Order fractions, decimals, and percents
Ordering fractions, decimals, and percents is a Grade 7 skill in Big Ideas Math, Course 2 that requires converting all values to a single form before comparing. The most efficient method is converting everything to decimals: divide the numerator by the denominator for fractions, move the decimal two places left for percents. For example, to order 3/5, 0.62, and 58%, convert to 0.60, 0.62, and 0.58—yielding 58% < 3/5 < 0.62. Students may also convert to fractions with a common denominator. Consistent form is the key: mixed comparisons without conversion lead to errors.
Key Concepts
To compare and order fractions, decimals, and percents, convert all numbers to the same format (usually decimals). Then compare the decimal values. When ordering negative numbers, remember that the number closer to zero on the number line is the larger number.
Common Questions
What is the easiest way to order fractions, decimals, and percents together?
Convert all values to decimals first. Divide fractions (numerator ÷ denominator) and divide percents by 100, then compare the decimal values directly.
How do you convert a percent to a decimal for comparison?
Divide by 100 or move the decimal point two places to the left. For example, 58% = 0.58.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/5 = 3 ÷ 5 = 0.60.
How do you order 3/5, 0.62, and 58% from least to greatest?
Convert: 3/5 = 0.60, 0.62 = 0.62, 58% = 0.58. Order the decimals: 0.58 < 0.60 < 0.62, so 58% < 3/5 < 0.62.
Can you compare fractions, decimals, and percents using fractions instead of decimals?
Yes—convert all to fractions with a common denominator. However, converting to decimals is usually faster and less error-prone.
What is a common mistake when ordering mixed forms?
Trying to compare without converting—for example, assuming 0.62 > 3/5 without calculating that 3/5 = 0.60, which could lead to incorrect ordering.