Q: 17. How many years are in 84 months?

The correct answer is: $7\text{ years}$ Explanation To convert months to years, divide the number of months by 12 (months per year). Steps: Formula: $$\text{years}=\frac{\text{months}}{12}$$ Substitute: $$\text{years}=\frac{84}{12}$$ Compute: $$\text{years}=7$$ Therefore, 84 months equals $7\text{ years}$.

Q: 1. Write 4.3125 as a fraction in simplest form.

The correct answer is: $69/16$ Explanation We convert the decimal part to a fraction and simplify. Steps: Separate the integer and decimal parts: $$4.3125 = 4 + 0.3125$$ Write the decimal as a fraction: $$0.3125 = \frac{3125}{10000}$$ Simplify the fraction by dividing numerator and denominator by $125$: $$\frac{3125}{10000} = \frac{25}{80} = \frac{5}{16}$$ Combine and convert to an improper fraction: $$4 + \frac{5}{16} = \frac{64}{16} + \frac{5}{16} = \frac{69}{16}$$ Therefore, $4.3125 = \frac{69}{16}$.

Q: Write and solve an equation that represents the following: Twenty more than a number is eighteen.

The correct answer is: $x = -2$ Explanation Let $x$ be the unknown number. "Twenty more than a number is eighteen" translates to the equation $x + 20 = 18$. Solve this equation to find $x$. Steps: Write the equation: $x + 20 = 18$ Subtract 20 from both sides: $x = 18 - 20$ Compute the result: $x = -2$ Therefore, the number is $-2$.

Q: We want to convert 54 degrees Celsius (°C) to degrees Fahrenheit (°F).

The correct answer is: $129.2^\circ\text{F}$ Explanation Use the Celsius-to-Fahrenheit conversion formula $F = C\times\frac{9}{5}+32$. For $C=54^\circ\text{C}$ substitute and compute. Steps: Formula: $$F = C\times\frac{9}{5}+32$$ Substitute: $$F = 54\times\frac{9}{5}+32$$ Calculate: $$F = 54\times1.8+32 = 97.2+32 = 129.2$$ Therefore, $54^\circ\text{C} = 129.2^\circ\text{F}$.

Q: How do you write 0.79 as a fraction?

The correct answer is: $79/100$ Explanation Write the decimal as a fraction by moving the decimal point two places (because there are two digits after the decimal) — this is equivalent to multiplying numerator and denominator by 100. Steps: Multiply to remove the decimal: $$0.79\times100=79$$ Write as a fraction: $$0.79=\frac{79}{100}$$ Simplify if possible: $$\gcd(79,100)=1\text{, so the fraction is already in lowest terms}$$ Therefore, $0.79=\frac{79}{100}$.

Question

How do you write -0.\overline{416} as a fraction?

Accepted Answer

The correct answer is: $-\frac{416}{999}$

Explanation

We convert the repeating decimal to a fraction.

Steps:

Let $x=-0.\overline{416}$
Multiply by $1000$ (period length $3$): $$1000x=-416.\overline{416}$$
Subtract the original equation from this: $$1000x-x=-416.\overline{416}-(-0.\overline{416})$$ which gives $$999x=-416$$
Solve for $x$: $$x=-\frac{416}{999}$$

The fraction is already in lowest terms (gcd$(416,999)=1$), so $-\frac{416}{999}$ is the final answer.