This answer key shows a full worked solution for each of the 10 unit conversion problems, including the conversion factor used in every step. Compare your factors, your calculations, and the bold final answers with units.
Problem 1: Feet to inches
Feet to inches: multiply by \(\frac{12\text{ in}}{1\text{ ft}}\).
\(5 \times 12 = 60\).
60 inches.
Problem 2: Inches to feet
Inches to feet: divide by 12.
\(84 : 12 = 7\).
7 feet.
Problem 3: Pounds to ounces
Multiply by \(\frac{16\text{ oz}}{1\text{ lb}}\): \(4 \times 16 = 64\).
64 ounces.
Problem 4: Gallons to quarts
Multiply by \(\frac{4\text{ qt}}{1\text{ gal}}\): \(3 \times 4 = 12\).
12 quarts.
Problem 5: Miles to feet
Multiply by \(\frac{5{,}280\text{ ft}}{1\text{ mi}}\): \(2.5 \times 5{,}280 = 13{,}200\).
Check: \(2 \times 5{,}280 = 10{,}560\) and half a mile is \(2{,}640\); \(10{,}560 + 2{,}640 = 13{,}200\).
13,200 feet.
Problem 6: Feet to yards
Divide by 3 because 3 feet equal 1 yard: \(18 : 3 = 6\).
6 yards.
Problem 7: Cups, pints, and quarts
Pints: 2 cups equal 1 pint, so \(12 : 2 = 6\) pints.
Quarts: 2 pints equal 1 quart, so \(6 : 2 = 3\) quarts.
6 pints and 3 quarts.
Problem 8: Metric lengths
(a) \(3.5 \times 1{,}000 = 3{,}500\) m.
(b) \(450 : 100 = 4.5\) m.
(a) 3,500 meters. (b) 4.5 meters.
Problem 9: Base paths
Distance: \(4 \times 90 = 360\) feet.
Yards: \(360 : 3 = 120\).
360 feet, or 120 yards.
Problem 10: Hiking trail
Trail length in feet: \(2 \times 5{,}280 = 10{,}560\).
Left: \(10{,}560 – 6{,}600 = 3{,}960\) feet.
In miles: \(3{,}960 : 5{,}280 = 0.75\).
3,960 feet, which is 0.75 mile.
See every chapter on the Grade 6 math page.