Converting improper fractions to mixed numbers
Convert the improper fraction 9/4 to a mixed number in lowest terms.
2 1/4
To convert an improper fraction to a mixed number, divide the numerator by the denominator: 9 ÷ 4 = 2 with remainder 1. Place the remainder over the denominator: 2 1/4. The answer is already in lowest terms.
Reduce the fraction 8/12 to lowest terms.
2/3
To reduce a fraction to lowest terms, divide both the numerator and denominator by their greatest common factor. For 8/12, the greatest common factor is 4. Divide both: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2/3.
Add the fractions: 1/4 + 2/4
3/4
When fractions have the same denominator, add the numerators and place the sum over the common denominator: 1 + 2 = 3, so 1/4 + 2/4 = 3/4. The answer is already in lowest terms.
A medication calculation results in 2.847 mL. Round this to the nearest hundredth.
2.85 mL
Look at the digit in the thousandths place (7). Since 7 is 5 or greater, increase the hundredths place by one. The 4 becomes 5, giving 2.85 mL.
A nurse administers 2.5 mL of medication in the morning and 1.75 mL in the evening. What is the total volume administered?
4.25 mL
Line up the decimal points and add:
2.5 + 1.75 ------ 4.25
The total volume is 4.25 mL. Accurate decimal addition is critical in medication administration to prevent dosing errors.
A medication order is for 0.25 mg per kg. The patient weighs 68 kg. What is the total dose?
17 mg
Multiply: 0.25 × 68 = 17 mg. When multiplying decimals, multiply as if they were whole numbers, then count the total decimal places in both factors (2 places in 0.25) and place the decimal point in the answer accordingly.
Convert 15/6 to a mixed number and reduce to lowest terms.
2 1/2
Divide the numerator by the denominator: 15 ÷ 6 = 2 with remainder 3. This gives 2 3/6. Reduce to lowest terms by dividing both numerator and denominator by 3: 2 1/2.
What is 15/20 reduced to lowest terms?
3/4
Find the greatest common factor of 15 and 20, which is 5. Divide both numerator and denominator by 5: 15 ÷ 5 = 3 and 20 ÷ 5 = 4, giving 3/4.
Add: 1/3 + 1/6 = ?
1/2
Find the lowest common denominator (LCD), which is 6. Convert 1/3 to sixths: 6 ÷ 3 = 2; 2 × 1 = 2, so 1/3 = 2/6. Now add: 2/6 + 1/6 = 3/6. Reduce to lowest terms: 1/2.
A dosage calculation yields 0.678 mg. Round this to the nearest tenth.
0.7 mg
Look at the digit in the hundredths place (7). Since 7 is 5 or greater, increase the tenths place by one. The 6 becomes 7, giving 0.7 mg. Most calculations require carrying division to at least two decimal places and rounding to the nearest tenth for accuracy.
Subtract 0.75 mg from 2.5 mg.
1.75 mg
Line up the decimal points and subtract:
2.50 - 0.75 ------ 1.75
The answer is 1.75 mg. Adding zeros as placeholders helps ensure accurate alignment.
Divide: 7.5 ÷ 2.5 = ?
3
When dividing decimals, move the decimal point in the divisor (2.5) to make it a whole number (25), then move the decimal point in the dividend (7.5) the same number of places (75). Now divide: 75 ÷ 25 = 3.
What is 22/8 converted to a mixed number in lowest terms?
2 3/4
Divide: 22 ÷ 8 = 2 with remainder 6, giving 2 6/8. Reduce by dividing both 6 and 8 by their greatest common factor of 2: 2 3/4.
Reduce 24/36 to lowest terms.
2/3
The greatest common factor of 24 and 36 is 12. Divide both by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving 2/3. Reducing fractions is essential in medication calculations to express answers in simplest form.
3/4 - 1/2 = ?
