Chapter 10: worked solutions and marking guide
39 review answers and 39 exam answers
Chapter review solutions
Convert 8 L 986 mL entirely to mL.
Each L is 1,000 mL. Multiply 8×1,000, then add 986: 8,986 mL.
Convert 2 ft to in.
One ft = 12 in; 2×12=24.
How many ounces of weight are in 7 lb 10 oz?
Each pound weighs 16 ounces. 7×16+10=122.
Convert 3 pints to cups.
Each pint has 2 cups; multiply by 3.
Convert 4 h 28 min to minutes.
4×60+28=268 minutes.
Find 2/3 of a quantity measuring 24 L.
Each of 3 parts is 8 L; 2 parts are 16 L.
Find 1/4 of a quantity measuring 24 cm.
Each of 4 parts is 6 cm; 1 parts are 6 cm.
Convert 6 m 61 cm entirely to cm.
Each m is 100 cm. Multiply 6×100, then add 61: 661 cm.
Convert 357 in to mixed yd and in.
Divide by 36: 9 groups and 33 leftover.
How many ounces of weight are in 11 lb 10 oz?
Each pound weighs 16 ounces. 11×16+10=186.
Convert 7 pints to cups.
Each pint has 2 cups; multiply by 7.
Convert 6 h 47 min to minutes.
6×60+47=407 minutes.
Find 1/2 of a quantity measuring 20 m.
Each of 2 parts is 10 m; 1 parts are 10 m.
Find 1/3 of a quantity measuring 12 L.
Each of 3 parts is 4 L; 1 parts are 4 L.
Convert 4 kg 851 g entirely to g.
Each kg is 1,000 g. Multiply 4×1,000, then add 851: 4,851 g.
Convert 8 yd to ft.
One yd = 3 ft; 8×3=24.
How many ounces of weight are in 9 lb 11 oz?
Each pound weighs 16 ounces. 9×16+11=155.
Convert 4 quarts to pints.
Each quart has 2 pints; multiply by 4.
Convert 2 h 18 min to minutes.
2×60+18=138 minutes.
Find 1/3 of a quantity measuring 30 cm.
Each of 3 parts is 10 cm; 1 parts are 10 cm.
Find 2/5 of a quantity measuring 50 cm.
Each of 5 parts is 10 cm; 2 parts are 20 cm.
Convert 5 L 988 mL entirely to mL.
Each L is 1,000 mL. Multiply 5×1,000, then add 988: 5,988 mL.
Convert 8 mi to ft.
One mi = 5,280 ft; 8×5,280=42,240.
How many ounces of weight are in 9 lb 8 oz?
Each pound weighs 16 ounces. 9×16+8=152.
Convert 9 quarts to pints.
Each quart has 2 pints; multiply by 9.
Convert 4 h 37 min to minutes.
4×60+37=277 minutes.
Find 1/3 of a quantity measuring 9 L.
Each of 3 parts is 3 L; 1 parts are 3 L.
Find 1/6 of a quantity measuring 36 L.
Each of 6 parts is 6 L; 1 parts are 6 L.
Convert 4 L 693 mL entirely to mL.
Each L is 1,000 mL. Multiply 4×1,000, then add 693: 4,693 mL.
Convert 10 yd to ft.
One yd = 3 ft; 10×3=30.
How many ounces of weight are in 7 lb 5 oz?
Each pound weighs 16 ounces. 7×16+5=117.
Convert 4 gallons to cups.
Each gallon has 16 cups; multiply by 4.
Convert 4 kg 251 g entirely to g. Explain or sketch the mathematical relationship.
Each kg is 1,000 g. Multiply 4×1,000, then add 251: 4,251 g. State which quantities or geometric properties justify the method.
A classmate claims 5 yd equals 150 ft. Explain the mistake. Explain or sketch the mathematical relationship.
The conversion factor is 3, so 5 yd equals 15 ft, not ten times that. State which quantities or geometric properties justify the method.
One parcel is 12 lb 7 oz. A second is 13 lb 2 oz. How many total ounces of weight? Explain or sketch the mathematical relationship.
Convert each parcel to ounces of weight, then add: 199+210=409. State which quantities or geometric properties justify the method.
Convert 9 gallons to quarts. Explain or sketch the mathematical relationship.
Each gallon has 4 quarts; multiply by 9. State which quantities or geometric properties justify the method.
Convert 827 seconds to minutes and seconds. Explain or sketch the mathematical relationship.
Each 60 seconds is one minute; 827=60×13+47. State which quantities or geometric properties justify the method.
Find 3/6 of a quantity measuring 60 m. Explain or sketch the mathematical relationship.
Each of 6 parts is 10 m; 3 parts are 30 m. State which quantities or geometric properties justify the method.
