Dosage Calculations Packet PDF | Nursing and Pharmacology Practice Problems with Step-by-Step Solutions

Dosage Calculations Packet


Unit I – Basic Mathematics Review
This unit will review Arabic and Roman numerals,
fractions, decimals, percentage, and ratio and proportion.

ARABIC AND ROMAN NUMERALS

Arabic and Roman numerals are used interchangeably to
express quantity or degree of measure. Roman numbers are
formed by combining the following letters according to the
rules stated below:

Arabic numbers Roman numbers
½ ss
1 I
5 V
10 X
50 L
100 C
500 D
1000 M

1. To repeat a Roman number doubles its value. I =1; II=2
2. To place a letter to the right of a Roman number adds its
value to that number. V=5; VI=6.
3. To place a letter to the left of a Roman number
decreases the value of that number by the amount
of the number added. V=5; IV=4.

Practice Problems

Write the Arabic numbers for the following:
1. III_____ 2. XVI _____ 3. XXXIX _____
4. VI_____ 5. CM______ 6. XXIV _____
1

,Write the Roman numbers for the following:
7. 2 _____ 8. 14 _____ 9. 40 _____ 10. 69 ______
11. 80 _____ 12.150 _____ 13. 99 _____ 14. 19 ______


Answers:
1. 3 2. 16 3. 39 4. 6 5. 900 6. 24
7. II 8. XIV 9. XL 10. LXIX
11. LXXX 12. CL 13. IC 14. XIX



FRACTIONS

Definition: A fraction is a part of a whole number. A
fraction has 2 parts, the top number is called the numerator
and the bottom number is called the denominator.

Example: ½ = 1 is the numerator and 2 is the denominator.

There are 4 types of fractions:

1. Proper fractions – the numerator is less than the
denominator. Example: ½.

2. Improper fractions – the numerator is greater than the
denominator. Example: 6/5.

3. Complex fractions – the numerator or denominator may
be either a fraction or a whole number.

Example: ½ or ½
2 ¾

4. Mixed number – there is a whole number and a fraction
combined. Example: 3 ½.

2

, To change a mixed number to an improper fraction, you
must multiply the whole number by the denominator
and add the numerator. Example: 3 ½ = 7/2.



Practice Problems

Reduce the following fractions to the lowest terms

2/4=_____ 10/20= _____ 2/8 = _____
3/6=_____ 15/20= _____ 8/12=_____
3/9=_____ 2/10= _____ 5/10=_____
4/6=_____ 3/12= _____ 3/15=_____

Answers:
1. ½ 2. ½ 3. 1/4 4. ½ 5. ¾ 6. 2/3
7. 1/3 8. 1/5 9. ½ 10. 2/3 11. ¼ 12. 1/5



Change the following improper fractions to mixed numbers

1. 6/4=_____ 2. 7/5=_____ 3. 15/8= _____
4. 3/2=_____ 5. 7/3=_____ 6. 11/10=_____

Answers:
1. 1 ½ 2. 1 2/5 3. 1 7/8 4. 1 ½ 5. 2 1/3 6. 1 1/10



Change the following mixed numbers to improper fractions

1. 3 ½= _____ 2. 6 ½=_____ 3. 10 ½=_____
4. 33 1/3= _____ 5. 8 ¾=_____ 6. 9 3/5=_____

Answers:
1. 7/2 2. 13/2 3. 21/2 4. 100/3 5. 35/4 6. 48/5
3

, Adding Fractions With Like Denominators:

1. Add the numerators.
2. Place the answer over the denominator.
3. Reduce the answer to the lowest term by dividing the
numerator and the denominator by the largest number
that can divide them both.

Example: 1/8 +1/8 =2/8

Divide the numerator and denominator by 2 and
2/8 becomes ¼.




Adding Fractions With Unlike Denominators:

1. Determine the smallest number that the denominators of
each fraction divide into evenly. This is called the least
common denominator(LCD).
2. Divide the denominator into the LCD and multiply the
results by the numerator.
3. Add the new numerators and place over the new
denominator.
4. Reduce to lowest terms.

Example:1/2 + 1/3 ( 2 and 3 will divide evenly into 6)
6 divided by 2 = 3 x 1 = 3
6 divided by 3 = 2 x 1 = 2
3+2 = 5
6 6 This is reduced to the lowest terms.




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