracting Decimal Numbers Keep the decimal points aligned

Multiplying Decimal Numbers (1 of 2)

Multiplying Decimal Numbers (2 of 2)

Dividing Decimal Numbers (1 of 2)

Dividing Decimal Numbers (2 of 2)

Estimating Answers Carefully enter the keystroke sequence when using a calculator. Think: Is the answer reasonable? Use rounding to estimate the size of the answer.

Multiplying Fractions (1 of 2)

Multiplying Fractions (2 of 2) It is often convenient to cancel before you multiply.

Dividing Fractions (1 of 4)

Dividing Fractions (2 of 4)

Dividing Fractions (3 of 4)

Dividing Fractions (4 of 4) The numerator of this fraction is 0.35, a decimal number. You can write an equivalent form of the fraction by multiplying the numerator and denominator by 100.

Complex Fractions (1 of 3) Complex fractions have fractions in their numerators and/or fractions in their denominators. A longer fraction line separates the main numerator from the main denominator, and indicates division.

Complex Fractions (2 of 3)

Complex Fractions (3 of 3)

Addition and Subtraction of Fractions (1 of 2) Add (or subtract) the numerators when the denominators are the same:

Addition and Subtraction of Fractions (2 of 2)

When the Denominators are Different use a Common Denominator (1 of 2)

When the Denominators are Different use a Common Denominator (2 of 2)

Percentages Percent (%) means parts per hundred (1 of 3)

Percentages Percent (%) means parts per hundred (2 of 3) Write 0.5% as a fraction.

Percentages Percent (%) means parts per hundred (3 of 3) There is another way to get the answer.

What is 20% of 300?

Percent of Change (1 of 2) Fraction of Change

Percent of Change (2 of 2) What is the percent of change? A daily dosage increases from 4 tablets to 5 tablets.