Practice Problems
Feel like practicing some of the methods in the book? This appendix provides some sample problems for you to try out using the different things you learned.
Chapter 1: Multiplication
Solve the following problems using finger multiplication.
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Solve the following problems using what you learned for multiplication by 11.
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Solve the following problems using 10 below the base method.
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Solve the following problems using 100 below the base method.
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Solve the following problems using 1,000 below the base method.
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Solve the following problems using 10 above the base method.
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Solve the following problems using 100 above the base method.
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Solve the following problems using 1,000 above the base method.
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Solve the following problems using the 10 above and below the base method.
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Solve the following problems using the 100 above and below the base method.
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Solve the following problems using the 1,000 above and below the base method.
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Solve the following problems using the method you learned for multiples and submultiples.
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Solve the following problems using the method you learned for combined problems.
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Solve the following problems using the vertically and crosswise method for two-digit numbers.
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Solve the following problems using the vertically and crosswise method for three-digit numbers.
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Chapter 2: Addition
Solve the following problems using left-to-right addition for two-digit numbers.
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Solve the following problems using left-to-right addition for three-digit numbers.
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Solve the following problems using left-to-right columnar addition.
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Solve the following problems using the addition method for numbers near 10 or a multiple of 10.
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Solve the following problems using number splitting.
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Chapter 3: Subtraction
Solve the following problems using left-to-right subtraction.
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Solve the following problems using the method for numbers near 10 or a multiple of 10.
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Solve the following problems using number splitting.
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Solve the following problems using the all from 9 and last from 10 method.
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Chapter 4: Division
Solve the following problems using the flag method for two-digit divisors.
| 1. | 4,305 ÷ 80 = ____ |
| 2. | 5,067 ÷ 25 = ____ |
| 3. | 6,033 ÷ 28 = ____ |
| 4. | 4,649 ÷ 93 = ____ |
| 5. | 5,657 ÷ 73 = ____ |
Solve the following problems using the flag method for three-digit divisors.
| 6. | 78,115 ÷ 767 = ____ |
| 7. | 32,316 ÷ 143 = ____ |
| 8. | 66,892 ÷ 141 = ____ |
| 9. | 16,771 ÷ 278 = ____ |
| 10. | 69,027 ÷ 842 = ____ |
Solve the following problems using the flag method for four-digit divisors.
11. 796,267 ÷ 8,667 = ____
12. 717,219 ÷ 7,682 = ____
13. 898,376 ÷ 3,442 = ____
14. 881,306 ÷ 7,256 = ____
15. 653,909 ÷ 3,595 = ____
Solve the following problems using auxiliary fractions.
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Chapter 5: Checking Your Answers with Digit Sums
See if the following problems are true or false using digit sums.
| 1. | 3,756 + 3,728 = 7,484 |
| 2. | 746 + 129 = 874 |
| 3. | 382 + 459 = 841 |
| 4. | 2,935 + 2,845 = 5,779 |
| 5. | 1,948 + 6,849 = 8,797 |
| 6. | 432 − 287 = 143 |
| 7. | 567 − 398 = 169 |
| 8. | 987 − 234 = 750 |
| 9. | 1,578 − 1,266 = 312 |
| 10. | 2,399 − 1,166 = 1,232 |
| 11. | 123 × 340 = 41,820 |
| 12. | 214 × 322 = 68,901 |
| 13. | 111 × 144 = 15,984 |
| 14. | 433 × 221 = 95,692 |
| 15. | 321 × 554 = 177,834 |
| 16. | 420 ÷ 21 = 20 |
| 17. | 375 ÷ 75 = 5 |
| 18. | 243 ÷ 3 = 82 |
| 19. | 343 ÷ 7 = 49 |
| 20. | 570 ÷ 19 = 30 |
Chapter 6: Fractions
Solve the following problems using what you learned for adding fractions.
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Solve the following problems using what you learned for subtracting fractions.
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Solve the following problems using what you learned for multiplying fractions.
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Solve the following problems using what you learned for dividing fractions.
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Solve the following problems using what you learned for adding decimals.
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Solve the following problems using what you learned for subtracting decimals.
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Solve the following problems using what you learned for multiplying decimals.
