Carly Worked For $5 \frac{1}{4}$ Hours And Earned \$\$ 46.20$. How Much Would She Earn If She Worked For $6 \frac{3}{4}$ Hours?Enter Your Answer In The Box.$\$ \square$[/tex\]

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Calculating Hourly Earnings: A Step-by-Step Guide

Understanding the Problem

In this problem, we are given that Carly worked for a certain number of hours and earned a specific amount of money. We need to find out how much she would earn if she worked for a different number of hours. To solve this problem, we will first calculate Carly's hourly earnings and then use that information to determine her earnings for the new number of hours.

Calculating Hourly Earnings

To calculate Carly's hourly earnings, we need to divide the amount of money she earned by the number of hours she worked. We are given that Carly worked for $5 \frac1}{4}$ hours and earned $46.2046.20$. We can convert the mixed number to an improper fraction $5 \frac{1{4} = \frac{21}{4}$.

Now, we can calculate Carly's hourly earnings by dividing her earnings by the number of hours she worked:

Hourly Earnings=EarningsNumber of Hours=46.20214\text{Hourly Earnings} = \frac{\text{Earnings}}{\text{Number of Hours}} = \frac{46.20}{\frac{21}{4}}

To divide a number by a fraction, we can multiply the number by the reciprocal of the fraction. The reciprocal of $\frac{21}{4}$ is $\frac{4}{21}$.

Hourly Earnings=46.20×421\text{Hourly Earnings} = 46.20 \times \frac{4}{21}

Now, we can multiply the numbers:

Hourly Earnings=46.20×421\text{Hourly Earnings} = \frac{46.20 \times 4}{21}

Hourly Earnings=184.8021\text{Hourly Earnings} = \frac{184.80}{21}

Hourly Earnings=8.80\text{Hourly Earnings} = 8.80

So, Carly's hourly earnings are $8.808.80$.

Calculating Earnings for the New Number of Hours

Now that we know Carly's hourly earnings, we can calculate her earnings for the new number of hours. We are given that she will work for $6 \frac3}{4}$ hours. We can convert the mixed number to an improper fraction $6 \frac{3{4} = \frac{27}{4}$.

Now, we can calculate Carly's earnings for the new number of hours by multiplying her hourly earnings by the new number of hours:

Earnings=Hourly Earnings×Number of Hours=8.80×274\text{Earnings} = \text{Hourly Earnings} \times \text{Number of Hours} = 8.80 \times \frac{27}{4}

To multiply a number by a fraction, we can multiply the number by the numerator and then divide by the denominator.

Earnings=8.80×27\text{Earnings} = 8.80 \times 27

Earnings=238.40\text{Earnings} = 238.40

Earnings=238.401\text{Earnings} = \frac{238.40}{1}

So, Carly's earnings for the new number of hours are $238.40238.40$.

Conclusion

In this problem, we calculated Carly's hourly earnings by dividing her earnings by the number of hours she worked. We then used that information to calculate her earnings for a new number of hours. By following these steps, we can determine how much Carly would earn if she worked for a different number of hours.

Key Takeaways

  • To calculate hourly earnings, divide earnings by the number of hours worked.
  • To calculate earnings for a new number of hours, multiply hourly earnings by the new number of hours.
  • Improper fractions can be used to represent mixed numbers.

Practice Problems

  • If a person works for $4 \frac{1}{2}$ hours and earns $60.0060.00$, how much would they earn if they worked for $5 \frac{3}{4}$ hours?
  • If a person earns $9.009.00$ per hour and works for $6 \frac{2}{3}$ hours, how much would they earn in total?
    Frequently Asked Questions: Calculating Hourly Earnings and Earnings for a New Number of Hours

Q: What is the formula for calculating hourly earnings?

A: The formula for calculating hourly earnings is:

Hourly Earnings=EarningsNumber of Hours\text{Hourly Earnings} = \frac{\text{Earnings}}{\text{Number of Hours}}

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as an improper fraction.

For example, to convert $5 \frac{1}{4}$ to an improper fraction, multiply 5 by 4 and add 1:

5×4=205 \times 4 = 20

20+1=2120 + 1 = 21

So, $5 \frac{1}{4} = \frac{21}{4}$.

Q: How do I calculate earnings for a new number of hours?

A: To calculate earnings for a new number of hours, multiply the hourly earnings by the new number of hours.

For example, if the hourly earnings are $8.808.80$ and the new number of hours is $6 \frac{3}{4}$, multiply the hourly earnings by the new number of hours:

Earnings=Hourly Earnings×Number of Hours=8.80×274\text{Earnings} = \text{Hourly Earnings} \times \text{Number of Hours} = 8.80 \times \frac{27}{4}

Q: What if I have a decimal number of hours? How do I calculate earnings for that?

A: If you have a decimal number of hours, you can multiply the hourly earnings by the decimal number of hours.

For example, if the hourly earnings are $8.808.80$ and the new number of hours is 3.5, multiply the hourly earnings by the decimal number of hours:

Earnings=Hourly Earnings×Number of Hours=8.80×3.5\text{Earnings} = \text{Hourly Earnings} \times \text{Number of Hours} = 8.80 \times 3.5

Q: Can I use a calculator to calculate hourly earnings and earnings for a new number of hours?

A: Yes, you can use a calculator to calculate hourly earnings and earnings for a new number of hours. Simply enter the numbers into the calculator and follow the instructions to calculate the result.

Q: What if I have a negative number of hours? How do I calculate earnings for that?

A: If you have a negative number of hours, you can multiply the hourly earnings by the negative number of hours. This will give you a negative earnings amount.

For example, if the hourly earnings are $8.808.80$ and the new number of hours is -3, multiply the hourly earnings by the negative number of hours:

Earnings=Hourly Earnings×Number of Hours=8.80×−3\text{Earnings} = \text{Hourly Earnings} \times \text{Number of Hours} = 8.80 \times -3

Q: Can I use a formula to calculate earnings for a new number of hours if I know the hourly earnings and the number of hours?

A: Yes, you can use a formula to calculate earnings for a new number of hours if you know the hourly earnings and the number of hours. The formula is:

Earnings=Hourly Earnings×Number of Hours\text{Earnings} = \text{Hourly Earnings} \times \text{Number of Hours}

Conclusion

Calculating hourly earnings and earnings for a new number of hours can be a simple process if you follow the correct steps. By using the formulas and examples provided in this article, you can calculate your earnings for any number of hours. Remember to always convert mixed numbers to improper fractions and to multiply hourly earnings by the new number of hours to calculate earnings for a new number of hours.