Math worksheet on multiplying and dividing by 10, 100, and 1000 with fluency exercises, mastery tasks, and real-world problem-solving questions.

Problem Analysis and Solution

The image contains three sections: Fluency, Mastery, and Problem Solving. Each section involves calculations related to multiplying and dividing by 10, 100, and 1000. Below is a detailed solution for each part.

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Section 1: Fluency

#### Task: Calculate the following.
1. a) \( 0.78 \times 10 \)
- Multiplying by 10 shifts the decimal point one place to the right.
- \( 0.78 \times 10 = 7.8 \)

2. b) \( 87.4 \times 10 \)
- Multiplying by 10 shifts the decimal point one place to the right.
- \( 87.4 \times 10 = 874 \)

3. c) \( 8.6 \times 100 \)
- Multiplying by 100 shifts the decimal point two places to the right.
- \( 8.6 \times 100 = 860 \)

4. d) \( 0.24 \times 1000 \)
- Multiplying by 1000 shifts the decimal point three places to the right.
- \( 0.24 \times 1000 = 240 \)

5. e) \( 7.01 \times 100 \)
- Multiplying by 100 shifts the decimal point two places to the right.
- \( 7.01 \times 100 = 701 \)

6. f) \( 26.7 \div 10 \)
- Dividing by 10 shifts the decimal point one place to the left.
- \( 26.7 \div 10 = 2.67 \)

7. g) \( 549.2 \div 100 \)
- Dividing by 100 shifts the decimal point two places to the left.
- \( 549.2 \div 100 = 5.492 \)

8. h) \( 17 \div 1000 \)
- Dividing by 1000 shifts the decimal point three places to the left.
- \( 17 \div 1000 = 0.017 \)

9. i) \( 0.08 \div 100 \)
- Dividing by 100 shifts the decimal point two places to the left.
- \( 0.08 \div 100 = 0.0008 \)

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Section 2: Mastery

#### Task: Complete the following.
1. a) \( \_\_ \times 10 = 67000 \)
- To find the missing number, divide 67000 by 10.
- \( 67000 \div 10 = 6700 \)
- Answer: \( 6700 \)

2. b) \( \_\_ \times 100 = 8600 \)
- To find the missing number, divide 8600 by 100.
- \( 8600 \div 100 = 86 \)
- Answer: \( 86 \)

3. c) \( 850 \times \_\_ = 850000 \)
- To find the missing number, divide 850000 by 850.
- \( 850000 \div 850 = 1000 \)
- Answer: \( 1000 \)

4. d) \( 15450 \times \_\_ = 15450000 \)
- To find the missing number, divide 15450000 by 15450.
- \( 15450000 \div 15450 = 1000 \)
- Answer: \( 1000 \)

5. e) \( 68000 + \_\_ = 68000 \)
- The sum remains the same, so the missing number must be 0.
- Answer: \( 0 \)

6. f) \( 1208000 + \_\_ = 1208 \)
- Subtract 1208 from 1208000 to find the missing number.
- \( 1208000 - 1208 = 1206792 \)
- Answer: \( -1206792 \)

7. g) \( \_\_ + 100 = 0.76 \)
- Subtract 100 from 0.76 to find the missing number.
- \( 0.76 - 100 = -99.24 \)
- Answer: \( -99.24 \)

8. h) \( 120 + \_\_ = 0.012 \)
- Subtract 120 from 0.012 to find the missing number.
- \( 0.012 - 120 = -119.988 \)
- Answer: \( -119.988 \)

9. i) \( 0.103 + \_\_ = 0.0103 \)
- Subtract 0.103 from 0.0103 to find the missing number.
- \( 0.0103 - 0.103 = -0.0927 \)
- Answer: \( -0.0927 \)

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Section 3: Problem Solving

#### Task: Solve the following problems.
1. a) There are 60 pins in each packet. There are 30 packets in each box. How many pins are there in 100 boxes?
- First, calculate the number of pins in one box:
\[
60 \text{ pins/packet} \times 30 \text{ packets/box} = 1800 \text{ pins/box}
\]
- Next, calculate the number of pins in 100 boxes:
\[
1800 \text{ pins/box} \times 100 \text{ boxes} = 180000 \text{ pins}
\]
- Answer: \( 180000 \)

2. b) What is 20 km in millimetres?
- Convert kilometers to meters:
\[
20 \text{ km} \times 1000 \text{ m/km} = 20000 \text{ m}
\]
- Convert meters to millimeters:
\[
20000 \text{ m} \times 1000 \text{ mm/m} = 20000000 \text{ mm}
\]
- Answer: \( 20000000 \)

3. c) How many pounds is five hundred 2p coins?
- First, calculate the total value in pence:
\[
500 \text{ coins} \times 2 \text{ p/coin} = 1000 \text{ p}
\]
- Convert pence to pounds (1 pound = 100 pence):
\[
1000 \text{ p} \div 100 = 10 \text{ pounds}
\]
- Answer: \( 10 \)

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Final Answers

1. Fluency:
- a) \( 7.8 \)
- b) \( 874 \)
- c) \( 860 \)
- d) \( 240 \)
- e) \( 701 \)
- f) \( 2.67 \)
- g) \( 5.492 \)
- h) \( 0.017 \)
- i) \( 0.0008 \)

2. Mastery:
- a) \( 6700 \)
- b) \( 86 \)
- c) \( 1000 \)
- d) \( 1000 \)
- e) \( 0 \)
- f) \( -1206792 \)
- g) \( -99.24 \)
- h) \( -119.988 \)
- i) \( -0.0927 \)

3. Problem Solving:
- a) \( 180000 \)
- b) \( 20000000 \)
- c) \( 10 \)

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Boxed Final Answers

\[
\boxed{
\begin{array}{l}
\text{Fluency: } 7.8, 874, 860, 240, 701, 2.67, 5.492, 0.017, 0.0008 \\
\text{Mastery: } 6700, 86, 1000, 1000, 0, -1206792, -99.24, -119.988, -0.0927 \\
\text{Problem Solving: } 180000, 20000000, 10
\end{array}
}
\]