Q: How many feet in one third of a mile?

The correct answer is: $1760\text{ ft}$ Explanation We convert one third of a mile to feet using the standard conversion factor $1\text{ mile} = 5280\text{ ft}$. Multiply that by $\tfrac{1}{3}$ to find one third of a mile. Steps: Conversion factor: $$1\text{ mile} = 5280\text{ ft}$$ Multiply by one third: $$\tfrac{1}{3}\times 5280\text{ ft}$$ Evaluate the product: $$\tfrac{5280}{3}\text{ ft} = 1760\text{ ft}$$ Therefore, one third of a mile equals $1760\text{ feet}$. Quick check: since $1\text{ mile}=1760\text{ yards}$ and $1\text{ yard}=3\text{ ft}$, $1\text{ mile}=1760\times3=5280\text{ ft}$, and dividing $5280$ by $3$ again gives $1760\text{ ft}$ (consistent).

Q: What is 125% as a fraction?

The correct answer is: $\frac{5}{4}$ Explanation Percent means "per hundred", so convert 125% to a fraction by writing it over 100 and simplifying. Steps: First step: $$\frac{125}{100}$$ Second step (simplify by dividing numerator and denominator by 25): $$\frac{125\div25}{100\div25}=\frac{5}{4}$$ Final step (mixed number form): $$1\frac{1}{4}$$ Therefore, 125% = $\frac{5}{4}$ (which is also $1\frac{1}{4}$).

Q: Express 0.4375 as a fraction in the simplest form.

The correct answer is: $\frac{7}{16}$ Explanation We convert the decimal to a fraction and simplify. Steps: First write 0.4375 as a fraction with denominator 10000: $$0.4375=\frac{4375}{10000}$$ Divide numerator and denominator by their common factor 125: $$\frac{4375}{10000}=\frac{4375\div125}{10000\div125}=\frac{35}{80}$$ Reduce further by dividing both by 5: $$\frac{35}{80}=\frac{35\div5}{80\div5}=\frac{7}{16}$$ Therefore, 0.4375 in simplest fractional form is $\frac{7}{16}$.

Q: Write 3/4 divided by 2 in the fraction.

The correct answer is: $\frac{3}{8}$ Explanation You divide by 2 by multiplying by its reciprocal (which is $\frac{1}{2}$). Then multiply numerators and denominators and simplify if possible. Steps: Write division as multiplication by the reciprocal: $$\frac{3}{4}\div2=\frac{3}{4}\times\frac{1}{2}$$ Multiply numerators and denominators: $$\frac{3\times1}{4\times2}=\frac{3}{8}$$ The fraction is already in simplest form: $$\frac{3}{8}$$ Therefore, $\frac{3}{4}$ divided by $2$ equals $\frac{3}{8}$.

Q: What is 0.875 as a fraction?

The correct answer is: $\frac{7}{8}$ Explanation We convert the decimal to a fraction by writing it over a power of 10 and then simplifying. Steps: Write the decimal as a fraction: $0.875=\frac{875}{1000}$ Divide numerator and denominator by their greatest common divisor $125$: $$\frac{875}{1000}=\frac{875\div125}{1000\div125}=\frac{7}{8}$$ Final simplified fraction: $\frac{7}{8}$ Therefore, $0.875=\frac{7}{8}$.

Q: What is 7/16 as a decimal?

The correct answer is: $0.4375$ Explanation We convert the fraction $\frac{7}{16}$ to a decimal by making the denominator a power of 10. Steps: Multiply numerator and denominator by 625 to get denominator $10000$: $$\frac{7}{16}=\frac{7\times625}{16\times625}=\frac{4375}{10000}$$ Write the fraction with denominator $10000$ as a decimal: $$\frac{4375}{10000}=0.4375$$ (Check) Long division $7\div16=0.4375$ gives the same result. Therefore, $\frac{7}{16}=0.4375$.

Question

How many feet in one third of a mile?

Accepted Answer

The correct answer is: $1760	ext{ ft}$

Explanation

We convert one third of a mile to feet using the standard conversion factor $1	ext{ mile} = 5280	ext{ ft}$. Multiply that by $	frac{1}{3}$ to find one third of a mile.

Steps:

Conversion factor: $$1	ext{ mile} = 5280	ext{ ft}$$
Multiply by one third: $$	frac{1}{3}	imes 5280	ext{ ft}$$
Evaluate the product: $$	frac{5280}{3}	ext{ ft} = 1760	ext{ ft}$$

Therefore, one third of a mile equals $1760	ext{ feet}$.

Quick check: since $1	ext{ mile}=1760	ext{ yards}$ and $1	ext{ yard}=3	ext{ ft}$, $1	ext{ mile}=1760	imes3=5280	ext{ ft}$, and dividing $5280$ by $3$ again gives $1760	ext{ ft}$ (consistent).