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Solve the following problems using what you learned for dividing decimals.
| 16. | 9.8 ÷ 0.7 = ____ |
| 17. | 1.69 ÷ 1.3 = ____ |
| 18. | 4.84 ÷ 0.22 = ____ |
| 19. | 34.3 ÷ 0.07 = ____ |
| 20. | 72.9 ÷ 0.081 = ____ |
Chapter 8: Percentages
Convert the following percentages into fractions.
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Convert the following fractions into percentages.
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Convert the following percentages to decimals.
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Find the percentage of the given quantity.
| 16. | 23% of 500 |
| 17. | 14% of 345 |
| 18. | 36.5% of 900 |
| 19. | 30% of 458 |
| 20. | 56.7% of 100 |
Express one quantity as a percentage of the other in the following problems.
21. Express 24 as a percentage of 48.
22. Express 38 as a percentage of 228.
23. Express 52 as a percentage of 235.
24. Express 20 as a percentage of 465.
25. Express 34 as a percentage of 436.
Approximate the percentages for the following problems.
26. Estimate 54 as a percentage of 234.
27. Estimate 16 as a percentage of 256.
28. Estimate 56 as a percentage of 456.
29. Estimate 34 as a percentage of 250.
30. Estimate 20 as a percentage of 458.
Solve the following problems using the osculation method.
- Find out if 7,680 is divisible by 80.
- Find out if 1,798 is divisible by 62.
- Find out if 1,785 is divisible by 17.
- Find out if 4,368 is divisible by 91.
- Find out if 3,024 is divisible by 54.
- Find out if 2,756 is divisible by 52.
- Find out if 5,487 is divisible by 59.
- Find out if 8,905 is divisible by 65.
- Find out if 4,617 is divisible by 81.
- Find out if 3,198 is divisible by 13.
- Find out if 3,055 is divisible by 65.
- Find out if 6,540 is divisible by 15.
- Find out if 2,166 is divisible by 38.
- Find out if 4,386 is divisible by 43.
- Find out if 2,880 is divisible by 60.
Chapter 10: Squared Numbers
Solve the following problems using what you learned for finding squares of numbers ending in 5.
1. 752 = ____
2. 252 = ____
3. 552 = ____
4. 452 = ____
5. 652 = ____
Solve the following problems using what you learned for finding squares of numbers ending in 50.
6. 522 = ____
7. 552 = ____
8. 532 = ____
9. 462 = ____
10. 452 = ____
Solve the following problems using the duplex method for two-digit squares.
11. 822 = ____
12. 262 = ____
13. 122 = ____
14. 842 = ____
15. 782 = ____
Solve the following problems using the duplex method for three-digit squares.
16. 6512 = ____
17. 9372 = ____
18. 9902 = ____
19. 3632 = ____
20. 3662 = ____
Solve the following problems using the duplex method for four-digit squares.
| 21. | 1,2342 |
| 22. | 5,4822 |
| 23. | 7,0112 |
| 24. | 6,3212 |
| 25. | 1,0822 |
Solve the following problems using what you learned for combined operations.
26. 642 + 922 = ____
27. 432 + 712 = ____
28. 292 + 912 = ____
29. 882 + 672 = ____
30. 772 + 912 = ____
Chapter 11: Cubed Numbers
Solve the following problems using what you learned for finding the cubes of two-digit numbers.
1. 543 = ____
2. 313 = ____
3. 693 = ____
4. 303 = ____
5. 453 = ____
Solve the following problems using what you learned for calculating cubes near a base.
6. 1113 = ____
7. 1003 = ____
8. 1093 = ____
9. 1143 = ____
10. 1023 = ____
Chapter 12: Numbers to the Fourth and Fifth Powers
Solve the following problems using what you learned for calculating numbers to the fourth power.
1. 794 = ____
2. 344 = ____
3. 704 = ____
4. 964 = ____
5. 234 = ____
Solve the following problems using what you learned for calculating numbers to the fifth power.
6. 285 = ____
7. 135 = ____
8. 425 = ____
9. 365 = ____
10. 185 = ____
Chapter 13: Square and Cube Roots
Solve the following problems using what you learned for finding the square roots of perfect squares.
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Solve the following problems using the duplexes to find square roots.
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Solve the following problems using what you learned for finding the cube roots of perfect cubes.
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