**Introduction**

Fractions are a way of representing parts of a whole. They are written as a numerator and a denominator, separated by a fraction bar. The numerator is the number of parts we are considering, and the denominator is the total number of parts. For example, the fraction ^{1}/_{2} represents one out of two equal parts.

**Types of fractions**

There are three main types of fractions:

There are three main types of fractions:

**Proper fractions:**These fractions have a numerator that is smaller than the denominator. For example,^{1}/_{2}is a proper fraction.**Improper fractions:**These fractions have a numerator that is larger than or equal to the denominator. For example,^{3}/_{2}is an improper fraction.**Mixed numbers:**These numbers are a combination of a whole number and a proper fraction. For example, 2^{1}/_{2}is a mixed number.

**Adding and subtracting fractions**

To add or subtract fractions, they must have the same denominator. Once they have the same denominator, the fractions can be added or subtracted as usual. For example, to add ^{1}/_{2} and ^{1}/_{4}, we would first need to convert ^{1}/_{4} to ^{2}/_{4} (by taking LCM of denominators). Then, we could add the two fractions, giving us ^{3}/_{4}.

**Multiplying and dividing fractions**

To multiply fractions, we multiply the numerators and the denominators. For example, to multiply ^{1}/_{2} and ^{2}/_{3}, we would multiply the numerators, giving us 2, and the denominators, giving us 6. So, the product of ^{1}/_{2} and ^{2}/_{3} is ^{1}/_{3}.

To divide fractions, we flip the second fraction and multiply. For example, to divide ^{1}/_{2} by ^{2}/_{3}, we would flip the second fraction, giving us ^{3}/_{2}, and then multiply, giving us ^{3}/_{4}.

**Equivalent fractions**

Equivalent fractions are fractions that have the same value. For example, ^{1}/_{2} and ^{2}/_{4} are equivalent fractions.

**Fractions on a number line**

Fractions can be represented on a number line by placing a dot at the appropriate location. For example, the fraction ^{1}/_{2} would be placed halfway between 0 and 1 on a number line.

**Fractions in real-world problems**

Fractions are used in many real-world problems. For example, we might use fractions to represent parts of a pizza, parts of a pie, or parts of a cake. We might also use fractions to represent discounts, sales, or percentages.

**Examples**

Here are some examples of fraction problems that students might encounter in class 5:

- Add
^{1}/_{2}and^{1}/_{4}. - Subtract
^{1}/_{2}from^{3}/_{4}. - Multiply
^{1}/_{2}and^{2}/_{3}. - Divide
^{1}/_{2}by^{2}/_{3}. - Find the equivalent fraction of
^{1}/_{2}that has a denominator of 12. - Place the fraction
^{1}/_{6}on a number line.

I hope this guide helps you understand fractions for class 5!