Comparing Fractions Calculator
To compare fractions, use cross multiplication or find a common denominator. For cross multiplication, multiply each numerator by the other fraction's denominator and compare the products. For the common denominator method, convert both fractions to equivalent fractions with the same denominator, then compare the numerators. The larger numerator indicates the larger fraction.
Use our free calculator below to compare two or more fractions instantly — with step-by-step solutions and visual comparison bars.
Comparing Fractions Calculator
How Do You Compare Fractions?
Comparing fractions means determining which fraction is larger, which is smaller, or whether two fractions are equal. When fractions share the same denominator, comparing them is straightforward — the larger numerator means the larger fraction. But when denominators differ, you need a reliable method to make a fair comparison.
Two proven approaches exist for comparing fractions with unlike denominators: cross multiplication and the common denominator method. Both give the same answer every time, so the best choice depends on the situation. Here's a quick comparison:
| Feature | Cross Multiplication | Common Denominator (LCD) |
|---|---|---|
| Best for | Comparing exactly two fractions | Comparing or ordering 3+ fractions |
| Speed | Fastest — only two multiplications | Slower — requires finding the LCD first |
| Steps | Multiply a × d and c × b, then compare | Find LCD, convert each fraction, compare numerators |
| Works for ordering? | Only pairwise (two at a time) | Yes — sort all numerators at once |
| Shows equivalent form? | No | Yes — gives equivalent fractions with same denominator |
How Do You Compare Fractions Using Cross Multiplication?
Cross multiplication is the fastest way to compare two fractions. Given two fractions a/b and c/d, multiply the numerator of each fraction by the denominator of the other. Then compare the two cross products: if a × d is greater than c × b, then a/b is the larger fraction.
Step 1: Cross multiply — 3 × 7 = 21 and 5 × 4 = 20
Step 2: Compare the products — 21 > 20
Result: Since 21 > 20, we know that 3/4 > 5/7.
How Do You Compare Fractions Using a Common Denominator?
The common denominator method converts both fractions to equivalent fractions that share the same denominator — specifically, the least common denominator (LCD). Once the denominators match, you simply compare the numerators.
Step 1: Find the LCD of 3 and 8 — LCD = 24
Step 2: Convert each fraction — 2/3 = 16/24 and 5/8 = 15/24
Step 3: Compare numerators — 16 > 15
Result: Since 16/24 > 15/24, we know that 2/3 > 5/8.
How Do You Compare Fractions With the Same Denominator?
When two fractions already share the same denominator, no conversion is needed — simply compare the numerators. The fraction with the larger numerator is the larger fraction. For example, 5/8 > 3/8 because 5 > 3. This is the simplest case and the foundation that both comparison methods above build upon.
How Do You Compare Fractions With the Same Numerator?
When fractions have the same numerator but different denominators, the fraction with the smaller denominator is actually the larger fraction. This is because dividing the same number into fewer pieces creates bigger pieces. For example, 3/4 > 3/5 because fourths are larger than fifths. Think of it as splitting a pizza: 3 slices of a pizza cut into 4 pieces gives you more pizza than 3 slices of one cut into 5.
How Do You Order Fractions From Least to Greatest?
When you need to compare three or more fractions, the most efficient approach is to convert all of them to a common denominator and then sort by numerator. Find the LCD of all the denominators, convert each fraction, and arrange them in ascending order of their new numerators. You can also convert each fraction to a decimal and sort the decimal values, which is especially convenient with a calculator.
Step 1: Find the LCD of 2, 8, and 3 — LCD = 24
Step 2: Convert — 1/2 = 12/24, 3/8 = 9/24, 2/3 = 16/24
Step 3: Sort by numerator — 9 < 12 < 16
Result: 3/8 < 1/2 < 2/3
This method works for any number of fractions and is the approach used by our calculator's "Compare Multiple" mode above. For a deeper look at finding the least common denominator, visit our LCD Calculator.
How Do You Compare Mixed Numbers?
To compare mixed numbers, first compare the whole-number parts. If one mixed number has a larger whole number, it is the larger value — for example, 3¼ > 2¾ because 3 > 2. If the whole numbers are equal, compare just the fractional parts using cross multiplication or common denominators. Alternatively, convert each mixed number to an improper fraction and compare using the methods above.
Step 1: Whole numbers are equal (both 2), so compare ⅓ vs ¼.
Step 2: Cross multiply — 1 × 4 = 4 and 1 × 3 = 3
Step 3: Since 4 > 3, we know ⅓ > ¼.
Result: 2⅓ > 2¼.
What Are Benchmark Fractions and How Do They Help?
Benchmark fractions are common reference points — typically 0, ¼, ½, ¾, and 1 — that help you estimate and compare fractions quickly without calculation. By determining whether a fraction is closer to 0, ½, or 1, you can often tell which of two fractions is larger just by mental estimation.
For example, 5/8 is slightly more than ½ (which is 4/8), while 3/10 is slightly less than ⅓ and well below ½. So you can quickly see that 5/8 > 3/10 without any computation. Benchmark fractions are especially useful for mental math, estimation exercises, and helping younger students build fraction number sense.