Convert units of length - yards, feet and inches - Exercise 1 ... - Free Printable

To solve the problems in the worksheet, we need to use the conversion factors provided:

1. 1 yard (yd) = 3 feet (ft)
2. 1 foot (ft) = 12 inches (in)

Using these relationships, we can convert between yards, feet, and inches. Let's solve each problem step by step.

---

Section 1: Converting Yards to Inches

#### Problem 1: \( 16 \, \text{yd} = \, ? \, \text{in} \)
- Step 1: Convert yards to feet.
\[
16 \, \text{yd} \times 3 \, \text{ft/yd} = 48 \, \text{ft}
\]
- Step 2: Convert feet to inches.
\[
48 \, \text{ft} \times 12 \, \text{in/ft} = 576 \, \text{in}
\]
- Answer: \( 16 \, \text{yd} = 576 \, \text{in} \)

#### Problem 2: \( 19 \, \text{yd} = \, ? \, \text{ft} \)
- Step 1: Convert yards to feet.
\[
19 \, \text{yd} \times 3 \, \text{ft/yd} = 57 \, \text{ft}
\]
- Answer: \( 19 \, \text{yd} = 57 \, \text{ft} \)

#### Problem 3: \( 7 \, \text{ft} = \, ? \, \text{in} \)
- Step 1: Convert feet to inches.
\[
7 \, \text{ft} \times 12 \, \text{in/ft} = 84 \, \text{in}
\]
- Answer: \( 7 \, \text{ft} = 84 \, \text{in} \)

#### Problem 4: \( 2 \, \text{yd} = \, ? \, \text{in} \)
- Step 1: Convert yards to feet.
\[
2 \, \text{yd} \times 3 \, \text{ft/yd} = 6 \, \text{ft}
\]
- Step 2: Convert feet to inches.
\[
6 \, \text{ft} \times 12 \, \text{in/ft} = 72 \, \text{in}
\]
- Answer: \( 2 \, \text{yd} = 72 \, \text{in} \)

#### Problem 5: \( 3 \, \text{yd} = \, ? \, \text{ft} \)
- Step 1: Convert yards to feet.
\[
3 \, \text{yd} \times 3 \, \text{ft/yd} = 9 \, \text{ft}
\]
- Answer: \( 3 \, \text{yd} = 9 \, \text{ft} \)

#### Problem 6: \( 16 \, \text{ft} = \, ? \, \text{in} \)
- Step 1: Convert feet to inches.
\[
16 \, \text{ft} \times 12 \, \text{in/ft} = 192 \, \text{in}
\]
- Answer: \( 16 \, \text{ft} = 192 \, \text{in} \)

#### Problem 7: \( 19 \, \text{yd} = \, ? \, \text{in} \)
- Step 1: Convert yards to feet.
\[
19 \, \text{yd} \times 3 \, \text{ft/yd} = 57 \, \text{ft}
\]
- Step 2: Convert feet to inches.
\[
57 \, \text{ft} \times 12 \, \text{in/ft} = 684 \, \text{in}
\]
- Answer: \( 19 \, \text{yd} = 684 \, \text{in} \)

#### Problem 8: \( 19 \, \text{yd} = \, ? \, \text{ft} \)
- Step 1: Convert yards to feet.
\[
19 \, \text{yd} \times 3 \, \text{ft/yd} = 57 \, \text{ft}
\]
- Answer: \( 19 \, \text{yd} = 57 \, \text{ft} \)

#### Problem 9: \( 7 \, \text{ft} = \, ? \, \text{in} \)
- Step 1: Convert feet to inches.
\[
7 \, \text{ft} \times 12 \, \text{in/ft} = 84 \, \text{in}
\]
- Answer: \( 7 \, \text{ft} = 84 \, \text{in} \)

#### Problem 10: \( 6 \, \text{yd} = \, ? \, \text{in} \)
- Step 1: Convert yards to feet.
\[
6 \, \text{yd} \times 3 \, \text{ft/yd} = 18 \, \text{ft}
\]
- Step 2: Convert feet to inches.
\[
18 \, \text{ft} \times 12 \, \text{in/ft} = 216 \, \text{in}
\]
- Answer: \( 6 \, \text{yd} = 216 \, \text{in} \)

