Let's analyze and solve the exercises from the image you provided.

1. Rewrite the decimals as fractions:

The task is to express each decimal as a fraction in its simplest form: a) $0.14$
b) $0.022$
c) $0.75$
d) $0.135$
e) $0.3742$
f) $0.405$
g) $0.5288$
h) $0.4315$

2. Calculate the remaining area of land:

• The land has a length of 28 m and width of 16 m.
• 27.5% of the land is used.
• Find the total area of the land, then subtract the used portion to determine the remaining area.

I will work through these step by step. Let me calculate. Decimal to fraction conversion from fractions import Fraction

Decimals provided in the problem

decimals = [0.14, 0.022, 0.75, 0.135, 0.3742, 0.405, 0.5288, 0.4315]

Convert to fractions in simplest form

fractions = [Fraction(d).limit_denominator() for d in decimals]

Land problem

Dimensions of the land

length = 28 # meters width = 16 # meters total_area = length * width # Total area in square meters

Percentage of land used

used_percentage = 27.5 / 100 # Convert percentage to decimal used_area = total_area * used_percentage # Area used in square meters

Remaining area

remaining_area = total_area - used_area

fractions, total_area, used_area, remaining_area### Solutions:

1. Rewriting decimals as fractions:

a) $0.14 = \frac{7}{50}$
b) $0.022 = \frac{11}{500}$
c) $0.75 = \frac{3}{4}$
d) $0.135 = \frac{27}{200}$
e) $0.3742 = \frac{1871}{5000}$
f) $0.405 = \frac{81}{200}$
g) $0.5288 = \frac{661}{1250}$
h) $0.4315 = \frac{863}{2000}$

2. Land problem:

• Total area of the land: $28 \times 16 = 448 \, \text{m}^2$
• Used area (27.5%): $448 \times 0.275 = 123.2 \, \text{m}^2$
• Remaining area: $448 - 123.2 = 324.8 \, \text{m}^2$

Let me know if you'd like further details or explanations!

Here are some related questions to expand your understanding:

1. How can you convert fractions back to decimals?
2. What steps ensure a fraction is in its simplest form?
3. How do you calculate percentages of different areas?
4. How would the results change if the percentage of land used were 30% instead?
5. Can you think of any real-world applications for calculating areas like this?

Tip: Always simplify fractions to their lowest terms for clarity and ease of use!