Fractions Comparison Calculator

Fractions comparison calculator uses two proper or improper fractions, `a/b` and `c/d` such that `b,d\ne0`, and compares them.It is an online tool specially programmed to find which one is bigger or smaller among two fractions. In other words, it figures out which symbol goes between the two fractions: `>`,`<` or `=`.
It is necessary to follow the next steps:

1. Enter two fractions `a/b` and `c/d` in the box. The numbers `a,b,c` and `d` must be integers such that `b` and `d` must be nonzero.
2. Press the "GENERATE WORK" button to make the computation;
3. Fractions comparison calculator will give the least common denominator of two or more entered numbers.

Input: Two fractions;
Output: A sign `>,<` or `=`.

Fractions comparison calculator gives us the stepwise procedure for comparing two fractions. Before determining which fraction is bigger or smaller, it calculates the decimal values of these fractions. This comparing of fractions can be of benefit for further applications.

What is Fraction?

A rational number is a number that can be expressed as the quotient or fraction `a/b` of two integers such that `b\ne0`. The top number `a` is called the numerator. The bottom nonzero number `b` is called the denominator. In case of `b=1`, the rational number is integer `a`. Integers and rational numbers are very important in daily life. There are three types of fractions:

• Proper fractions
  Proper fractions are rational numbers `a/b, b\ne0,` where the numerator is smaller than the denominator, `a < b`. Since `a < b`, then the proper fraction is always smaller than `1`. For example, the proper fraction is `3/5`;
  
• Improper fractions
  Improper fractions are rational numbers `a/b, b\ne0,` where the numerator is bigger than the denominator, `a > b`. Since `a > b`, then the proper fraction is always bigger than `1`. Improper fractions can be equivalently written as a mixed number. The mixed number is an integer plus a proper fraction. For example, the improper fraction is `13/15 = 2frac{3}{5}`;
• Equivalent fractions
  Equivalent fractions are two or more fractions with the equal numerical values. For example, `1/3` and `9/27` are equivalent fractions. So, we can write `1/3=3/27`

How to Compare Fractions?

First of all, there are three signs that we use when comparing fractions:

• Larger than (`>`);
• Smaller than (`>`);
• Equal to (`=`);

Sometimes, we use the sign "Different than" `(\ne)`.
To compare fractions with unlike denominators, it is necessary to convert them into equivalent fractions with the common denominator. Fractions with the same denominator are called like fractions. More precisely, we are looking for the the least common denominator (LCD), but any other common denominator can help.The common denominator of two fractions is the least common multiple (LCM) of the denominators of these fractions. If the denominators of the given fractions are equal to each other, then the LCD of these fractions is the denominator of these fractions. After finding the LCD, we will rewrite the original fractions as equivalent fractions using the LCD. Therefore,

• If the LCD is positive, then the fraction with the larger numerator is the larger fraction;
• If the LCD is negative, then the fraction with the larger numerator is the smaller fraction.

In the case of mixed numbers, we convert them to improper fractions and apply the previous procedure.

In a comparison of negative and positive fractions, it follows that any negative fraction is less than any positive fraction.
For example, let us compare fractions `7/9` and `3/4`. The LCD of `7/9` and `3/4` is equal to the LCM of `9` and `4`. So, it holds

If we rewrite the original inputs as equivalent fractions using the LCD, we get

Since `28>27`, then `7/9` is bigger than `3/4`.

The fractions comparison work with steps shows the complete step-by-step calculation for finding which one is bigger or smaller among two fractions `7/9` and `3/4` using the LCD and LCM. For any other fractions, just supply two proper or improper fractions and click on the "GENERATE WORK" button. The grade school students may use this comparing fractions calculator to generate the work, verify the results of comparing numbers, derived by hand or do their homework problems efficiently.

Real World Problems Using Fractions Comparison

Fractions comparison is useful to write fractions in order from least to greatest or from greatest to least. Comparison of fractions becomes a gateway concept that will embolden studying in almost all field of sciences. For instance, in geometry, if we divide a square or some other shape into four parts, then each part has the area one-fourth of the square. Further, we can compare areas of some parts. In order to get real insign it’s important to know relation between information, represented as fractions, i.e. which is bigger, smaller or equal than another. Since fractions are used in real world in many different ways, for example in the cooking and construction, this concept of comparing two fractions can be very helpful.

Fraction Comparison Practice Problems

Practice Problem 1:
Which of the fractions is bigger, `4/7` or `5/9` ?

Practice Problem 2:
Johnny ate `5/16` of a pizza and Melaena ate `2/7` of the same pizza. Who ate more pizza?

The fractions comparison calculator, formula, step by step calculation, real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the values and representations of fractions and consider the relation between the numerator and denominator of two fractions.