Fractions are a fun and important part of math that help us understand parts of a whole. Whether you’re sharing snacks with friends or measuring ingredients for a recipe, fractions are all around us! Let’s explore the key points about fractions so you can master them with ease.
What is a Fraction?
A fraction represents a part of a whole or a part of a group. It consists of two numbers:
- The numerator (top number) shows how many parts we are considering.
- The denominator (bottom number) shows how many equal parts the whole is divided into.
For example, in the fraction 1/4, the numerator (1) represents one part, while the denominator (4) tells us that the whole is divided into four equal parts.
The word “fraction” comes from the Latin term “fractio”, which means “a breaking” or “to break”. This reflects the concept of fractions as parts of a whole that have been broken into smaller, equal parts. For example, if you break a whole pizza into smaller pieces, each piece is a fraction of the pizza.
1/8 of a pizza indicates that a pizza has been divided into 8 equal parts and 1 part has been taken out of that.
1/6 of a doughnut shows that a doughnut has been split into 6 equal parts and 1 part is taken.
Halves, Thirds and Quarters
Some of the most common fractions you’ll see are halves, thirds, and quarters.
Halves: When something is split into 2 equal parts, each part is called a half. We write this as the fraction 1/2. Imagine cutting a pizza into 2 equal pieces – each piece is half of the pizza.
Thirds: If something is divided into 3 equal parts, each part is called a third. This is written as 1/3. For example, if you split a chocolate bar into 3 equal pieces, each piece is one third.
Quarters: When something is divided into 4 equal parts, each part is called a quarter or one-fourth. We write this as 1/4. If you cut an apple into 4 equal slices, each slice is a quarter of the apple.
Fractions on a Number Line
A number line is a straight line with numbers marked on it. It is a great way to visualize fractions and understand where they fit between whole numbers. Let’s see how to place fractions like 1/2, 1/3, and 1/4 on a number line.
Draw a Number Line: Start by drawing a straight line and mark whole numbers, like 0, 1, 2, and so on. The space between any two whole numbers will be where we place fractions.
Dividing the Space: To place fractions, we divide the space between two whole numbers into equal parts:
- For halves, divide the space into 2 equal parts.
- For thirds, divide the space into 3 equal parts.
- For quarters, divide the space into 4 equal parts.
Marking Fractions:
- 1/2 will be exactly halfway between 0 and 1.
- 1/3 will be one-third of the way between 0 and 1, and 2/3 will be two-thirds of the way.
- 1/4 will be one-fourth of the way, with 2/4 halfway, and 3/4 three-fourths of the way between 0 and 1.
Using a number line helps us see that fractions are just parts of the space between whole numbers!
Types of Fractions
Unit Fractions
A unit fraction is a special type of fraction where the numerator (the top number) is always 1. The denominator (the bottom number) can be any whole number, and it tells us how many equal parts the whole is divided into.
Like Fractions
Like fractions are fractions that have the same denominator. The denominator tells us how many equal parts the whole is divided into, so if two fractions have the same denominator, they are dealing with the same-sized parts.
Example:
- 1/4, 2/4 and 3/4 are like fractions because both have a denominator of 4. This indicates that both fractions are divided into 4 equal parts.
- 5/8 and 7/8 are also like fractions because they both have the denominator 8.
Unlike Fractions
Unlike fractions are fractions that have different denominators. Since the pieces are different sizes, we need to find a common denominator to compare, add or subtract them.
Example:
- 1/3 and 1/5 are unlike fractions because their denominators are different (3 and 5).
- 3/4 and 1/6 are also unlike fractions because their denominators are different (4 and 6).
Equivalent Fractions
Fractions that represent the same value but have different numerators and denominators (e.g., 1/2 = 2/4).
Proper Fractions
The numerator is smaller than the denominator (e.g., 2/5). These represent parts of a whole.
Improper Fractions
The numerator is larger than or equal to the denominator (e.g., 7/4). These can be converted into mixed numbers.
Mixed Fractions
A combination of a whole number and a fraction.
Practise Quiz On Fraction
FAQs on Fractions
- A fraction represents a part of a whole, while a ratio compares parts to each other. For example, a fraction 1/4 represents one part of four, while a ratio (like 1:4) compares one item to four others.
Fractions only represent positive parts or values of a whole and do not include negative values.
Rational numbers include both positive and negative values, as well as zero and integers.
Every fraction is a rational number, but not every rational number is a fraction. Rational numbers have a broader definition that includes both positive and negative values and can represent a wider range of numbers beyond just positive parts of a whole.
No, a fraction cannot be negative.