Let’s solve each pattern step by step. We’re looking for an equation that turns the “In (x)” number into the “Out (y)” number.
We’ll check if it’s addition, subtraction, multiplication, or division — or a combination.
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Problem 1:
In: 2 → Out: 16
In: 3 → Out: 24
In: 4 → Out: 32
In: 5 → Out: 40
Check differences:
16 - 2 = 14? No, because 24 - 3 = 21 → not same.
Try multiplying:
2 × 8 = 16
✔
3 × 8 = 24
✔
4 × 8 = 32
✔
5 × 8 = 40
✔
→ Equation:
y = 8x
---
Problem 2:
In: 21 → Out: 7
In: 18 → Out: 6
In: 15 → Out: 5
In: 12 → Out: 4
Check dividing:
21 ÷ 3 = 7
✔
18 ÷ 3 = 6
✔
15 ÷ 3 = 5
✔
12 ÷ 3 = 4
✔
→ Equation:
y = x ÷ 3 or
y = x/3
---
Problem 3:
In: 4 → Out: 10
In: 5 → Out: 11
In: 6 → Out: 12
In: 7 → Out: 13
Check adding:
4 + 6 = 10
✔
5 + 6 = 11
✔
6 + 6 = 12
✔
7 + 6 = 13
✔
→ Equation:
y = x + 6
---
Problem 4:
In: 15 → Out: 11
In: 10 → Out: 6
In: 9 → Out: 5
In: 5 → Out: 1
Check subtracting:
15 - 4 = 11
✔
10 - 4 = 6
✔
9 - 4 = 5
✔
5 - 4 = 1
✔
→ Equation:
y = x - 4
---
Problem 5:
In: 5 → Out: 15
In: 7 → Out: 21
In: 9 → Out: 27
In: 11 → Out: 33
Check multiplying:
5 × 3 = 15
✔
7 × 3 = 21
✔
9 × 3 = 27
✔
11 × 3 = 33
✔
→ Equation:
y = 3x
---
Problem 6:
In: 5 → Out: 35
In: 6 → Out: 42
In: 8 → Out: 56
In: 9 → Out: 63
Check multiplying:
5 × 7 = 35
✔
6 × 7 = 42
✔
8 × 7 = 56
✔
9 × 7 = 63
✔
→ Equation:
y = 7x
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Final Answer:
1. y = 8x
2. y = x ÷ 3
3. y = x + 6
4. y = x - 4
5. y = 3x
6. y = 7x
Parent Tip: Review the logic above to help your child master the concept of 5th grade input output tables worksheet.
