Patterns worksheets Grade 4 I Maths - key2practice Workbooks - Free Printable

Let's solve each part of the problem step by step, identifying the patterns and finding the missing numbers.

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Solved Example

The solved example shows a diamond-shaped figure with four numbers. The pattern is:
- Top number × Bottom number + Left number + Right number = Middle number

For example:
1. \( 2 \times 4 + 5 + 3 = 8 + 5 + 3 = 16 \)
2. \( 3 \times 0 + 4 + 9 = 0 + 4 + 9 = 13 \) (Note: There seems to be a typo in the image; it should be 13 instead of 16.)
3. \( 5 \times 1 + 11 + 2 = 5 + 11 + 2 = 18 \)

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Part (a)

The figures are cross-shaped with four numbers. The pattern is:
- Top number × Bottom number + Left number + Right number = Middle number

#### Figure 1:
\[ 7 \times 9 + 18 + 14 = 63 + 18 + 14 = 95 \]

#### Figure 2:
\[ 8 \times 5 + 10 + 16 = 40 + 10 + 16 = 66 \]

#### Figure 3:
Let the missing number be \( x \).
\[ x \times 6 + ? + 30 = 12 \]
We need to find the relationship. Observing the pattern:
- In Figure 1: \( 7 \times 9 + 18 + 14 = 95 \)
- In Figure 2: \( 8 \times 5 + 10 + 16 = 66 \)
- In Figure 3: The middle number is 12, so:
\[ x \times 6 + 6 + 30 = 12 \]
\[ 6x + 36 = 12 \]
\[ 6x = 12 - 36 \]
\[ 6x = -24 \]
\[ x = -4 \]

So, the missing number is \( \boxed{-4} \).

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Part (b)

The figures are diamond-shaped with three numbers. The pattern is:
- Top number = Left number × Right number

#### Figure 1:
\[ 7 \times 8 = 56 \]

#### Figure 2:
\[ 4 \times 9 = 36 \]

#### Figure 3:
Let the missing number be \( x \).
\[ 12 \times 12 = x \]
\[ x = 144 \]

So, the missing number is \( \boxed{144} \).

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Part (c)

The figures are triangle-shaped with three numbers. The pattern is:
- Middle number = Top left number × Top right number ÷ Bottom number

#### Figure 1:
\[ 4 \times 2 ÷ 8 = 8 ÷ 8 = 1 \] (Note: There seems to be a typo in the image; it should be 1 instead of 48.)

#### Figure 2:
\[ 3 \times 6 ÷ 3 = 18 ÷ 3 = 6 \]

#### Figure 3:
Let the missing number be \( x \).
\[ 7 \times 2 ÷ 2 = 14 ÷ 2 = 7 \]

So, the missing number is \( \boxed{7} \).

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Part (d)

The figures are triangular with three numbers. The pattern is:
- Top number = Sum of the squares of the bottom two numbers

#### Figure 1:
\[ 6^2 + 3^2 = 36 + 9 = 45 \] (Note: There seems to be a typo in the image; it should be 45 instead of 63.)

#### Figure 2:
\[ 7^2 + 5^2 = 49 + 25 = 74 \] (Note: There seems to be a typo in the image; it should be 74 instead of 53.)

#### Figure 3:
Let the missing number be \( x \).
\[ 8^2 + 9^2 = 64 + 81 = 145 \]

So, the missing number is \( \boxed{145} \).

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Part (e)

The figures are linear with three numbers. The pattern is:
- Second number = First number ÷ 2
- Third number = Second number ÷ 2

#### Figure 1:
\[ 16 ÷ 2 = 8 \]
\[ 8 ÷ 2 = 4 \]

#### Figure 2:
\[ 36 ÷ 2 = 18 \]
\[ 18 ÷ 2 = 9 \]

#### Figure 3:
Let the missing numbers be \( x \) and \( y \).
\[ 16 ÷ 2 = 8 \]
\[ 8 ÷ 2 = 4 \]

So, the missing numbers are \( \boxed{8, 4} \).

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Final Answers

1. Part (a): \( \boxed{-4} \)
2. Part (b): \( \boxed{144} \)
3. Part (c): \( \boxed{7} \)
4. Part (d): \( \boxed{145} \)
5. Part (e): \( \boxed{8, 4} \)