Fractions are an essential part of mathematics and often make an appearance in everyday life. From baking a cake to planning a road trip, a fundamental understanding of fractions can prove to be incredibly useful. In this article, we’ll explore three different ways to work with fractions: simplification, addition and subtraction, and multiplication and division.

1. Simplification:

Simplifying fractions is the process of reducing them to their simplest form. To do this, find the greatest common divisor (GCD) of the numerator (top number) and denominator (bottom number). Then divide both the numerator and denominator by this common factor.

For example, let’s simplify the fraction 18/24:

– GCD of 18 and 24 is 6.

– Divide both numbers by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.

– So, the simplified fraction is 3/4.

2. Addition and Subtraction:

Adding or subtracting fractions becomes much easier if they have a common denominator. If they don’t, you’ll need to find the least common multiple (LCM) of their denominators before proceeding. Once you’ve established a common denominator, simply add or subtract the numerators while keeping the denominator the same. Afterward, simplify if possible.

For example, let’s add 2/5 + 3/10:

– Find LCM of 5 and 10: The LCM is 10.

– Convert both fractions to have a denominator of 10:

– (2/5) x (2/2) = 4/10

– (3/10) already has a denominator of 10.

– Add numerators: 4 + 3 =7

– Final fraction is: 7/10. No further simplification is needed.

3. Multiplication and Division:

Multiplying fractions is straightforward: Multiply the numerators, then multiply the denominators, and simplify if necessary. For example, let’s multiply 2/3 x 4/5:

– Multiply numerators: 2 x 4 = 8.

– Multiply denominators: 3 x 5 =15.

– So, the result is: 8/15. No further simplification is needed.

Dividing fractions requires a slightly different approach. To divide two fractions, flip the divisor (the second fraction) and convert the operation to multiplication. Then proceed with multiplying as usual. For example, let’s divide 6/7 ÷ 3/4:

– Flip the divisor and change division to multiplication: 6/7 x 4/3.

– Multiply numerators: 6 x 4 =24.

– Multiply denominators: 7 x 3 =21.

– So, the result is: 24/21. Simplify to get the final answer: 8/7.

Understanding these three methods of working with fractions will empower you to quickly and confidently address any fraction-based problem that you may encounter. Keep practicing, and soon enough, fractions will become second nature!