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Chapter 8: Problem 49

Translate to an equation and solve. What number is \(15 \%\) of \(9 \frac{1}{2} ?\)

Short Answer

Expert verified
Answer: 1.425

Step by step solution

01

Write the problem as an equation

The problem asks us to find what number is 15% of 9.5. We can represent this as an equation using the formula: \(x = \frac{15}{100} \cdot 9.5\)
02

Calculate the value of the fraction

We can simplify the fraction by dividing the numerator (15) by the denominator (100): \(\frac{15}{100} = 0.15\)
03

Multiply the decimal by 9.5

Now, we can determine the final answer by multiplying the decimal (0.15) by 9.5: \( x = 0.15 \cdot 9.5\)
04

Calculate the final result

After multiplying the decimal and 9.5, we get: \( x = 1.425\) So, 15% of 9.5 equals to 1.425.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equation Translation
To tackle problems like "What number is 15% of 9.5?", we start by transforming the question into a mathematical equation. This process is known as equation translation. Here's how it works:
  • Read the problem carefully. "What number is 15% of 9.5?" suggests we need to find a number (let's call it \(x\)).
  • Identify "15% of"鈥攖his indicates we're taking 15% of another number.
  • The mathematical way to express "15% of 9.5" is to multiply 9.5 by 15 divided by 100 (since percent means per hundred).
  • Thus, the equation becomes \(x = \frac{15}{100} \times 9.5\).
Using equation translation helps in converting words into numbers, leading the way to solve percentage problems effectively.
Fractions to Decimals
Once we have our equation \(x = \frac{15}{100} \times 9.5\), the next step involves converting the fraction \(\frac{15}{100}\) into a decimal. This represents 15%, which is read as 15 per hundred. Here鈥檚 how you do it:
  • The fraction \(\frac{15}{100}\) simply means 15 divided by 100.
  • Perform the division: \(15 \div 100 = 0.15\).
Now, you've made the equation a little easier to work with by replacing the fraction with its decimal form, \(0.15\). Understanding this conversion is crucial, as decimals are often more convenient for calculations.
Decimal Multiplication
Having transformed the fraction to a decimal, the final task is decimal multiplication. We need to calculate \(x\) using the equation \(x = 0.15 \times 9.5\). Here is how to do it:
  • Align the numbers for multiplication: 0.15 multiplied by 9.5.
  • Ignore the decimal points temporarily and multiply as if they were whole numbers: 15 and 95.
  • After multiplying, insert the decimal point in the result based on the original numbers' places. Since 0.15 and 9.5 have a total of three decimal places (two in 0.15 and one in 9.5), place the decimal in your answer so that it has three decimal places.
  • The result of \(0.15 \times 9.5\) is hence \(1.425\).
By mastering decimal multiplication, you ensure accurate solutions to percentage problems, providing clarity and precision in math operations.

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Most popular questions from this chapter

Write each decimal number as a percent. $$0.004$$

Draw a circle graph showing each percent. A poll shows that \(36 \%\) of participants agree with a proposed bill, \(48 \%\) disagree, and the rest have no opinion. (GRAPH CANT COPY)

Translate to an equation and solve. \(120 \%\) of what number is \(65.52 ?\)

Write each decimal number as a percent. $$0.065$$

The following table contains the Jones family's net monthly income and expenses. $$\begin{aligned} &2\\\ &\begin{array}{l|l} \text { Income } & \text { Expenses } \\ \hline \text { Mr. Jones: } \$ 2252.70 & \text { Mortgage: } \$ 1680 \\ \hline \text { Mrs. Jones: } \$ 2597.30 & \text { Car Loan } 1: \$ 380 \\ \hline & \text { Car Loan } 2: \$ 465 \\ \hline & \text { Credit Card Payments: } \$ 220 \\ \hline & \text { Utilities: } \$ 485 \\ \hline & \text { Groceries: } \$ 450 \\ \hline \end{array} \end{aligned}$$ a. Complete the following table with the percent of the total monthly income that each expense represents. (Round each percent to one decimal place.) $$\begin{array}{l|c|c|c|c|c|c} & \text { Mortgage } & \text { Car loan 1 } & \text { Car loan 2 } & \begin{array}{c} \text { Credit card } \\ \text { payments } \end{array} & \text { Utilities } & \text { Groceries } \\ \hline \begin{array}{l} \text { Percent of total } \\ \text { monthly income } \end{array} & & & & & & \end{array}$$ b. What is the total percent of the family's income paid toward expenses? c. What percent of the family's income is left after all expenses are paid? d. Draw a circle graph showing the percent of the total monthly income that each expense represents, along with the percent remaining after all expenses are paid. (Circle can't copy)
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