Extend the Patterns using Addition and Subtraction — Printable ... - Free Printable

Problem Analysis:

The task involves observing two patterns and using the given relation to extend the patterns. Each section provides a relation between Pattern A and Pattern B, and we need to use this relation to fill in the missing values.

Step-by-Step Solution:

#### Section 1:
Patterns:
- Pattern A: 3, 13, 23, 33, 43
- Pattern B: 6, 26, 46, 66, 86
- Relation: Pattern B = 2 × Pattern A

Explanation:
Each term in Pattern B is obtained by multiplying the corresponding term in Pattern A by 2.

- For Pattern A = 3, Pattern B = 2 × 3 = 6
- For Pattern A = 13, Pattern B = 2 × 13 = 26
- For Pattern A = 23, Pattern B = 2 × 23 = 46
- For Pattern A = 33, Pattern B = 2 × 33 = 66
- For Pattern A = 43, Pattern B = 2 × 43 = 86

All values are already filled correctly based on the relation.

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#### Section 2:
Patterns:
- Pattern A: 3, 5, 7, 9, 11
- Pattern B: 15, 25, ?, ?, ?
- Relation: Pattern B = 5 × Pattern A

Explanation:
Each term in Pattern B is obtained by multiplying the corresponding term in Pattern A by 5.

- For Pattern A = 3, Pattern B = 5 × 3 = 15
- For Pattern A = 5, Pattern B = 5 × 5 = 25
- For Pattern A = 7, Pattern B = 5 × 7 = 35
- For Pattern A = 9, Pattern B = 5 × 9 = 45
- For Pattern A = 11, Pattern B = 5 × 11 = 55

Filled Values:
- Pattern B: 15, 25, 35, 45, 55

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#### Section 3:
Patterns:
- Pattern A: 4, 5, ?, ?, ?
- Pattern B: 40, 50, 60, 70, 80
- Relation: Pattern A = Pattern B ÷ 10

Explanation:
Each term in Pattern A is obtained by dividing the corresponding term in Pattern B by 10.

- For Pattern B = 40, Pattern A = 40 ÷ 10 = 4
- For Pattern B = 50, Pattern A = 50 ÷ 10 = 5
- For Pattern B = 60, Pattern A = 60 ÷ 10 = 6
- For Pattern B = 70, Pattern A = 70 ÷ 10 = 7
- For Pattern B = 80, Pattern A = 80 ÷ 10 = 8

Filled Values:
- Pattern A: 4, 5, 6, 7, 8

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#### Section 4:
Patterns:
- Pattern A: 3, 6, ?, ?, ?
- Pattern B: 1, 2, 3, 4, 5
- Relation: Pattern A = 3 × Pattern B

Explanation:
Each term in Pattern A is obtained by multiplying the corresponding term in Pattern B by 3.

- For Pattern B = 1, Pattern A = 3 × 1 = 3
- For Pattern B = 2, Pattern A = 3 × 2 = 6
- For Pattern B = 3, Pattern A = 3 × 3 = 9
- For Pattern B = 4, Pattern A = 3 × 4 = 12
- For Pattern B = 5, Pattern A = 3 × 5 = 15

Filled Values:
- Pattern A: 3, 6, 9, 12, 15

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Final Answer:

1. Pattern B: 6, 26, 46, 66, 86 (already correct)
2. Pattern B: 15, 25, 35, 45, 55
3. Pattern A: 4, 5, 6, 7, 8
4. Pattern A: 3, 6, 9, 12, 15

$$
\boxed{
\begin{array}{c}
\text{Pattern B: 15, 25, 35, 45, 55} \\
\text{Pattern A: 4, 5, 6, 7, 8} \\
\text{Pattern A: 3, 6, 9, 12, 15}
\end{array}
}
$$