Fractions
What is a Fraction?
A fraction is a way to represent a part of a whole or a division of a quantity into equal parts. It consists of two main parts:
Numerator: The numerator is the number on the top of the fraction. It represents the number of equal parts you have.
Denominator: The denominator is the number on the bottom of the fraction. It represents the total number of equal parts that make up the whole.
Types of Fractions:
Proper Fractions: The numerator is less than the denominator. Example: 3/4
Improper Fractions: The numerator is greater than or equal to the denominator. Example, 7/4, 5/5, and 12/3 are improper fractions.
Mixed Fractions: A whole number combined with a proper fraction. For example, 2 1/2, 3 3/4, and 1 5/8 are mixed numbers. Please scroll down this page to see the exercises about converting a mixed number into an improper fraction.
Equivalent Fractions: Different fractions that represent the same value. For example: 1/2 = 2/4 = 4/8
Like Fractions: Fractions with the same denominator. For example: 2/7 and 5/7
Unlike Fractions: Fractions with different denominators. For example: 3/8 and 2/5
These are the key types of fractions you'll encounter in math. Understanding these will help you work with fractions more easily!
Adding and Subtracting Fractions
Adding and subtracting fractions follow the same basic rules! Whether you're adding or subtracting, if the fractions have the same denominator (the bottom number), you only need to add or subtract the numerators (the top numbers). The denominator stays the same, so you copy it over.
If the fractions have different denominators, the first step is to find a common denominator. This is usually the least common denominator (LCD), the smallest number that both denominators can divide into evenly. Once you have a common denominator, convert both fractions so they have this denominator, then proceed to add or subtract the numerators.
Multiplying Fractions
To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators to get the new denominator. For example, to multiply 2/3 and 3/4, you get (2 * 3) / (3 * 4) = 6/12 = 1/2.
Dividing Fractions
Dividing Fractions: To divide fractions, follow these steps: Keep, Change, Flip. Keep the first fraction as it is, Change the division sign to multiplication, and Flip the second fraction (the divisor). Then, multiply across the numerators and denominators. It’s that easy—Keep, Change, Flip!
For example, to divide 1/2 by 3/5, keep the first fraction 1/2, change the operation to multiplication, and flip the second fraction: (1/2) * (5/3) = 5/6.
Simplifying Fractions
To simplify a fraction, you want to reduce it to its simplest form.
Here's how you do it:
Identify the Greatest Common Factor (GCF):
The GCF is the largest number that divides evenly into the numerator (the top number) and the denominator (the bottom number).Divide Both Numbers by the GCF:
Once you've found the GCF, divide the numerator and the denominator by this number.
Simplifying Fractions
Mixed Numbers or Mixed Fractions
A mixed number, sometimes called a mixed fraction, combines an integer (whole number) and a fraction (part of a whole number).
Converting mixed fraction into an improper fraction :
To convert a mixed fraction into an improper fraction, you can follow these steps:
Multiply the whole number by the denominator of the fractional part.
Add the result to the numerator of the fractional part.
Write the result as the numerator of the improper fraction, keeping the original denominator the same.
Please refer to the example on the right, where we convert 3 and 1/2 into an improper fraction. Remember, the denominator remains the same, so our focus is on finding the numerator.
Mixed Number Exercises
Answers to Mixed Number Exercises
Please watch the video below to check your answers.
Practical Uses of Fractions: Fractions are used in various real-life situations, such as cooking (measuring ingredients), construction (calculating measurements), and finances (calculating interest rates).
Fractions are a fundamental concept in mathematics, and understanding how to work with them is essential for many mathematical and practical applications. Practice and applying these concepts will help you become proficient in using fractions.