A selection of free mathematics resources (calculators, exercises, games, quizzes, course reminders) that allow you to learn how to do calculations with fractions.

### Definition

- Note :`a/b`=a:b
- Example :`1/2` = 1:2 = 0,5
### Simplifying a fraction

### Irreducible fraction

### Equal fractional writing

- When we multiply the numerator and denominator of a fractional writing by the same non-zero number, we obtain a fractional writing that is equal to it.
- When you divide the numerator and denominator of a fractional number by the same non-zero number, you get a fractional number that is equal to it.
### Fraction comparison

**Equality of fractions****Fractions have the same denominator****Fractions have the same numerators****Fractions have different numerators and denominators**### Adding fractions with the same denominator

### Adding fractions with different denominators

### Subtraction of fractions with the same denominator

### Subtracting fractions with different denominators

### Product of fractions

### Division of fractions

For any pair of integers a, b with b not zero, the ratio a:b is called a **fraction** the ratio a:b, it is denoted `a/b`, a is called the
numerator
and b the
denominator.

A fraction is also called a rational number.

To **simplify a fraction** we start by
decomposing the numerator and denominator into a product of prime numbers.
When the same number appears in both the numerator and denominator, we can **simplify the fraction**.

Example : `56/32` = `(2*2*2*7)/(2*2*2*2*2)` = `7/4`

A **fraction is said to be irreducible** if its numerator and denominator are prime to each other
To ** put a fraction into its irreducible form** sous sa forme **irréductible**, we divide the numerator and denominator by their
gcd
.

Two **fractions are equal** if it is possible to go from one to the other by multiplying or dividing the numerator and denominator by the same number.

Simply compare the numerators.

The largest is the one with the smallest numerator.

We return to the case where the denominators are equal by applying the equality condition of a fraction.

These are the calculation techniques that the fraction comparator will use in this example to compare the fractions `19/11` and `13/7`.

The **sum of two fractions** with the same denominator has the same denominator, so its numerator is equal to the sum of the numerators.

Therefore, we have the formula:`a/k+b/k=(a+b)/k`

The following example : `1/3+4/3` shows how to add two fractions that have the same numeratorr.

We reduce the fractions to the same denominator, to get back to the case of adding fractions with the same denominator.

The **difference of two fractions** with the same denominator has the same denominator, its numerator is equal to the difference of the numerators.

Therefore, we have the formula:`a/k-b/k=(a-b)/k`

The following example: `4/3-2/3` shows how to subtract two fractions that have the same numerator.

We reduce the fractions to the same denominator, to get back to the case of subtracting fractions with the same denominator.

The **product of two fractions** is equal to the product of the numerators over the product of the denominators.

`3/4*7/3` = `21/12`

The following example `3/4*7/5` : shows how to multiply two fractions.

Dividing by a fraction is the same as multiplying by the inverse of that fraction, using this rule it is possible to turn a fraction quotient into a fraction product and apply the rules for simplifying a product of fractions.

Example:`(-8/3)/(2/3)` = `-8/3*3/2` = `-8/2` = -4

- binomial_coefficient : calculation of binomial coefficients. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- compare_fractions : compare two fractions. The calculator allows to compare two fractions, indicating the steps of the calculations.
- denominator : denominator of a fraction. The denominator function allows the calculation of the denominator of a fraction.
- fraction : fraction calculator. Fraction calculator that allows to do all types of calculations step by step on fractions.
- gcd : gcd calculation online. GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.
- lcm : least common multiple. LCM calculator to calculate the least common multiple (LCM).
- numerator : numerator of a fraction. The numerator function allows the calculation of the numerator of a fraction.
- partial_fraction_decomposition : Partial fraction decomposition calculator. The calculator allows a rational fraction to be broken down into simple elements.
- percentage : Percentage calculator. This percentage calculator converts fractions or numbers in percent.
- prime_factorization : prime factorization calculator. The function prime_factorization is used to calculate online the decomposition of an integer into prime factors.

