Scenario: Speed Calculations - Calculate rates using complex fractions!
If you walk ⅔ kilometers in ¾ hours, what is your walking speed in kilometers per hour?
Problem: Speed = Distance ÷ Time = (⅔) ÷ (¾)
Step 1: Write as a complex fraction
(⅔) ÷ (¾) = (⅔)/(¾)
Step 2: Apply the rule: Complex Fraction = Numerator ÷ Denominator
(⅔)/(¾) = ⅔ ÷ ¾
Step 3: Multiply by the reciprocal
⅔ ÷ ¾ = ⅔ × 4/3 = (2×4)/(3×3) = 8/9
Step 4: Interpret the result
Speed = 8/9 kilometers per hour ≈ 0.89 km/h
Answer: Your walking speed is 8/9 kilometers per hour.
A complex fraction is a fraction where the numerator, denominator, or both contain fractions.
(⅔)/(¾) - fraction over fraction
2/(½) - whole number over fraction
(1½)/3 - mixed number over whole number
Complex Fraction = Numerator ÷ Denominator
Then use "Keep, Change, Flip" for division
If you drink ½ cup per minute, how many cups do you drink in ¼ hour?
Solution: ¼ hour = 15 minutes
Cups = ½ cup/min × 15 min = 7.5 cups
Simplify: (3/5)/(6/7)
Solution: (3/5)/(6/7) = 3/5 ÷ 6/7 = 3/5 × 7/6 = 21/30 = 7/10
Simplify: (1.2)/(3/4)
Solution: (1.2)/(3/4) = 1.2 ÷ 3/4 = 1.2 × 4/3 = 4.8/3 = 1.6
A car travels 1½ miles in ⅔ hours. What is the car's speed in miles per hour?
Your solution:
Simplify: (2/3)/(4/5)
Your solution: