Fractions and Operations Quiz

Study Notes

Proper fractions have a denominator larger than the numerator.
Improper fractions have a numerator that is greater than their denominator. They represent values greater than 1.
Mixed numbers include an integer and a fraction.
To convert an improper fraction to a mixed number, divide the denominator into the numerator. The quotient is the integer part of the mixed number. The remainder becomes the numerator of the fractional part.
Example: 7/2 can be written as 3 1/2.

Adding and Subtracting fractions:
- Fractions must have the same denominator before adding or subtracting.
- Find the least common multiple (LCM) of the denominators.
- Convert each fraction to have the LCM as its denominator.
- Add or subtract the numerators while keeping the denominator the same.
Multiplying fractions:
- Multiply the numerators and multiply the denominators together.
- Simplify the resulting fraction if possible.
Dividing fractions:
- Flip the second fraction (the divisor) and multiply it by the first fraction.
- Simplify the resulting fraction if possible.
Complex Fractions: Fractions within fractions.
- Simplify by:
  - Identifying the main fraction bar and simplifying the numerator and denominator separately if possible.
  - Dividing the numerator by the denominator or multiplying the numerator by the reciprocal of the denominator.
- Example: (3/1 - 3/4) / 5/8
  - Simplify the numerator: (3/1 - 3/4) = (12/4 - 3/4) = 9/4
  - Divide the numerator (9/4) by the denominator (5/8) - this becomes (9/4) * (8/5) = 72/20
  - Simplify: 72/20 = 18/5.

A unit rate is a ratio that compares two quantities where the second quantity is 1.
Example: A car travels 60 miles every hour. The unit rate would be 60 miles/1 hour.
To calculate the distance traveled over a longer period, multiply the unit rate by the time duration.
Example: 60 miles/1 hour * 8 hours = 480 miles.

A technician took 1/4 of the solution from a container and then divided it by 1/4.
- Solution: This is a fraction division problem. Dividing by 1/4 is the same as multiplying by 4. So, the technician has 1/4 of the original solution * 4 = 1 whole unit of the original solution left.
A healthcare professional split 12 ounces of powdered medicine into four equal amounts.
- Solution: This is a simple division problem. 12 ounces / 4 = 3 ounces per amount.
A pharmacy received 125 fluid ounces of medication and made 50 smaller containers from it.
- Solution: This is a division problem. 125 fluid ounces / 50 containers = 2.5 fluid ounces per container.
375 milliliters of IV solution drip into a patient every 3 hours.
- Solution: The unit rate is 125 mL/1 hour (375 mL / 3 hours).
- To find the total amount in 8 hours, multiply the unit rate by 8 hours: 125 mL/1 hour * 8 hours = 1000 mL.