- Quiz on the calculation of the GCD (fractions): This Greatest Common Divisor quiz gives practice in calculating the GCD of two integers.
- fraction game (fractions): Online fraction game suitable for anyone looking for a good math game online.
- Fraction calculation game (fractions): This math game is based on the calculation of whole fractions. To win this quiz, you just have to find the result of an operation between two fractions.
- fraction comparison game (fractions): The purpose of this integer fraction comparison game is to find the operator (> or <) to place between the fractions being compared.
- irreducible fraction of an expression (fractions): To pass this quiz on irreducible fractions, you just have to find the irreducible form of an operation between several fractions.
- Fraction to percentage transformation game (fractions): In this game of transforming a whole fraction into a percentage, children must choose the correct answer from a list of suggestions.

- Exercise 1129, simplify a fraction using the gcd - fractions : This activity on fractions allows to practice simplifying an integer fraction using the GCD.
- Exercise 1130, fraction and cross product - fractions : This corrected exercise on fractions aims to complete a fractional expression so that an equality is verified.
- Exercise 1131, simplifying a fraction - fractions : The purpose of this corrected fraction exercise is to simplify a fractional expression.
- Exercise 1132, evaluating a fractional expression - fractions : The purpose of this exercise is to give an approximate value to one decimal place of an algebraic.
- Exercise 1212, sum of a fraction and an integer - operations on integers and decimals : The objective of this corrected calculus exercise is to add a fraction with a whole number.
- Exercise 1213, simplifying the denominator of a fraction - operations on integers and decimals : The objective of this corrected math exercise is to simplify a fraction after calculating its denominator.
- Exercise 1214, simplifying a fraction - operations on integers and decimals : The objective of this math exercise is to simplify a fraction that has a fraction as the denominator.
- Exercise 1217, calculate the product of two fractions - operations on integers and decimals : This exercise allows you to apply the techniques of simplification of fractions to calculate the product of two fractions.
- Exercise 1219, compare two fractions - fractions : The purpose of this exercise is to compare two fractions, choosing the appropriate comparison operator from the list provided.
- Exercise 1220, add, subtract, multiply 2 fractions - fractions : This corrected exercise aims to practice addition, subtraction or multiplication of 2 fractions.
- Exercise 1312, fraction and inverse of a number - decimal writing and operations on relative numbers - fractions : The objective of this exercise is to put the product of a number by the inverse of another number in fraction form.
- Exercise 1313, approximate value of a fraction - decimal writing and operations on relative numbers : This exercise allows to practice calculations with decimals, the goal is to give the approximate value of a fraction to one decimal place.
- Exercise 1314, simplification of a decomposed fraction - decimal writing and operations on relative numbers - fractions : The objective of this activity is to simplify a fraction whose numerator and denominator are composed of products of whole numbers.
- Exercise 1315, simplification of a fraction of relative numbers - decimal writing and operations on relative numbers - fractions : This exercise allows to learn how to simplify a fraction whose numerator and denominator are composed of product of relative numbers.
- Exercise 1316, simplifying a fraction of fractions - decimal writing and operations on relative numbers - fractions : The objective of this exercise is to simplify a fraction whose numerator and denominator are fractions, in other words, a fraction of fractions.
- Exercise 1328, comparison of fractions - comparisons of numbers, fractions, expressions - fractions : The objective of this solved exercise is to compare two fractions using the correct operator.
- Exercise 1429, irreducible form of a fraction - fractions - integers and rational numbers : The purpose of this exercise is to put a fraction into its irreducible form.
- Exercise 1434, simplify an expression containing fractions - fractions : The objective of this corrected calculus exercise is to simplify an expression containing fractions.
- Exercise 1436, simplifying fractions and square roots - mathematics exams and competitions - fractions - square roots : The objective of this exercise is to reduce a fraction, simplify a square root, and calculate a fraction that contains powers.
- Exercise 1437, simplify a fraction with the pgcd - mathematics exams and competitions - fractions - integers and rational numbers : The objective of this exercise is to calculate the gcd of two numbers and simplify a fraction.
- Exercise 1520, prime numbers and fraction simplification - fractions - integers and rational numbers : The purpose of this exercise is to simplify a fraction using the decomposition of a number into a product of prime factors.
- Exercise 1539, simplifying a fraction division - fractions : The purpose of this exercise is to use algebraic computation techniques to determine the irreducible form of a division of fractions.
- Exercise 1541, simplifying a product of fractions - fractions : The purpose of this corrected calculus exercise is to use algebraic calculus techniques to simplify a product of fractions.
- Exercise 14110, simplification of square roots - square roots : The purpose of this corrected math exercise is to simplify a square root.

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