Chapter 14: worked solutions and marking guide
39 review answers and 39 exam answers
Chapter review solutions
Calculate 0.3 × 7.
The displayed decimal contains 3 tenths. Multiply the number of equal units by 7: 21 tenths = 2.1.
Calculate 1.88 × 2.
Repeated addition or distribution: 188 hundredths ×2=376 hundredths=3.76.
Calculate 2.60 × 17, where 17 is a whole number.
Use (10+7) groups: 260 hundredths ×17=4420 hundredths = 44.20.
Calculate 0.84 ÷ 6.
Share 84 hundredths equally among 6 groups: 14 hundredths each = 0.14.
Calculate 1.60 ÷ 2.
160 hundredths ÷2=80 hundredths = 0.80. Verify by multiplying.
Divide 5.75 equally among 5 people. How much does each receive?
Convert to hundredths: 575÷5=115 hundredths = 1.15. Exchange hundreds/tenths when needed.
41.49 liters of juice are shared equally into 9 containers. How many liters per container?
4149 hundredths ÷9=461 hundredths = 4.61 liters. Check 4.61×9=41.49.
Calculate 0.7 × 3.
The displayed decimal contains 7 tenths. Multiply the number of equal units by 3: 21 tenths = 2.1.
Calculate 1.90 × 8.
Repeated addition or distribution: 190 hundredths ×8=1520 hundredths=15.20.
Calculate 2.40 × 13, where 13 is a whole number.
Use (10+3) groups: 240 hundredths ×13=3120 hundredths = 31.20.
Calculate 0.12 ÷ 6.
Share 12 hundredths equally among 6 groups: 2 hundredths each = 0.02.
Calculate 11.22 ÷ 6.
1122 hundredths ÷6=187 hundredths = 1.87. Verify by multiplying.
Divide 9.32 equally among 4 people. How much does each receive?
Convert to hundredths: 932÷4=233 hundredths = 2.33. Exchange hundreds/tenths when needed.
18.64 liters of juice are shared equally into 8 containers. How many liters per container?
1864 hundredths ÷8=233 hundredths = 2.33 liters. Check 2.33×8=18.64.
Calculate 0.5 × 5.
The displayed decimal contains 5 tenths. Multiply the number of equal units by 5: 25 tenths = 2.5.
Calculate 3.47 × 3.
Repeated addition or distribution: 347 hundredths ×3=1041 hundredths=10.41.
Calculate 2.06 × 18, where 18 is a whole number.
Use (10+8) groups: 206 hundredths ×18=3708 hundredths = 37.08.
Calculate 0.36 ÷ 6.
Share 36 hundredths equally among 6 groups: 6 hundredths each = 0.06.
Calculate 5.79 ÷ 3.
579 hundredths ÷3=193 hundredths = 1.93. Verify by multiplying.
Divide 6.60 equally among 5 people. How much does each receive?
Convert to hundredths: 660÷5=132 hundredths = 1.32. Exchange hundreds/tenths when needed.
22.32 liters of juice are shared equally into 4 containers. How many liters per container?
2232 hundredths ÷4=558 hundredths = 5.58 liters. Check 5.58×4=22.32.
Calculate 0.8 × 5.
The displayed decimal contains 8 tenths. Multiply the number of equal units by 5: 40 tenths = 4.0.
Calculate 4.19 × 3.
Repeated addition or distribution: 419 hundredths ×3=1257 hundredths=12.57.
Calculate 2.17 × 21, where 21 is a whole number.
Use (20+1) groups: 217 hundredths ×21=4557 hundredths = 45.57.
Calculate 0.08 ÷ 4.
Share 8 hundredths equally among 4 groups: 2 hundredths each = 0.02.
Calculate 2.30 ÷ 2.
230 hundredths ÷2=115 hundredths = 1.15. Verify by multiplying.
Divide 11.00 equally among 5 people. How much does each receive?
Convert to hundredths: 1100÷5=220 hundredths = 2.20. Exchange hundreds/tenths when needed.
