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Chapter 7: Problem 62

Convert the given fraction to a percent. $$ \frac{7}{8} $$

Short Answer

Expert verified
\( \frac{7}{8} \) is 87.5%.

Step by step solution

01

Understanding the Conversion

To convert a fraction into a percentage, you need to multiply the fraction by 100. This is because 'percent' means 'per hundred'.
02

Set Up the Equation

Write the fraction as an equation that involves multiplying by 100: \( \frac{7}{8} \times 100 \).
03

Multiply the Fraction

Perform the multiplication: \( \frac{7}{8} \times 100 = \frac{700}{8} \).
04

Simplify the Fraction

Divide 700 by 8 to simplify the fraction. \( 700 \div 8 = 87.5 \).
05

Write the Result as a Percentage

The result from the division is your percentage. Thus, \( \frac{7}{8} \) is equal to 87.5%.

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Key Concepts

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

Multiplying Fractions
When you multiply fractions, you need to multiply the numerators together and the denominators together. For example, to multiply \( \frac{7}{8} \times \frac{100}{1} \), you do the following:
  • Multiply the numerators: \( 7 \times 100 = 700 \)
  • Multiply the denominators: \( 8 \times 1 = 8 \)
This gives you \( \frac{700}{8} \), which is the result of the multiplication. Multiplying fractions might seem daunting at first, but with practice, it becomes easier. The key is to perform the multiplication step by step, keeping your work neat and organized.
Simplifying Fractions
Simplifying fractions is an important step to make a fraction easier to work with. After performing a multiplication, as in our example with \( \frac{700}{8} \), the next step is to simplify. To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). In this case:
  • Check the GCD for 700 and 8, which turns out to be 8.
  • Divide both by 8: \( \frac{700 \div 8}{8 \div 8} = \frac{87.5}{1} \)
Here, simplifying has brought us to 87.5, which is an easier number to understand and use. Simplification can often convert complex fractions into simple whole or decimal numbers, making calculations seamless and more intuitive.
Division in Fractions
Division in fractions is a key step, especially when it comes to simplifying. In our example, once \( \frac{700}{8} \) is achieved after multiplication, the next task is to divide. This division is straightforward but essential:
  • You find how many times 8 goes into 700, which is 87.5 times.
  • Write or use division notation: \( 700 \div 8 = 87.5 \)
This division step converts the fraction into a single number that is part of the process to find a percentage. It is captivating to see how division turns a fraction into a clean, interpretable number, aiding tremendously in fraction to percent conversions.

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Most popular questions from this chapter

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