Mental maths worksheet featuring problems on addition, fractions, number patterns, and data interpretation.

Let's solve the problems step by step:

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Section 1: Mental Maths

#### 1. Four tens + 23 = ______
- Four tens = \( 4 \times 10 = 40 \)
- Adding 23: \( 40 + 23 = 63 \)

Answer: 63

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#### 2. Write the largest number you can with the figures 2, 1, 3, and 5.
- To form the largest number, arrange the digits in descending order: 5, 3, 2, 1.
- The largest number is 5321.

Answer: 5321

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#### 3. Shade the fraction \( \frac{1}{5} \) in one of these diagrams.
- We need to shade \( \frac{1}{5} \) of the total squares in one of the diagrams.
- Diagram (a) has 5 squares, so shading 1 square represents \( \frac{1}{5} \).
- Diagram (b) has 9 squares, so shading \( \frac{1}{5} \) would be approximately 2 squares (but not exact).
- Diagram (c) has 6 squares, so shading \( \frac{1}{5} \) would be approximately 1 square (but not exact).

Shade 1 square in diagram (a).

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#### 4. Complete the last basic number fact in the set below:
\[
\begin{aligned}
&9 \times 4 = 36 \\
&36 \div 4 = 9 \\
&4 \times 9 = 36 \\
&\boxed{\text{ }} + \boxed{\text{ }} = \boxed{\text{ }}
\end{aligned}
\]
- The pattern involves multiplication and division facts. The missing operation should be addition.
- From the previous facts, we know \( 9 + 4 = 13 \).

Answer: 9 + 4 = 13

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#### 5. Write in figures five thousand and twelve.
- Five thousand = 5000
- Twelve = 12
- Combined: 5000 + 12 = 5012

Answer: 5012

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#### 6. Work out this sum: \( \left( \frac{1}{2} \text{ of } 96 \right) + 2 = \)
- \( \frac{1}{2} \) of 96: \( \frac{1}{2} \times 96 = 48 \)
- Adding 2: \( 48 + 2 = 50 \)

Answer: 50

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#### 7. ▼▼□▲▲□▼______
- The pattern alternates between two triangles (▼), a square (□), two triangles (▲), and another square (□).
- The next shape in the sequence is a triangle (▼).

Answer: ▼

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#### 8. Use the number patterns to complete the last line:
\[
\begin{aligned}
&3 \times 4 = 10 + 2 \\
&3 \times 5 = 12 + 3 \\
&3 \times 6 = 14 + 4 \\
&3 \times 7 = 16 + 5 \\
&\boxed{\text{ }} \times \boxed{\text{ }} = \boxed{\text{ }} + \boxed{\text{ }}
\end{aligned}
\]
- The pattern shows:
- The first number is always 3.
- The second number increases by 1 each time (4, 5, 6, 7, ...).
- The result is split into two parts: \( 3 \times n = (2n + 6) + n \).

For \( n = 8 \):
- \( 3 \times 8 = 24 \)
- Split as \( 24 = (2 \times 8 + 6) + 8 = 22 + 8 \)

Answer: 3 × 8 = 22 + 8

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Section 2: Additional Problems

#### 9. Fill in the missing numbers in this clockwise pattern.
- The pattern appears to involve multiples of 6:
- \( 6 \times 1 = 6 \)
- \( 6 \times 2 = 12 \)
- \( 6 \times 3 = 18 \)
- \( 6 \times 4 = 24 \)
- \( 6 \times 5 = 30 \)
- \( 6 \times 6 = 36 \)
- \( 6 \times 7 = 42 \)

The missing numbers are:
- Top right: \( 12 \)
- Bottom left: \( 18 \)

Answer: 12, 18

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#### 10. \( \square \div 4 = 5 \)
- Let \( x \) be the missing number.
- \( x \div 4 = 5 \)
- Solving for \( x \): \( x = 5 \times 4 = 20 \)

Answer: 20

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#### 11. 37 rounded off to the nearest 10 = ______
- 37 is closer to 40 than to 30 when rounding to the nearest 10.

Answer: 40

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#### 12. Toffees are 5¢ each but if I buy a packet of ten for 35¢ I save myself ______ cents.
- Cost of 10 toffees at 5¢ each: \( 10 \times 5 = 50 \) cents.
- Cost of a packet of 10 toffees: 35¢.
- Savings: \( 50 - 35 = 15 \) cents.

Answer: 15

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#### 13. \( 5 \times \square = 3 \times 10 \)
- Simplify the right side: \( 3 \times 10 = 30 \)
- Solve for the missing number: \( 5 \times x = 30 \)
- \( x = \frac{30}{5} = 6 \)

Answer: 6

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#### 14. When zero is taken away from a number, the answer is always:
- Subtracting 0 from any number leaves the number unchanged.

Answer: (d) the same as the number

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#### 15. XXIV – XVIII = ______
- Convert Roman numerals to Arabic:
- XXIV = 24
- XVIII = 18
- Subtract: \( 24 - 18 = 6 \)
- Convert 6 back to Roman numerals: VI

Answer: VI

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#### 16. Tom has ______ times as many marbles as Amy but only 10 more than ______ on this bar graph.
- From the bar graph:
- Amy has 10 marbles.
- Tom has 30 marbles.
- Roy has 40 marbles.
- Kate has 60 marbles.
- June has 70 marbles.

- Tom has \( \frac{30}{10} = 3 \) times as many marbles as Amy.
- Tom has 10 more marbles than Roy (since Roy has 20 marbles).

Answer: 3, Roy

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#### 17. This diagram shows that the fraction \( \frac{1}{2} \) is the same as the fraction ______
- The diagram shows:
- Two halves shaded, representing \( \frac{2}{4} \).
- Two quarters shaded, representing \( \frac{2}{4} \).

Thus, \( \frac{1}{2} = \frac{2}{4} \).

Answer: \( \frac{2}{4} \)

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Final Answers:

\[
\boxed{
\begin{array}{l}
1. 63 \\
2. 5321 \\
3. \text{Shade 1 square in diagram (a)} \\
4. 9 + 4 = 13 \\
5. 5012 \\
6. 50 \\
7. ▼ \\
8. 3 \times 8 = 22 + 8 \\
9. 12, 18 \\
10. 20 \\
11. 40 \\
12. 15 \\
13. 6 \\
14. \text{(d) the same as the number} \\
15. VI \\
16. 3, \text{Roy} \\
17. \frac{2}{4}
\end{array}
}
\]