14.43 liters of juice are shared equally into 3 containers. How many liters per container?
1443 hundredths ÷3=481 hundredths = 4.81 liters. Check 4.81×3=14.43.
Calculate 0.5 × 9.
The displayed decimal contains 5 tenths. Multiply the number of equal units by 9: 45 tenths = 4.5.
Calculate 2.46 × 6.
Repeated addition or distribution: 246 hundredths ×6=1476 hundredths=14.76.
Calculate 1.95 × 14, where 14 is a whole number.
Use (10+4) groups: 195 hundredths ×14=2730 hundredths = 27.30.
Calculate 0.45 ÷ 3.
Share 45 hundredths equally among 3 groups: 15 hundredths each = 0.15.
Calculate 0.3 × 9. Explain how place value or a model can check your result.
The displayed decimal contains 3 tenths. Multiply the number of equal units by 9: 27 tenths = 2.7. A correct explanation should name the relevant fractional place values and verify the answer.
Calculate 2.10 × 3. Explain how place value or a model can check your result.
Repeated addition or distribution: 210 hundredths ×3=630 hundredths=6.30. A correct explanation should name the relevant fractional place values and verify the answer.
Calculate 2.25 × 11, where 11 is a whole number. Explain how place value or a model can check your result.
Use (10+1) groups: 225 hundredths ×11=2475 hundredths = 24.75. A correct explanation should name the relevant fractional place values and verify the answer.
Calculate 0.04 ÷ 2. Explain how place value or a model can check your result.
Share 4 hundredths equally among 2 groups: 2 hundredths each = 0.02. A correct explanation should name the relevant fractional place values and verify the answer.
Calculate 3.16 ÷ 2. Explain how place value or a model can check your result.
316 hundredths ÷2=158 hundredths = 1.58. Verify by multiplying. A correct explanation should name the relevant fractional place values and verify the answer.
Divide 13.36 equally among 8 people. How much does each receive? Explain how place value or a model can check your result.
Convert to hundredths: 1336÷8=167 hundredths = 1.67. Exchange hundreds/tenths when needed. A correct explanation should name the relevant fractional place values and verify the answer.
6.08 liters of juice are shared equally into 2 containers. How many liters per container? Explain how place value or a model can check your result.
608 hundredths ÷2=304 hundredths = 3.04 liters. Check 3.04×2=6.08. A correct explanation should name the relevant fractional place values and verify the answer.
Practice examination solutions
Calculate 1.57 × 19, where 19 is a whole number.
Use (10+9) groups: 157 hundredths ×19=2983 hundredths = 29.83.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 8.75 ÷ 5.
875 hundredths ÷5=175 hundredths = 1.75. Verify by multiplying.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 1.54 × 14, where 14 is a whole number.
Use (10+4) groups: 154 hundredths ×14=2156 hundredths = 21.56.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.44 ÷ 4.
Share 44 hundredths equally among 4 groups: 11 hundredths each = 0.11.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.55 ÷ 5.
Share 55 hundredths equally among 5 groups: 11 hundredths each = 0.11.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 2.45 × 26, where 26 is a whole number. Explain how place value or a model can check your result.
Use (20+6) groups: 245 hundredths ×26=6370 hundredths = 63.70. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
13.68 liters of juice are shared equally into 4 containers. How many liters per container?
1368 hundredths ÷4=342 hundredths = 3.42 liters. Check 3.42×4=13.68.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 10.22 ÷ 7.
1022 hundredths ÷7=146 hundredths = 1.46. Verify by multiplying.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
31.68 liters of juice are shared equally into 8 containers. How many liters per container? Explain how place value or a model can check your result.
3168 hundredths ÷8=396 hundredths = 3.96 liters. Check 3.96×8=31.68. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
13.68 liters of juice are shared equally into 6 containers. How many liters per container?
1368 hundredths ÷6=228 hundredths = 2.28 liters. Check 2.28×6=13.68.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 0.8 × 9.
The displayed decimal contains 8 tenths. Multiply the number of equal units by 9: 72 tenths = 7.2.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 1.47 × 16, where 16 is a whole number.