1/4
Find the LCD, which is 4. Convert 1/2 to fourths: 4 ÷ 2 = 2; 2 × 1 = 2, so 1/2 = 2/4. Now subtract: 3/4 - 2/4 = 1/4.
Round 4,567 to the nearest thousand.
5,000
Look at the hundreds place (5). Since 5 or greater, round up. The 4 in the thousands place becomes 5, giving 5,000.
Add: 0.125 + 0.25 + 0.5 = ?
0.875
Line up decimal points and add:
0.125 0.250 + 0.500 ------- 0.875
Multiply: 1.5 × 0.4 = ?
0.6
Multiply: 15 × 4 = 60. Count total decimal places (1 + 1 = 2), so place the decimal two places from the right: 0.60 or 0.6.
Convert 100/25 to a mixed number or whole number.
A. 4
Divide the numerator by the denominator: 100 ÷ 25 = 4 with no remainder. When there is no remainder, the answer is a whole number.
What is 50/100 reduced to lowest terms?
1/2
The greatest common factor of 50 and 100 is 50. Divide both by 50: 50 ÷ 50 = 1 and 100 ÷ 50 = 2, giving 1/2.
Add: 2/5 + 1/10 = ?
1/2
The LCD is 10. Convert 2/5 to tenths: 10 ÷ 5 = 2; 2 × 2 = 4, so 2/5 = 4/10. Add: 4/10 + 1/10 = 5/10. Reduce by dividing both by 5: 1/2.
A calculation results in 1.243 mL. Round to the nearest tenth.
1.2 mL
Look at the hundredths place (4). Since 4 is less than 5, the tenths place stays the same. Drop the 4, giving 1.2 mL.
A patient's IV bag contains 1000 mL. After 487.5 mL has infused, how much remains?
512.5 mL
Subtract:
1000.0 - 487.5 -------- 512.5
The remaining volume is 512.5 mL.
A vial contains 100 mg in 2.5 mL. How many mg are in 1 mL?
40 mg
Divide: 100 ÷ 2.5 = 40 mg/mL. Move the decimal in 2.5 one place right to make it 25, then move the decimal in 100 one place right to make it 1000. Divide: 1000 ÷ 25 = 40.
Convert 17/5 to a mixed number in lowest terms.
3 2/5
Divide: 17 ÷ 5 = 3 with remainder 2. Place the remainder over the denominator: 3 2/5. The fraction is already in lowest terms.
Reduce 18/24 to lowest terms.
3/4
The greatest common factor of 18 and 24 is 6. Divide both by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Always reduce fractions to lowest terms in medication dosage calculations.
A patient is to receive 1 1/2 tablets in the morning and 2 1/3 tablets in the evening. What is the total number of tablets the patient will receive in one day?
3 5/6 tablets
Step 1: Convert mixed numbers to improper fractions:
Step 2: Find the lowest common denominator (LCD). The LCD of 2 and 3 is 6.
Step 3: Convert to equivalent fractions with denominator of 6:
Step 4: Add the fractions: 9/6 + 14/6 = 23/6
Step 5: Convert the improper fraction to a mixed number: 23 ÷ 6 = 3 with remainder 5, so 23/6 = 3 5/6 tablets
When adding mixed numbers with different denominators, convert to improper fractions first, find the LCD, change to equivalent fractions, add, and convert back to a mixed number if necessary.
Round 0.9847 to the nearest hundredth.
0.98
Look at the thousandths place (4). Since 4 is less than 5, the hundredths place remains unchanged at 8, giving 0.98.
Add: 16.4 + 21.8 + 13.2 = ?
51.4
Line up decimal points and add:
16.4 21.8 + 13.2 ------ 51.4
Decimal point errors are a major source of medication errors, making careful alignment essential for patient safety.
Multiply: 0.125 × 8 = ?
1.0
Multiply: 125 × 8 = 1000. The factor 0.125 has 3 decimal places, so place the decimal three places from the right: 1.000 or 1.0. Accurate multiplication and division of decimals is essential for safe medication dosage calculations.