A fraction is a number that describes how many equal parts of a whole are being considered. It is written with a numerator on top and a denominator on the bottom.
The whole is divided into 2 equal parts, and 1 part is taken.
The whole is divided into 4 equal parts, and 3 parts are taken.
A fraction is not only a “piece of a pizza.” In mathematics, the same fraction can represent several ideas.
| Meaning | Example | Explanation |
|---|---|---|
| Part of a whole | \(\dfrac{3}{5}\) | 3 of 5 equal parts are selected. |
| Division | \(\dfrac{3}{5}=3\div5\) | The numerator is divided by the denominator. |
| Ratio | \(\dfrac{3}{5}\) | 3 parts are compared with 5 parts. |
| Point on a number line | \(\dfrac{3}{5}=0.6\) | The value is located between 0 and 1. |
Before solving fraction problems, identify the type of fraction. This helps you choose the right method.
The numerator is smaller than the denominator. Its value is between 0 and 1.
The numerator is greater than or equal to the denominator. Its value is at least 1.
A whole number and a proper fraction written together.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole-number part. The remainder becomes the numerator of the fractional part. The denominator stays the same.
Compute the division \(17\div4\).
Find the greatest whole number of groups of \(4\) inside \(17\). Since \(4\cdot4=16\) and \(4\cdot5=20\), the quotient is \(4\).
Find the remainder: \(17-16=1\). This leftover \(1\) becomes the numerator of the fractional part.
Keep the original denominator \(4\). Therefore, the mixed number is \(4\dfrac{1}{4}\).
Equivalent fractions have the same value even though they look different. You create equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero number.
\(\dfrac{1}{2}\)
\(\dfrac{2}{4}\)
A fraction is in simplest form when the numerator and denominator have no common factor except 1. The fastest method is to divide both by their greatest common divisor.
Find the greatest common divisor of 12 and 18.
You can also divide by smaller common factors until nothing remains.
The negative sign can be written in front of the fraction, in the numerator, or in the denominator. These mean the same thing.
To compare fractions, first check whether the denominators or numerators are the same. If not, use a common denominator or cross multiplication.
When denominators are the same, the larger numerator gives the larger fraction.
When numerators are the same, the smaller denominator gives the larger fraction because each piece is bigger.
Cross multiply and compare the products.
Fractions can be added or subtracted only when they refer to equal-sized parts. That is why we need a common denominator.
Keep the denominator and add the numerators.
Find the least common denominator, rewrite both fractions, then add the numerators.
Add whole parts with whole parts and fraction parts with fraction parts. If the fraction part becomes improper, convert it.
Keep the denominator and subtract the numerators.
If the fraction part on top is too small, borrow 1 whole and turn it into a fraction with the same denominator.
Multiply numerator by numerator and denominator by denominator. Simplify before or after multiplying.
Before multiplying, you may cancel common factors across numerator and denominator.
To divide by a fraction, multiply by its reciprocal. This is often called “keep, change, flip.”
Enter any fraction. The graph shows its decimal value on a number line and displays a visual bar model. Improper fractions are allowed, so you can see values greater than 1.
Use this tool to compare two fractions. The page simplifies both fractions and compares their actual values.
To find a fraction of a number, multiply the number by the fraction.
If a fraction is used, subtract it from 1 to find the remaining part.
If a fraction of the total is known, divide the known amount by the fraction.
Do not add denominators when adding fractions.
You cannot add or subtract fractions with different denominators directly.
When dividing by a fraction, multiply by the reciprocal of the second fraction.