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Chapter 6: Problem 69

In the following exercises, convert each fraction to a percent. $$\frac{7}{4}$$

Short Answer

Expert verified
175\%

Step by step solution

01

Convert the fraction to a decimal

Divide the numerator by the denominator: \[ \frac{7}{4} = 1.75 \]
02

Convert the decimal to a percent

Multiply the decimal by 100 to get the percentage: \[ 1.75 \times 100 = 175\% \]

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Key Concepts

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

converting fractions
Converting fractions to percentages is a common math skill that helps us understand proportions better. For instance, when we say \(\frac{7}{4}\), we want to represent it as a percent. The first step is to convert the fraction into a decimal.

This is done by dividing the numerator (the top number) by the denominator (the bottom number). In this case, we do \(7 \div 4 = 1.75\). Notice that we are transforming the fraction into a form that's easier to work with in percentage terms.

Once you have the decimal representation, you can proceed to the next step of converting it to a percentage.
decimal to percent
After converting a fraction to a decimal, the next step is to transform that decimal into a percent. A percentage represents a part out of 100, which means you multiply the decimal by 100.

For our example, we take \(1.75\) and multiply it by \(100\). This operation looks like this:

\[1.75 \times 100 = 175\]

Thus, converting \(1.75\) into a percentage gives you \175\%. This tells us that \(\frac{7}{4}\) is equal to \175\% when expressed as a percentage. This operation is the key link between decimals and percentages.
basic arithmetic
Understanding basic arithmetic is essential for solving many math problems, including converting fractions to percentages. Arithmetic skills include:
  • Addition
  • Subtraction
  • Multiplication
  • Division


In our exercise of converting \(\frac{7}{4}\) to a percent, we mainly use division and multiplication.

First, we divided the numerator by the denominator to get the decimal form: \[7 \div 4 = 1.75\]

Second, we multiplied the resulting decimal by \(100\) to get the percentage: \[1.75 \times 100 = 175\]

These steps showcase the basic arithmetic operations involved in converting fractions to percentages. Mastering these operations makes tackling similar problems straightforward.

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Most popular questions from this chapter

In the following exercises, find the sale price. Takwanna saw a cookware set she liked on sale for \(\$ 145\) off. The original price of the cookware was \(\$ 312\) .

In the following exercises, solve the percent problem. Mara received \(\$ 31.80\) commission when she sold a \(\$ 795\) suit. What was her rate of commission?

According to Time magazine (7/19/2011) annual global seafood consumption rose from 22 pounds per person in 1960 to 38 pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)

In the following exercises, translate and solve using proportions. What percent of \(3,100\) is 930\(?\)

In the following exercises, solve the proportion problem. An 8 ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get?
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