Let's solve each of these rectangle area problems step by step. The
area of a rectangle is calculated using the formula:
$$
\text{Area} = \text{length} \times \text{width}
$$
We'll be working with
fractions, so we’ll need to multiply fractions and simplify where necessary.
---
1)
Dimensions:
- Length = $ \frac{2}{5} $ yd
- Width = $ \frac{10}{7} $ yd
$$
\text{Area} = \frac{2}{5} \times \frac{10}{7} = \frac{20}{35} = \frac{4}{7} \text{ yd}^2
$$
✔ Answer: $ \boxed{\frac{4}{7}} $ yd²
---
2)
Dimensions:
- Length = $ 3\frac{1}{2} $ ft = $ \frac{7}{2} $ ft
- Width = $ 1\frac{1}{4} $ ft = $ \frac{5}{4} $ ft
$$
\text{Area} = \frac{7}{2} \times \frac{5}{4} = \frac{35}{8} = 4\frac{3}{8} \text{ ft}^2
$$
✔ Answer: $ \boxed{4\frac{3}{8}} $ ft²
---
3)
Dimensions:
- Length = $ \frac{9}{4} $ in
- Width = $ \frac{10}{8} $ in = $ \frac{5}{4} $ in (simplified)
$$
\text{Area} = \frac{9}{4} \times \frac{5}{4} = \frac{45}{16} = 2\frac{13}{16} \text{ in}^2
$$
✔ Answer: $ \boxed{2\frac{13}{16}} $ in²
---
4)
Dimensions:
- Length = $ 2\frac{2}{9} $ ft = $ \frac{20}{9} $ ft
- Width = $ \frac{7}{8} $ ft
$$
\text{Area} = \frac{20}{9} \times \frac{7}{8} = \frac{140}{72} = \frac{35}{18} = 1\frac{17}{18} \text{ ft}^2
$$
✔ Answer: $ \boxed{1\frac{17}{18}} $ ft²
---
5)
Dimensions:
- Length = $ 1\frac{1}{5} $ in = $ \frac{6}{5} $ in
- Width = $ \frac{9}{4} $ in
$$
\text{Area} = \frac{6}{5} \times \frac{9}{4} = \frac{54}{20} = \frac{27}{10} = 2\frac{7}{10} \text{ in}^2
$$
✔ Answer: $ \boxed{2\frac{7}{10}} $ in²
---
6)
Dimensions:
- Length = $ \frac{14}{3} $ yd
- Width = $ \frac{1}{7} $ yd
$$
\text{Area} = \frac{14}{3} \times \frac{1}{7} = \frac{14}{21} = \frac{2}{3} \text{ yd}^2
$$
✔ Answer: $ \boxed{\frac{2}{3}} $ yd²
---
7)
Dimensions:
- Length = 6 in
- Width = $ \frac{5}{9} $ in
$$
\text{Area} = 6 \times \frac{5}{9} = \frac{30}{9} = \frac{10}{3} = 3\frac{1}{3} \text{ in}^2
$$
✔ Answer: $ \boxed{3\frac{1}{3}} $ in²
---
8)
Dimensions:
- Length = $ \frac{5}{2} $ yd
- Width = $ \frac{6}{5} $ yd
$$
\text{Area} = \frac{5}{2} \times \frac{6}{5} = \frac{30}{10} = 3 \text{ yd}^2
$$
✔ Answer: $ \boxed{3} $ yd²
---
9)
Dimensions:
- Length = $ 2\frac{1}{8} $ ft = $ \frac{17}{8} $ ft
- Width = $ \frac{8}{9} $ ft
$$
\text{Area} = \frac{17}{8} \times \frac{8}{9} = \frac{136}{72} = \frac{17}{9} = 1\frac{8}{9} \text{ ft}^2
$$
✔ Answer: $ \boxed{1\frac{8}{9}} $ ft²
---
✔ Final Answers Summary:
| Problem | Area |
|--------|------|
| 1) | $ \frac{4}{7} $ yd² |
| 2) | $ 4\frac{3}{8} $ ft² |
| 3) | $ 2\frac{13}{16} $ in² |
| 4) | $ 1\frac{17}{18} $ ft² |
| 5) | $ 2\frac{7}{10} $ in² |
| 6) | $ \frac{2}{3} $ yd² |
| 7) | $ 3\frac{1}{3} $ in² |
| 8) | $ 3 $ yd² |
| 9) | $ 1\frac{8}{9} $ ft² |
Let me know if you'd like this formatted as a printable worksheet or want explanations for any specific steps!
Parent Tip: Review the logic above to help your child master the concept of area worksheet with fractions.
