Multiply and Divide by 10 100 - Free Printable

Problem Overview:

The worksheet focuses on multiplying and dividing numbers by 10 and 100, with some problems involving decimals. The goal is to solve each problem by applying the rules of multiplication and division by powers of 10.

Key Rules for Multiplying and Dividing by 10 and 100:

1. Multiplying by 10: Move the decimal point one place to the right.
- Example: \( 3.4 \times 10 = 34 \)
2. Dividing by 10: Move the decimal point one place to the left.
- Example: \( 34 \div 10 = 3.4 \)
3. Multiplying by 100: Move the decimal point two places to the right.
- Example: \( 3.4 \times 100 = 340 \)
4. Dividing by 100: Move the decimal point two places to the left.
- Example: \( 340 \div 100 = 3.4 \)

Solution to Each Problem:

#### Section 1: Basic Problems
1. \( 850 \div \_\_ = 85 \)
- To get from 850 to 85, divide by 10.
- Answer: \( 10 \)

2. \( 40.9 \times 10 = \_\_ \)
- Multiply 40.9 by 10 (move the decimal point one place to the right).
- Answer: \( 409 \)

3. \( 8310 \div \_\_ = 83.1 \)
- To get from 8310 to 83.1, divide by 100.
- Answer: \( 100 \)

4. \( 76.5 \times 10 = \_\_ \)
- Multiply 76.5 by 10 (move the decimal point one place to the right).
- Answer: \( 765 \)

5. \( 61.5 \times \_\_ = 615 \)
- To get from 61.5 to 615, multiply by 10.
- Answer: \( 10 \)

6. \( \_\_ \div 10 = 64.1 \)
- To get 64.1 when divided by 10, multiply 64.1 by 10.
- Answer: \( 641 \)

#### Section 2: Intermediate Problems
7. \( \_\_ \times 100 = 7020 \)
- To get 7020 when multiplied by 100, divide 7020 by 100.
- Answer: \( 70.2 \)

8. \( \_\_ \div 100 = 46.8 \)
- To get 46.8 when divided by 100, multiply 46.8 by 100.
- Answer: \( 4680 \)

9. \( 51.9 \times \_\_ = 5190 \)
- To get from 51.9 to 5190, multiply by 100.
- Answer: \( 100 \)

10. \( \_\_ \times 100 = 4030 \)
- To get 4030 when multiplied by 100, divide 4030 by 100.
- Answer: \( 40.3 \)

11. \( \_\_ \div 10 = 49 \)
- To get 49 when divided by 10, multiply 49 by 10.
- Answer: \( 490 \)

12. \( \_\_ \div 10 = 32.7 \)
- To get 32.7 when divided by 10, multiply 32.7 by 10.
- Answer: \( 327 \)

#### Section 3: Advanced Problems
13. \( \_\_ \div 100 = 30.5 \)
- To get 30.5 when divided by 100, multiply 30.5 by 100.
- Answer: \( 3050 \)

14. \( 4400 \div 100 = \_\_ \)
- Divide 4400 by 100 (move the decimal point two places to the left).
- Answer: \( 44 \)

15. \( 14.3 \times 10 = \_\_ \)
- Multiply 14.3 by 10 (move the decimal point one place to the right).
- Answer: \( 143 \)

16. \( 92.5 \times 100 = \_\_ \)
- Multiply 92.5 by 100 (move the decimal point two places to the right).
- Answer: \( 9250 \)

17. \( 235 \div 10 = \_\_ \)
- Divide 235 by 10 (move the decimal point one place to the left).
- Answer: \( 23.5 \)

18. \( \_\_ \times 100 = 4950 \)
- To get 4950 when multiplied by 100, divide 4950 by 100.
- Answer: \( 49.5 \)

19. \( 1.7 \times \_\_ = 170 \)
- To get from 1.7 to 170, multiply by 100.
- Answer: \( 100 \)

20. \( \_\_ \div 100 = 44.1 \)
- To get 44.1 when divided by 100, multiply 44.1 by 100.
- Answer: \( 4410 \)

21. \( 2840 \div 100 = \_\_ \)
- Divide 2840 by 100 (move the decimal point two places to the left).
- Answer: \( 28.4 \)

#### Section 4: Complex Problems
22. \( \_\_ \times 100 = 4620 \)
- To get 4620 when multiplied by 100, divide 4620 by 100.
- Answer: \( 46.2 \)

23. \( 21.3 \times \_\_ = 2130 \)
- To get from 21.3 to 2130, multiply by 100.
- Answer: \( 100 \)

