Converting Between Percents and Fractions
Converting between percents and fractions is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 5: Ratios and Rates. Students convert percents to fractions by writing the percent over 100 and simplifying, and convert fractions to percents by setting up a proportion or multiplying by 100. This skill is foundational for working with ratios, data, and real-world percent problems.
Key Concepts
To convert a percent to a fraction, use the definition: $25\% = \frac{25}{100}$, then simplify if possible. To convert a fraction to a percent, create an equivalent fraction with a denominator of 100, like $\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100} = 40\%$.
Common Questions
How do you convert a percent to a fraction?
Write the percent as a fraction with 100 in the denominator, then simplify. For example, 75% = 75/100 = 3/4.
How do you convert a fraction to a percent?
Multiply the fraction by 100. For example, 3/5 = (3/5) x 100 = 60%. Alternatively, set up the proportion: 3/5 = x/100, then x = 60.
What are common percent-fraction equivalents to know?
Common equivalents: 50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 40% = 2/5, 33% ≈ 1/3, 66% ≈ 2/3, 10% = 1/10.
Where is converting percent to fraction taught in Big Ideas Math Advanced 1?
Converting between percents and fractions is covered in Chapter 5: Ratios and Rates of Big Ideas Math Advanced 1, the Grade 6 math textbook.