Greater Than Or Less Than Calculator
Our free arithmetic calculator solves greater than less than problems. Get worked examples, visual aids, and downloadable results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
a > b if a - b > 0 | a < b if a - b < 0 | a = b if a - b = 0
To compare two values, subtract one from the other. If the difference is positive, the first value is greater. If negative, it is less. If zero, they are equal. For fractions a/b and c/d, cross-multiply: if ad > bc, then a/b > c/d.
Worked Examples
Example 1: Comparing Two Fractions
Problem:Which is greater: 3/4 or 5/7?
Solution:Method 1 - Cross-multiplication: 3 x 7 = 21, 5 x 4 = 20. Since 21 > 20, we get 3/4 > 5/7.\nMethod 2 - Decimal conversion: 3/4 = 0.75, 5/7 = 0.71428...\n0.75 > 0.71428, confirming 3/4 > 5/7.\nDifference: 0.75 - 0.71428 = 0.03571
Result:3/4 > 5/7 (3/4 is greater by approximately 0.0357)
Example 2: Comparing Decimal and Percentage
Problem:Compare 0.375 and 37.5%.
Solution:Convert 37.5% to decimal: 37.5 / 100 = 0.375\nConvert 0.375 to fraction: 375/1000 = 3/8\n0.375 = 0.375\nThe two values are exactly equal.
Result:0.375 = 37.5% (they are equal)
Frequently Asked Questions
How do you compare fractions to determine which is greater or less?
There are several reliable methods to compare fractions. The most common is cross-multiplication: for fractions a/b and c/d, multiply a times d and compare with c times b. If a times d is greater, then a/b is greater. You can also convert both fractions to a common denominator using the LCM and then compare the numerators directly. Another approach is converting each fraction to its decimal equivalent by dividing the numerator by the denominator. Each method has advantages depending on the context and the numbers involved.
What do the greater than and less than symbols mean?
The greater than symbol (>) means the number on the left is larger than the number on the right. The less than symbol (<) means the left number is smaller. A helpful mnemonic is that the open end of the symbol always faces the larger number, like a hungry alligator eating the bigger value. The equals sign (=) means both values are the same. These comparison operators are fundamental in mathematics and appear throughout algebra, calculus, and computer programming. There are also combined symbols like greater than or equal to and less than or equal to.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy