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Chapter 7: Problem 10

Convert the percent to a fraction. $$77 \%$$

Short Answer

Expert verified
77% as a fraction is \( \frac{77}{100} \).

Step by step solution

01

Understand the Meaning of Percent

Percent means 'per hundred'. So 77% means 77 per 100.
02

Write the Percentage as a Fraction

Write 77% as a fraction over 100: \( \frac{77}{100} \)
03

Simplify the Fraction (if possible)

Examine if the fraction can be simplified. In this case, 77 and 100 have no common factors other than 1. Thus, \( \frac{77}{100} \) is already in its simplest form.

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Key Concepts

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

percent to fraction conversion
Percent to fraction conversion is a fundamental mathematical skill. Understanding percentages is crucial as they are used everywhere - from shopping discounts to statistical data. Percent means 'per hundred', so converting a percent to a fraction involves straightforward steps.

For example, converting 77% to a fraction involves knowing that 77% simply means 77 out of 100. This is written mathematically as:\( \frac{77}{100} \)

This fraction tells us that 77 parts of 100 are being considered. Remember, this is the starting point before further simplification.
simplifying fractions
Simplifying fractions means reducing them to their smallest possible form, where the numerator and the denominator have no common factors other than 1.

Let's look at the fraction from our percent-to-fraction conversion: \( \frac{77}{100} \). Here are the steps to simplify it:
  • Identify the greatest common divisor (GCD) of both the numerator (77) and the denominator (100).
  • Check the factors of 77: 1, 7, 11, 77.
  • Check the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
  • Both 77 and 100 have no common factors other than 1.
  • Since their GCD is 1, the fraction \( \frac{77}{100} \) is already in its simplest form.
mathematical notation
Mathematical notation helps us convey complex concepts in a simple and readable manner. Understanding how to read and write this notation is important for mastering math.

In our example, the notation \( \frac{77}{100} \) tells us that '77' is the numerator and '100' is the denominator. This fraction notation is key to understanding ratios and proportions in mathematics.

Here are a few useful tips about mathematical notation:
  • Numerator is the top number in a fraction, representing parts considered.
  • Denominator is the bottom number, representing total equal parts.
  • The fraction line (/) separates the numerator from the denominator.

Knowing these basic notations can make solving and understanding mathematical problems much easier.

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Most popular questions from this chapter

The amount of 8000 dollar is invested at \(4 \%\) for 3 years. a. Compute the ending balance if the bank calculates simple interese? b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest? (TABLE CAN NOT COPY)

Find the decimal and fraction equivalents of the percent given in the sentence. One year, the average U.S. income tax rate was \(18.2 \%\)

The maximum recommended heart rate (in beats per minute) is given by 220 minus a person's age. For acrobic activity, it is recommended that individuals exercise at \(60 \%-85 \%\) of their maximum recommended heart rate. This is called the aerobic range. a. Find the maximum recommended heart rate for a 42 -year-old. b. Find the aerobic range for a 42 -year-old.

If a bank compounds interest quarterly for 2 years, how many total compounding periods are there?

Of the 87 panthers living in the wild in Florida, 11 are thought to live in Everglades National Park. To the nearest tenth of a percent, what percent is a his? (Source: U.S. Fish and Wildlife Services) (IMAGES CANNOT COPY)
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