Converting Between Percents & Fractions - Sixth Grade Mathematics
Converting between percents and fractions allows you to seamlessly shift between rates per hundred and simplified rational numbers, selecting the most effective tool for computation.
Converting Percents to Fractions
Because a percent is fundamentally a ratio per 100, converting any percent into a fraction follows a three-step protocol.
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| CONVERTING PERCENTS TO FRACTIONS PROTOCOL |
| |
| Step 1: Drop the percent symbol (%). |
| Step 2: Write the number as the numerator over a denominator of 100. |
| Step 3: If the numerator contains a decimal, multiply numerator and |
| denominator by powers of 10 to make it an integer. |
| Step 4: Simplify the fraction to simplest form by dividing by GCF. |
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Worked Examples:
Example A: Convert 48% to a fraction:
- Write over 100: 48/100.
- Divide top and bottom by GCF (4): (48 / 4) / (100 / 4) = 12/25.
Example B: Convert 12.5% to a fraction:
- Write over 100: 12.5/100.
- Multiply top and bottom by 10 to clear decimal: 125/1,000.
- Divide by GCF (125): 125 / 125 = 1; 1,000 / 125 = 8.
- Result: 1/8.
Converting Fractions to Percents
There are two primary methods for converting fractions into percents depending on the denominator.
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| TWO PATHWAYS TO CONVERT FRACTION TO PERCENT |
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| Method 1: Scaling | Scale the denominator | 4/5 = (4 * 20) / (5 * 20) |
| to Denominator 100| to 100 using an | = 80/100 = 80% |
| (Mental Shortcut) | equivalent fraction | (Fastest when factor of 100)|
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| Method 2: Division| Divide numerator by | 5/8: 5 / 8 = 0.625 |
| to Decimal to % | denominator; multiply | Multiply by 100: |
| (Universal) | decimal by 100 | 0.625 * 100 = 62.5% |
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Method 1: Scaling When Denominator Divides 100
If the denominator is a factor of 100 (such as 2, 4, 5, 10, 20, 25, or 50), find the multiplier that scales the denominator to 100 and multiply the numerator by that same factor: For 7/20: 20 * 5 = 100, so multiply 7 * 5 = 35; result is 35%. For 9/25: 25 * 4 = 100, so multiply 9 * 4 = 36; result is 36%.
Method 2: Universal Long Division
When the denominator does not scale evenly into 100 (such as 3, 6, 7, 8, or 12), divide the numerator by the denominator using long division, and then multiply the resulting quotient by 100: For 1/3: 1 / 3 = 0.3333... Multiply by 100: 33.333...% = 33 and 1/3%. For 5/6: 5 / 6 = 0.8333... Multiply by 100: 83.333...% = 83 and 1/3%.
Essential Benchmark Equivalency Matrix
Memorizing standard benchmark equivalencies dramatically accelerates computation.
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| ESSENTIAL BENCHMARK FRACTION-PERCENT PAIRS |
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| Fraction | Percent | Fraction | Percent |
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| 1/2 | 50% | 1/8 | 12.5% (12 1/2%) |
| 1/4 | 25% | 3/8 | 37.5% (37 1/2%) |
| 3/4 | 75% | 5/8 | 62.5% (62 1/2%) |
| 1/5 | 20% | 7/8 | 87.5% (87 1/2%) |
| 2/5 | 40% | 1/3 | 33 1/3% (33.3%) |
| 3/5 | 60% | 2/3 | 66 2/3% (66.7%) |
| 4/5 | 80% | 1/10 | 10% |
+-----------------+-------------------+-----------------+-----------------+
Exercises
Exercise 1. Convert each percent to a fraction in simplest form: (a) 65%; (b) 8%; (c) 140%; (d) 37.5%.
Exercise 2. Convert each fraction to a percent using the scaling method: (a) 13/20; (b) 17/50; (c) 7/10.
Exercise 3. Use long division to convert 7/16 into a percent. Show the decimal quotient and the final percent.
Solutions
Solution to Exercise 1. For (a) 65%: 65/100; divide top and bottom by 5 to get 13/20. For (b) 8%: 8/100; divide top and bottom by 4 to get 2/25. For (c) 140%: 140/100; divide by 20 to get 7/5 (or 1 and 2/5). For (d) 37.5%: 37.5/100 = 375/1,000; divide top and bottom by 125 to get 3/8.
Solution to Exercise 2. For (a) 13/20: multiply numerator and denominator by 5: (13 * 5) / (20 * 5) = 65/100 = 65%. For (b) 17/50: multiply numerator and denominator by 2: (17 * 2) / (50 * 2) = 34/100 = 34%. For (c) 7/10: multiply numerator and denominator by 10: (7 * 10) / (10 * 10) = 70/100 = 70%.
Solution to Exercise 3. Set up long division for 7 divided by 16: 16 into 7.0000 goes 0.4375 times. Multiply the decimal quotient by 100 to convert to a percent: 0.4375 * 100 = 43.75%. The fraction 7/16 equals 43.75% (or 43 and 3/4%).