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Nursing Math: Dosage and Calculations/

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Ratio and ProportionMetric System

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Conversions: Weight

Conversions: Volume

Conversions: Pounds and Kilograms

The ratio and proportion method is one of the ways to solve dosage calculations. A ratio is two numbers separated by a colon (:). A colon indicates the need to divide. A proportion is two ratios of equal value. A proportion can be written as two fractions or ratios on either side of a double colon (::). A double colon and an equal sign are interchangeable. In a proportion equation, the first and last numbers are called the extremes, and the second and third numbers are the means. When setting up the proportion, you will need to put the ratios in the same arrangement. One of the ratios will contain an x indicating the unknown value. Next you will cross-multiply the means and extremes, and then divide both sides by the number before the x.

RATIO

Two Numbers Separated by a Colon

*Two Numbers Separated by a Colon*

A ratio indicates a connection between two numbers that is separated by a colon.

Colon Indicates Division

*Colon Same as Division-sign*

A colon signifies the use of division. A colon is interchangeable with a division sign.

PROPORTION

Equation with Two Equal Ratios

*Potion is Filled with Two Equal Radios*

A proportion is an equation that has two equal ratios. For example: 1/3 = 3/9.

Double Colons Indicates Equal Sign

*Double Colon Same as Equal Sign*

When there is a double colon between two ratios, it indicates an equivalent value between the ratios. A double colon is interchangeable with an equal sign.

Extremes

*Extreme X*

The extremes in a proportion are the first and last numbers. For example: in 1/3 = 3/9, 1 and 9 are the extremes.

Means

*Mean M*

The means are the second and third numbers in a proportion. For example: in 1/3 = 3/9, 3 and 3 are the means.

CALCULATING THE DOSE

Set up the Proportion

*Set Up Potion*

When setting up the proportion, you will need to put the ratio in the same arrangement. For example: mg/mL = mg/mL. When you are setting up the proportion remember that one of the ratios will contain an “x” because the amount is unknown. Example: 100mg/5mL = 160mg/xmL)

Cross-Multiply Means and Extremes

*Cross-Multiply Mean M and Extreme X*

The second part of the equation is to cross-multiply the means and extremes. Using the above proportion it would look like 100x = 5 x 160.

Divide Both Sides by the Number Before Unknown Variable

*Divide Both Sides by the Number Before Question-mark*

The final step to determine the dose is to divide both sides by the number before x. Example: 100x/100 = 800/100. This would give you x = 8mL.

Picmonic's rapid review multiple-choice quiz allows you to assess your knowledge.

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