Use (10+6) groups: 147 hundredths ×16=2352 hundredths = 23.52.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.12 ÷ 4.
Share 12 hundredths equally among 4 groups: 3 hundredths each = 0.03.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 1.38 × 2.
Repeated addition or distribution: 138 hundredths ×2=276 hundredths=2.76.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.9 × 7.
The displayed decimal contains 9 tenths. Multiply the number of equal units by 7: 63 tenths = 6.3.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 11.28 ÷ 6.
1128 hundredths ÷6=188 hundredths = 1.88. Verify by multiplying.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Divide 5.88 equally among 4 people. How much does each receive? Explain how place value or a model can check your result.
Convert to hundredths: 588÷4=147 hundredths = 1.47. Exchange hundreds/tenths when needed. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Calculate 0.20 ÷ 4.
Share 20 hundredths equally among 4 groups: 5 hundredths each = 0.05.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 1.88 × 8.
Repeated addition or distribution: 188 hundredths ×8=1504 hundredths=15.04.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 3.75 ÷ 3. Explain how place value or a model can check your result.
375 hundredths ÷3=125 hundredths = 1.25. Verify by multiplying. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Calculate 3.17 × 6. Explain how place value or a model can check your result.
Repeated addition or distribution: 317 hundredths ×6=1902 hundredths=19.02. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Calculate 3.28 ÷ 2.
328 hundredths ÷2=164 hundredths = 1.64. Verify by multiplying.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.2 × 4.
The displayed decimal contains 2 tenths. Multiply the number of equal units by 4: 8 tenths = 0.8.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.30 ÷ 2.
Share 30 hundredths equally among 2 groups: 15 hundredths each = 0.15.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Divide 14.07 equally among 7 people. How much does each receive?
Convert to hundredths: 1407÷7=201 hundredths = 2.01. Exchange hundreds/tenths when needed.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 3.88 × 6.
Repeated addition or distribution: 388 hundredths ×6=2328 hundredths=23.28.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
7.32 liters of juice are shared equally into 2 containers. How many liters per container?
732 hundredths ÷2=366 hundredths = 3.66 liters. Check 3.66×2=7.32.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 0.8 × 4.
The displayed decimal contains 8 tenths. Multiply the number of equal units by 4: 32 tenths = 3.2.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Divide 13.92 equally among 6 people. How much does each receive?
Convert to hundredths: 1392÷6=232 hundredths = 2.32. Exchange hundreds/tenths when needed.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 3.56 × 21, where 21 is a whole number.
Use (20+1) groups: 356 hundredths ×21=7476 hundredths = 74.76.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 9.12 ÷ 6.
912 hundredths ÷6=152 hundredths = 1.52. Verify by multiplying.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
9.73 liters of juice are shared equally into 7 containers. How many liters per container?
973 hundredths ÷7=139 hundredths = 1.39 liters. Check 1.39×7=9.73.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
25.44 liters of juice are shared equally into 8 containers. How many liters per container?
2544 hundredths ÷8=318 hundredths = 3.18 liters. Check 3.18×8=25.44.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 3.46 × 8.
Repeated addition or distribution: 346 hundredths ×8=2768 hundredths=27.68.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.5 × 8.
The displayed decimal contains 5 tenths. Multiply the number of equal units by 8: 40 tenths = 4.0.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Calculate 0.60 ÷ 4. Explain how place value or a model can check your result.
Share 60 hundredths equally among 4 groups: 15 hundredths each = 0.15. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Divide 14.64 equally among 8 people. How much does each receive?
Convert to hundredths: 1464÷8=183 hundredths = 1.83. Exchange hundreds/tenths when needed.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Divide 13.35 equally among 5 people. How much does each receive?
Convert to hundredths: 1335÷5=267 hundredths = 2.67. Exchange hundreds/tenths when needed.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Calculate 0.7 × 6. Explain how place value or a model can check your result.
The displayed decimal contains 7 tenths. Multiply the number of equal units by 6: 42 tenths = 4.2. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.