Compare Fractions

Compare fractions, mixed numbers, decimals, and percentages using the LCD method.

Compare fractions, decimals, percentages, or mixed numbers. Uses LCD method to find which value is greater.

Value 1
?
Compare
Value 2
Fractions (3/4), mixed (1 1/2), decimals (0.75), percents (25%) | Max 15 chars
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help_outlineHow to Useexpand_more

Comparing Fractions with the LCD Method

When comparing fractions with different denominators, finding the Lowest Common Denominator (LCD) allows you to rewrite each fraction with the same base, making comparison straightforward.

Step-by-Step Process:

  1. Identify the denominators of both fractions
  2. Calculate the LCD (Least Common Multiple of denominators)
  3. Convert each fraction to an equivalent fraction with the LCD
  4. Compare the numerators - larger numerator means larger fraction
infoWhat is Compare Fractions?expand_more

Comparing fractions is the process of determining which fraction represents a larger or smaller quantity. This skill is fundamental in mathematics and has practical applications in cooking, construction, finance, and everyday decision-making.

The LCD (Lowest Common Denominator) method is one of the most reliable techniques for comparing fractions. By expressing both fractions with identical denominators, you can directly compare their numerators to determine which is greater.

Our calculator handles not just simple fractions, but also mixed numbers (like 2 1/4), decimals (like 0.875), and percentages (like 75%) - converting everything to comparable values automatically.

functionsFormulaexpand_more

LCD Method Formula:

Given fractions a/b and c/d:

1. Find LCD = LCM(b, d)

2. Convert: a/b = (a × LCD/b) / LCD

3. Convert: c/d = (c × LCD/d) / LCD

4. Compare the new numerators

Cross-Multiplication Method:

To compare a/b and c/d:

Calculate: a × d and b × c

If a × d > b × c, then a/b > c/d

If a × d < b × c, then a/b < c/d

lightbulbExamplesexpand_more

Example 1: Compare 5/6 and 3/8

LCD of 6 and 8 = 24

5/6 = 20/24 (multiply by 4/4)

3/8 = 9/24 (multiply by 3/3)

Result: 20 > 9, so 5/6 > 3/8

Example 2: Compare 2/3 and 3/4

LCD of 3 and 4 = 12

2/3 = 8/12 (multiply by 4/4)

3/4 = 9/12 (multiply by 3/3)

Result: 8 < 9, so 2/3 < 3/4

Example 3: Compare 75% and 4/5

Convert 75% to fraction: 75/100 = 3/4

LCD of 4 and 5 = 20

3/4 = 15/20 and 4/5 = 16/20

Result: 15 < 16, so 75% < 4/5

quizFAQexpand_more
What is the LCD method for comparing fractions?expand_more
The LCD (Lowest Common Denominator) method involves finding the smallest number that both denominators divide into evenly. You then convert both fractions to equivalent fractions with this common denominator and compare the numerators. The fraction with the larger numerator is the larger fraction.
Why use LCD instead of just converting to decimals?expand_more
While decimals work well for simple comparisons, the LCD method keeps values exact without rounding errors. It's especially useful for fractions that produce repeating decimals (like 1/3 = 0.333...) and is the standard method taught in schools for understanding fraction relationships.
Can I compare mixed numbers and fractions?expand_more
Yes! First convert the mixed number to an improper fraction. For example, 2 1/4 becomes 9/4. Then use the LCD method to compare. Our calculator handles this conversion automatically for you.
How do I compare more than two fractions?expand_more
Find the LCD of all denominators, convert each fraction to an equivalent fraction with the LCD, then order them by their numerators. You can use our calculator multiple times to compare pairs, or sort by decimal values.
What's the fastest method to compare two fractions?expand_more
Cross-multiplication is often the quickest: multiply the first numerator by the second denominator and compare it to the first denominator times the second numerator. However, for understanding and teaching purposes, the LCD method is preferred.