Let’s solve each problem step by step. We’re finding the
scale factor — that’s just how many times bigger (or smaller) the new shape is compared to the original.
To find the scale factor, we divide:
>
Scale Factor = New Dimension ÷ Original Dimension
We’ll do this for each pair of shapes.
---
Problem 1:
Original side = 6.5 cm
New side = 29.25 cm
→ Scale factor = 29.25 ÷ 6.5
Let’s calculate:
29.25 ÷ 6.5 = ?
Multiply both numbers by 10 to make it easier:
292.5 ÷ 65 = 4.5
✔
So, scale factor =
4.5
---
Problem 2:
Original side = 3.25 ft
New side = 8.45 ft
→ Scale factor = 8.45 ÷ 3.25
Calculate:
8.45 ÷ 3.25 = ?
Multiply numerator and denominator by 100:
845 ÷ 325 = 2.6
✔
Scale factor =
2.6
---
Problem 3:
Original side = 7.75 in
New side = 31 in
→ Scale factor = 31 ÷ 7.75
Calculate:
31 ÷ 7.75 = ?
Multiply both by 100:
3100 ÷ 775 = 4
✔
Scale factor =
4
---
Problem 4:
Original side = 5.5 m
New side = 22 m
→ Scale factor = 22 ÷ 5.5 = 4
✔
Scale factor =
4
---
Problem 5:
Original side = 3.5 yd
New side = 10.5 yd
→ Scale factor = 10.5 ÷ 3.5 = 3
✔
Scale factor =
3
---
Problem 6:
Original side = 4.25 cm
New side = 12.75 cm
→ Scale factor = 12.75 ÷ 4.25
Calculate:
12.75 ÷ 4.25 = 3
✔
Scale factor =
3
---
Problem 7:
Original side = 8.75 in
New side = 26.25 in
→ Scale factor = 26.25 ÷ 8.75
Calculate:
26.25 ÷ 8.75 = 3
✔
Scale factor =
3
---
Problem 8:
Original side = 6.75 ft
New side = 47.25 ft
→ Scale factor = 47.25 ÷ 6.75
Calculate:
47.25 ÷ 6.75 = 7
✔
Scale factor =
7
---
Problem 9:
Original side = 1.25 m
New side = 5 m
→ Scale factor = 5 ÷ 1.25 = 4
✔
Scale factor =
4
---
Problem 10:
Original side = 9.5 yd
New side = 76 yd
→ Scale factor = 76 ÷ 9.5
Calculate:
76 ÷ 9.5 = 8
✔
Scale factor =
8
---
Final Answer:
1. 4.5
2. 2.6
3. 4
4. 4
5. 3
6. 3
7. 3
8. 7
9. 4
10. 8
Parent Tip: Review the logic above to help your child master the concept of 7th grade math scale factor worksheet.
