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Chapter 7: Problem 14

Convert the given percent to a fraction, and simplify the result. $$ 177 \% $$

Short Answer

Expert verified
\(177\% = \frac{177}{100}\), already in simplest form.

Step by step solution

01

Write the Percent as a Fraction

To convert a percentage to a fraction, write it over 100. For instance, 177% becomes \( \frac{177}{100} \).
02

Simplify the Fraction

The fraction \( \frac{177}{100} \) is in its simplest form. 177 and 100 do not have any common factors other than 1, so the fraction cannot be simplified further.

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Key Concepts

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

Simplifying Fractions
When converting a percentage to a fraction, you'll often encounter the need to simplify the fraction. Simplifying a fraction means reducing it to its most concise form, where the numerator and denominator have no common factors other than 1. For example, let's say we have the fraction \( \frac{4}{8} \). Both 4 and 8 can be divided by 4, their greatest common divisor, to simplify this to \( \frac{1}{2} \). Simplification involves:
  • Finding the greatest common divisor (GCD) of the numerator and denominator.
  • Dividing both the numerator and the denominator by this GCD.
After simplification, the fraction is in its simplest form, which helps in making the fraction more understandable and in many mathematical operations, it makes calculations simpler.
Prealgebra Concepts
Prealgebra is a crucial foundational math concept that introduces you to basic operations and how numbers interact with each other. One important concept in prealgebra is converting between different representations of numbers鈥攍ike percentages, decimals, and fractions. This is essential because:
  • It helps in understanding real-world mathematical problems.
  • Facilitates easier calculations and comparisons.
When converting a percentage to a fraction, the percentage is first expressed as a fraction with a denominator of 100. For instance, 177% becomes \( \frac{177}{100} \). This conversion is part of prealgebra skills, involving multiplication, division, and understanding number properties. It's an important skill because it bridges elementary math to more advanced topics like algebra.
Fractions and Percentages
Fractions and percentages are different ways to express parts of a whole. They are closely related and can often be converted into one another to make interpreting data easier.To convert a percentage into a fraction:
  • Write the percentage number over 100.
  • Simplify the fraction if possible.
For example, 177% as a fraction is \( \frac{177}{100} \). In percentages, the whole is always considered as 100%, which makes conversion to fractions quite straightforward.Understanding how percentages and fractions are connected helps in various applications like shopping discounts, statistics, and more. Recognizing this relationship aids in problem-solving, enabling a smoother transition between different math problems and real-life situations.

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Most popular questions from this chapter

A bartender making a salary of $$\$ 4,200$$ per month has her salary increased to $$\$ 4,300$$ per month. Find the percent increase correct to the nearest tenth of a percent.

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Aisha } & 39 \\ \text { Akbar } & 31 \\ \text { Fernando } & 36 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

The balance on a 8-year loan is $9,768. If the simple interest rate is 4% per year, what was the principal borrowed?

A business owner borrows $$\$ 7,300$$ for 2 months. At the end of the 2-month loan period, the interest owed is $$\$ 73$$. What was the simple yearly interest rate (as a percent)?

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Mercy } & 56 \\ \text { Hans } & 53 \\ \text { Lisa } & 41 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.
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