---

Section 2: Converting Inches to Feet and Yards

#### Problem 11: \( 156 \, \text{in} = \, ? \, \text{ft} \)
- Step 1: Convert inches to feet.
\[
156 \, \text{in} \div 12 \, \text{in/ft} = 13 \, \text{ft}
\]
- Answer: \( 156 \, \text{in} = 13 \, \text{ft} \)

#### Problem 12: \( 57 \, \text{ft} = \, ? \, \text{yd} \)
- Step 1: Convert feet to yards.
\[
57 \, \text{ft} \div 3 \, \text{ft/yd} = 19 \, \text{yd}
\]
- Answer: \( 57 \, \text{ft} = 19 \, \text{yd} \)

#### Problem 13: \( 180 \, \text{in} = \, ? \, \text{yd} \)
- Step 1: Convert inches to feet.
\[
180 \, \text{in} \div 12 \, \text{in/ft} = 15 \, \text{ft}
\]
- Step 2: Convert feet to yards.
\[
15 \, \text{ft} \div 3 \, \text{ft/yd} = 5 \, \text{yd}
\]
- Answer: \( 180 \, \text{in} = 5 \, \text{yd} \)

#### Problem 14: \( 204 \, \text{in} = \, ? \, \text{ft} \)
- Step 1: Convert inches to feet.
\[
204 \, \text{in} \div 12 \, \text{in/ft} = 17 \, \text{ft}
\]
- Answer: \( 204 \, \text{in} = 17 \, \text{ft} \)

#### Problem 15: \( 63 \, \text{ft} = \, ? \, \text{yd} \)
- Step 1: Convert feet to yards.
\[
63 \, \text{ft} \div 3 \, \text{ft/yd} = 21 \, \text{yd}
\]
- Answer: \( 63 \, \text{ft} = 21 \, \text{yd} \)

#### Problem 16: \( 612 \, \text{in} = \, ? \, \text{yd} \)
- Step 1: Convert inches to feet.
\[
612 \, \text{in} \div 12 \, \text{in/ft} = 51 \, \text{ft}
\]
- Step 2: Convert feet to yards.
\[
51 \, \text{ft} \div 3 \, \text{ft/yd} = 17 \, \text{yd}
\]
- Answer: \( 612 \, \text{in} = 17 \, \text{yd} \)

#### Problem 17: \( 204 \, \text{in} = \, ? \, \text{ft} \)
- Step 1: Convert inches to feet.
\[
204 \, \text{in} \div 12 \, \text{in/ft} = 17 \, \text{ft}
\]
- Answer: \( 204 \, \text{in} = 17 \, \text{ft} \)

#### Problem 18: \( 105 \, \text{ft} = \, ? \, \text{yd} \)
- Step 1: Convert feet to yards.
\[
105 \, \text{ft} \div 3 \, \text{ft/yd} = 35 \, \text{yd}
\]
- Answer: \( 105 \, \text{ft} = 35 \, \text{yd} \)

#### Problem 19: \( 72 \, \text{in} = \, ? \, \text{yd} \)
- Step 1: Convert inches to feet.
\[
72 \, \text{in} \div 12 \, \text{in/ft} = 6 \, \text{ft}
\]
- Step 2: Convert feet to yards.
\[
6 \, \text{ft} \div 3 \, \text{ft/yd} = 2 \, \text{yd}
\]
- Answer: \( 72 \, \text{in} = 2 \, \text{yd} \)

#### Problem 20: \( 144 \, \text{in} = \, ? \, \text{ft} \)
- Step 1: Convert inches to feet.
\[
144 \, \text{in} \div 12 \, \text{in/ft} = 12 \, \text{ft}
\]
- Answer: \( 144 \, \text{in} = 12 \, \text{ft} \)

---

Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 576 \, \text{in} \\
2. & 57 \, \text{ft} \\
3. & 84 \, \text{in} \\
4. & 72 \, \text{in} \\
5. & 9 \, \text{ft} \\
6. & 192 \, \text{in} \\
7. & 684 \, \text{in} \\
8. & 57 \, \text{ft} \\
9. & 84 \, \text{in} \\
10. & 216 \, \text{in} \\
11. & 13 \, \text{ft} \\
12. & 19 \, \text{yd} \\
13. & 5 \, \text{yd} \\
14. & 17 \, \text{ft} \\
15. & 21 \, \text{yd} \\
16. & 17 \, \text{yd} \\
17. & 17 \, \text{ft} \\
18. & 35 \, \text{yd} \\
19. & 2 \, \text{yd} \\
20. & 12 \, \text{ft} \\
\end{array}
}
\]