24. \( 925 \div \_\_ = 92.5 \)
- To get from 925 to 92.5, divide by 10.
- Answer: \( 10 \)

25. \( \_\_ \times 10 = 384 \)
- To get 384 when multiplied by 10, divide 384 by 10.
- Answer: \( 38.4 \)

26. \( 6610 \div 100 = \_\_ \)
- Divide 6610 by 100 (move the decimal point two places to the left).
- Answer: \( 66.1 \)

27. \( \_\_ \div 100 = 40.1 \)
- To get 40.1 when divided by 100, multiply 40.1 by 100.
- Answer: \( 4010 \)

28. \( \_\_ \times 100 = 2600 \)
- To get 2600 when multiplied by 100, divide 2600 by 100.
- Answer: \( 26 \)

29. \( \_\_ \times 100 = 7500 \)
- To get 7500 when multiplied by 100, divide 7500 by 100.
- Answer: \( 75 \)

30. \( 32.2 \times \_\_ = 3220 \)
- To get from 32.2 to 3220, multiply by 100.
- Answer: \( 100 \)

#### Section 5: Final Problems
31. \( 634 \div \_\_ = 63.4 \)
- To get from 634 to 63.4, divide by 10.
- Answer: \( 10 \)

32. \( 5420 \div 100 = \_\_ \)
- Divide 5420 by 100 (move the decimal point two places to the left).
- Answer: \( 54.2 \)

33. \( \_\_ \div 100 = 77.6 \)
- To get 77.6 when divided by 100, multiply 77.6 by 100.
- Answer: \( 7760 \)

34. \( \_\_ \div 100 = 61.8 \)
- To get 61.8 when divided by 100, multiply 61.8 by 100.
- Answer: \( 6180 \)

35. \( 87.7 \times \_\_ = 877 \)
- To get from 87.7 to 877, multiply by 10.
- Answer: \( 10 \)

36. \( 66.5 \times 100 = \_\_ \)
- Multiply 66.5 by 100 (move the decimal point two places to the right).
- Answer: \( 6650 \)

37. \( \_\_ \times 100 = 2010 \)
- To get 2010 when multiplied by 100, divide 2010 by 100.
- Answer: \( 20.1 \)

38. \( 782 \div \_\_ = 78.2 \)
- To get from 782 to 78.2, divide by 10.
- Answer: \( 10 \)

39. \( \_\_ \div 10 = 49.1 \)
- To get 49.1 when divided by 10, multiply 49.1 by 10.
- Answer: \( 491 \)

40. \( 31.8 \times \_\_ = 3180 \)
- To get from 31.8 to 3180, multiply by 100.
- Answer: \( 100 \)

41. \( 31.5 \times 10 = \_\_ \)
- Multiply 31.5 by 10 (move the decimal point one place to the right).
- Answer: \( 315 \)

42. \( \_\_ \times 10 = 153 \)
- To get 153 when multiplied by 10, divide 153 by 10.
- Answer: \( 15.3 \)

43. \( 8840 \div 100 = \_\_ \)
- Divide 8840 by 100 (move the decimal point two places to the left).
- Answer: \( 88.4 \)

44. \( 9030 \div \_\_ = 90.3 \)
- To get from 9030 to 90.3, divide by 100.
- Answer: \( 100 \)

45. \( 61.2 \times 10 = \_\_ \)
- Multiply 61.2 by 10 (move the decimal point one place to the right).
- Answer: \( 612 \)

Final Answer:

\[
\boxed{
\begin{array}{lll}
1) & 10 & 2) & 409 & 3) & 100 \\
4) & 765 & 5) & 10 & 6) & 641 \\
7) & 70.2 & 8) & 4680 & 9) & 100 \\
10) & 40.3 & 11) & 490 & 12) & 327 \\
13) & 3050 & 14) & 44 & 15) & 143 \\
16) & 9250 & 17) & 23.5 & 18) & 49.5 \\
19) & 100 & 20) & 4410 & 21) & 28.4 \\
22) & 46.2 & 23) & 100 & 24) & 10 \\
25) & 38.4 & 26) & 66.1 & 27) & 4010 \\
28) & 26 & 29) & 75 & 30) & 100 \\
31) & 10 & 32) & 54.2 & 33) & 7760 \\
34) & 6180 & 35) & 10 & 36) & 6650 \\
37) & 20.1 & 38) & 10 & 39) & 491 \\
40) & 100 & 41) & 315 & 42) & 15.3 \\
43) & 88.4 & 44) & 100 & 45) & 612 \\
\end{array}
}
\]