Word Problems of Converting Percent, Fractions, and Decimals

Some GED word problems mix percentages, fractions, and decimals in the same question. The key is fluency: knowing how to convert between all three forms quickly and accurately. Once you can do that, any combination becomes manageable, and these problems often turn out to be simpler than they first appear.

What Are Percent-Fraction-Decimal Word Problems?

These problems involve two or more of the three representations of part-of-a-whole. For example, a problem might tell you that 0.35 of a class passed an exam and ask what fraction that is, or state that \(\color{blue}{\frac{3}{8}}\) of a budget was spent and ask for the decimal and percent. The conversions you need:

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• Decimal to Fraction: \(\color{blue}{0.35 = \frac{35}{100} = \frac{7}{20}}\)
• Decimal to Percent: \(\color{blue}{0.35 \times 100 = 35}\)%
• Fraction to Decimal: \(\color{blue}{\frac{3}{8} = 3}\) ÷ \(\color{blue}{8 = 0.375}\)
• Fraction to Percent: \(\color{blue}{0.375 \times 100 = 37.5}\)%
• Percent to Decimal: 60% ÷ \(\color{blue}{100 = 0.60}\)
• Percent to Fraction: 60% = \(\color{blue}{\frac{60}{100} = \frac{3}{5}}\)

How to Solve These Word Problems

Step 1, Identify the given form and the target form

Read the problem. What is given (percent, fraction, or decimal)? What form does the answer need to be in?

Step 2, Convert to the target form

Use the conversion rules above. When in doubt, convert everything to decimals first. They are easiest to compare and calculate with.

Step 3, Solve the question

Apply arithmetic (multiply, compare, add, etc.) using the converted values.

Step-by-Step Summary

1. Read the problem; identify all numbers and their forms (%, fraction, decimal).
2. Convert to a common form (decimals recommended).
3. Perform the required operation (compare, calculate, find percent of a number).
4. Convert the answer to the form the problem requests.

Watch: Converting Between Fractions, Decimals, and Percents

Math with Mr. J covers all conversions in a comprehensive lesson perfect for mixed-form problems:

Worked Examples

Example 1: A school collected 0.35 of its fundraising goal. Write this as a fraction in simplest form and as a percent.

Fraction: \(\color{blue}{0.35 = \frac{35}{100} = \frac{7}{20}}\). Percent: \(\color{blue}{0.35 \times 100 = 35\%}\).
Answer: \(\color{blue}{\frac{7}{20}}\); 35%

Example 2: Express \(\color{blue}{\frac{3}{8}}\) as a decimal and a percent.

Decimal: \(\color{blue}{3 &\text{ div }; 8 = 0.375}\). Percent: \(\color{blue}{0.375 \times 100 = 37.5\%}\).
Answer: 0.375; 37.5%

Example 3: A store sold 0.6 of its inventory. Express this as a fraction and percent. If the store started with 250 items, how many were sold?

Fraction: \(\color{blue}{0.6 = \frac{3}{5}}\). Percent: \(\color{blue}{60\%}\). Items sold: \(\color{blue}{0.6 \times 250 = 150}\).
Answer: \(\color{blue}{\frac{3}{5}}\); 60%; 150 items

Example 4: 40% of a 75-question test is reading questions. Write 40% as a fraction and find the number of reading questions.

Fraction: \(\color{blue}{40\% = \frac{2}{5}}\). Questions: \(\color{blue}{0.40 \times 75 = 30}\).
Answer: \(\color{blue}{\frac{2}{5}}\); 30 reading questions

More Practice: Fractions and Decimals Video Review

Math Antics reinforces fraction-decimal connections, which are foundational for these mixed-form problems:

Exercises

1. Express 0.24 as a fraction in simplest form and as a percent.
2. A survey found \(\color{blue}{\frac{7}{20}}\) of respondents prefer coffee. Write this as a decimal and a percent.
3. A class scored an average of 85% on a test. Write 85% as a fraction in simplest form and as a decimal.
4. 0.5 of a pizza was eaten. If the pizza was cut into 16 slices, how many slices were eaten? Write the portion as a percent.
5. Convert \(\color{blue}{\frac{5}{8}}\) to a decimal and percent. Is it more or less than 60%?

Answers

1. \(\color{blue}{\frac{6}{25}; 24\%}\)
2. \(\color{blue}{0.35; 35\%}\)
3. \(\color{blue}{\frac{17}{20}; 0.85}\)
4. \(\color{blue}{8 \text{ slices }; 50\%}\)
5. \(\color{blue}{0.625; 62.5\%; \text{ more than } 60\%}\)

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Frequently Asked Questions

What is the easiest way to convert between all three forms?

Use decimals as a “hub.” Convert everything to a decimal first: divide the fraction, or divide the percent by 100. Once you have a decimal, multiply by 100 for the percent, or place over a power of 10 and simplify for the fraction.

How do I simplify a fraction from a decimal like 0.375?

Write it as \(\color{blue}{\frac{375}{1000}}\), then find the GCF of 375 and 1000 (= 125), and divide: 375 ÷ \(\color{blue}{125 = 3}\); 1000 ÷ \(\color{blue}{125 = 8}\). So \(\color{blue}{0.375 = \frac{3}{8}}\).

Why is it helpful to convert to decimals when comparing?

Decimals have a uniform place-value structure. You can compare 0.625 and 0.60 by looking at the hundredths digit, which is much faster than finding a common denominator for \(\color{blue}{\frac{5}{8}}\) and \(\color{blue}{\frac{3}{5}}\).

Related Topics

• Word Problems Involving Comparing Percent and Fractions
• Representing Percentage
• Fractional and Decimal Percentages
• Convert Between Fractions and Decimals
• Solving Percentage Word Problems