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Chapter 7: Problem 61

Convert the fraction to a percent. $$1 \frac{3}{4}$$

Short Answer

Expert verified
175\%

Step by step solution

01

Convert Mixed Number to Improper Fraction

First, convert the mixed number to an improper fraction. For the mixed number \(1 \frac{3}{4}\), multiply the whole number (1) by the denominator (4), and then add the numerator (3).\[1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}\]
02

Divide the Improper Fraction

Now, convert the improper fraction to a decimal by dividing the numerator by the denominator.\[\frac{7}{4} = 7 \div 4 = 1.75\]
03

Convert Decimal to Percent

Finally, convert the decimal to a percent by multiplying by 100.\[1.75 \times 100 = 175\% Therefore, \(1 \frac{3}{4}\) as a percent is 175\%\]

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Key Concepts

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

Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For example, in the number \(1 \frac{3}{4}\), 1 is the whole number, and \(\frac{3}{4}\) is the fraction. To use mixed numbers in calculations like conversion to percent, we first need to change them into improper fractions. This makes further operations easier and more straightforward.
Improper Fractions
An improper fraction is where the numerator (top number) is larger than the denominator (bottom number). To convert a mixed number like \(1 \frac{3}{4}\) into an improper fraction, follow these steps:
  • Multiply the whole number by the denominator: \(1 \times 4 = 4\)
  • Add the numerator to this result: \(4 + 3 = 7\)
  • Place this sum over the original denominator, which gives us \(\frac{7}{4}\)
This improper fraction is now easier to work with for further conversion into decimal and percent forms.
Percent Conversion
Percent conversion involves changing a fraction or decimal into a percentage. A percent represents a portion out of 100. After converting our mixed number \(1 \frac{3}{4}\) into the improper fraction \(\frac{7}{4}\), and then into the decimal 1.75, we multiply by 100 to get the percent. The calculation looks like this:
\(p = 1.75 \times 100 = 175\text{ %}\)
Therefore, \(1 \frac{3}{4}\) converts to 175%.
This means that \(1 \frac{3}{4}\) is the same as 175 out of 100 parts or 175%.
Decimal Conversion
Decimal conversion is the process of converting a fraction to its decimal form. For the fraction \(\frac{7}{4}\), we do this by dividing the numerator by the denominator:
\(\frac{7}{4} = 7 \text{ divided by } 4 = 1.75\)
This is a crucial step before converting the value to a percent.
Using decimals allows for a straightforward calculation to percentages, as you only need to multiply by 100.

Understanding how to convert between these forms will enhance your math skills and make complex calculations more accessible.

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Most popular questions from this chapter

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