Dividing fractions
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
What is 3/5 ÷ 1/10?
Check 2
A quotient of 2⅔ pieces, with each piece 3/4 m long, leaves what length after cutting two full pieces?
Challenge 1
A rectangular patch has area 7/8 m² and width 1/4 m. Find its length and verify it.
Show a hint
Use the area relationship: divide the total area by the known width, then multiply to check.
Show the worked solution
3½ m.
Since area equals length times width, length is (7/8) ÷ (1/4) = 7/2 m. Checking the two lengths gives (7/2) × (1/4) = 7/8 m².
Challenge 2
You have 5¼ L of juice and cups holding 3/8 L. Can you fill 15 cups? Explain with an exact calculation.
Show a hint
Convert the mixed number and divide by one cup's capacity.
Show the worked solution
No; exactly 14 cups can be filled.
(21/4) ÷ (3/8) = (21/4) × (8/3) = 14. Fifteen cups would need 45/8 = 5⅝ L.
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