A quantity of 32 cm is reduced by 2/4 of the original amount. Then 1/4 of what remains is used. How much is left? Explain or sketch the mathematical relationship.
After first use, 32−16=16 cm. Second use is 16÷4=4 cm; final 12 cm. State which quantities or geometric properties justify the method.
Practice examination solutions
How many ounces of weight are in 11 lb 2 oz?
Each pound weighs 16 ounces. 11×16+2=178.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A quantity of 48 L is reduced by 3/4 of the original amount. Then 1/2 of what remains is used. How much is left? Explain or sketch the mathematical relationship.
After first use, 48−36=12 L. Second use is 12÷2=6 L; final 6 L. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Find 5/6 of a quantity measuring 24 L.
Each of 6 parts is 4 L; 5 parts are 20 L.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 2/8 of a quantity measuring 64 m.
Each of 8 parts is 8 m; 2 parts are 16 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 6 m 18 cm entirely to cm.
Each m is 100 cm. Multiply 6×100, then add 18: 618 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 3/5 of a quantity measuring 50 m. Explain or sketch the mathematical relationship.
Each of 5 parts is 10 m; 3 parts are 30 m. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Convert 7 m 41 cm entirely to cm.
Each m is 100 cm. Multiply 7×100, then add 41: 741 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 8 ft to in.
One ft = 12 in; 8×12=96.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 4 h 43 min to minutes.
4×60+43=283 minutes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 6 h 48 min to minutes.
6×60+48=408 minutes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Rename 58 oz as pounds and ounces.
58 = 16×3+10.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 3/5 of a quantity measuring 45 cm.
Each of 5 parts is 9 cm; 3 parts are 27 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Explain how a gallon can equal 16 cups even though 1 gallon is 4 quarts. Explain or sketch the mathematical relationship.
Use the unit chain gallon→4 quarts→2 pints each→2 cups each. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Convert 3 L 109 mL entirely to mL.
Each L is 1,000 mL. Multiply 3×1,000, then add 109: 3,109 mL.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Explain how a gallon can equal 16 cups even though 1 gallon is 4 quarts.
Use the unit chain gallon→4 quarts→2 pints each→2 cups each.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Convert 7 h 41 min to minutes.
7×60+41=461 minutes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 2/5 of a quantity measuring 40 m.
Each of 5 parts is 8 m; 2 parts are 16 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 35 ft to mixed yd and ft.
Divide by 3: 11 groups and 2 leftover.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 2/8 of a quantity measuring 32 m.
Each of 8 parts is 4 m; 2 parts are 8 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 2/3 of a quantity measuring 12 L.
Each of 3 parts is 4 L; 2 parts are 8 L.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 7 mi to ft.
One mi = 5,280 ft; 7×5,280=36,960.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 1/2 of a quantity measuring 24 cm.
Each of 2 parts is 12 cm; 1 parts are 12 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 5 quarts to cups.
Each quart has 4 cups; multiply by 5.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 6 h 42 min to minutes.
6×60+42=402 minutes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 5 quarts to pints.
Each quart has 2 pints; multiply by 5.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 3 yd to ft.
One yd = 3 ft; 3×3=9.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 2 kg 745 g entirely to g. Explain or sketch the mathematical relationship.
Each kg is 1,000 g. Multiply 2×1,000, then add 745: 2,745 g. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Convert 4 L 989 mL entirely to mL.
Each L is 1,000 mL. Multiply 4×1,000, then add 989: 4,989 mL.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many ounces of weight are in 11 lb 12 oz?
Each pound weighs 16 ounces. 11×16+12=188.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rope is 6 mi. Another is 31,678 ft. Which is longer and by how much? Explain or sketch the mathematical relationship.
6 mi = 31,680 ft; compare with 31,678. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Convert 2 quarts to pints.
Each quart has 2 pints; multiply by 2.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many ounces of weight are in 8 lb 1 oz?
Each pound weighs 16 ounces. 8×16+1=129.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 6 km 352 m entirely to m.
Each km is 1,000 m. Multiply 6×1,000, then add 352: 6,352 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Convert 6 h 50 min to minutes.
6×60+50=410 minutes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many ounces of weight are in 5 lb 5 oz? Explain or sketch the mathematical relationship.
Each pound weighs 16 ounces. 5×16+5=85. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Convert 3 gallons to quarts.
Each gallon has 4 quarts; multiply by 3.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Find 4/6 of a quantity measuring 48 L.
Each of 6 parts is 8 L; 4 parts are 32 L.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many days are in 1 week and 4 days? Explain or sketch the mathematical relationship.
1×7+4=11. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Find 3/4 of a quantity measuring 12 L.
Each of 4 parts is 3 L; 3 parts are 9 L.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.