Mastering Arithmetic: Easy Ways to Perform Basic Operations with Fractions, Decimals, and Percentages

Arithmetic is a fundamental branch of mathematics that deals with the properties and manipulation of numbers. It is a core concept in education and a vital skill in everyday life. Arithmetic operations include addition, subtraction, multiplication, and division, which form the building blocks of more advanced mathematical concepts such as algebra, geometry, and calculus.

In this article, we will provide a guide on how to do arithmetic operations in a simple and easy-to-understand way. We will cover basic arithmetic concepts, such as the order of operations, fractions, decimals, and percentages. We will also provide examples to illustrate each concept and help you become comfortable with doing arithmetic.

Order of Operations

One of the most important concepts in arithmetic is the order of operations. This concept tells us the sequence in which we should perform arithmetic operations to get the correct answer. The order of operations is as follows:

Parentheses (solve expressions inside parentheses first)
Exponents (solve any exponents or powers)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Let's look at an example to illustrate the order of operations:

3 + 2 x 4

Using the order of operations, we first perform the multiplication, and then we add:

3 + 8 = 11

If we didn't follow the order of operations and added before multiplying, we would get the wrong answer:

(3 + 2) x 4 = 20

Fractions

Fractions are numbers that represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). To add or subtract fractions, we need to have a common denominator. To multiply fractions, we multiply the numerators and denominators together. To divide fractions, we invert the second fraction and multiply:

Let's look at some examples to illustrate these concepts:

Addition:

1/4 + 2/5

To add these fractions, we need to find a common denominator. We can use the least common multiple (LCM) of the denominators, which is 20 in this case:

1/4 x 5/5 = 5/20
2/5 x 4/4 = 8/20

Now that we have a common denominator, we can add the numerators:

5/20 + 8/20 = 13/20

Subtraction:

5/6 - 1/3

To subtract these fractions, we need to find a common denominator. We can use the LCM of the denominators, which is 6 in this case:

5/6 x 1/1 = 5/6
1/3 x 2/2 = 2/6

Now that we have a common denominator, we can subtract the numerators:

5/6 - 2/6 = 3/6

We can simplify this fraction by dividing both the numerator and denominator by 3:

3/6 = 1/2

Multiplication:

3/4 x 2/3

To multiply these fractions, we simply multiply the numerators and denominators:

3/4 x 2/3 = 6/12

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6:

6/12 = 1/2

Division:

1/2 ÷ 1/4

To divide these fractions, we invert the second fraction and multiply:

1/2 x 4/1 = 4/2

We can simplify this fraction by dividing both the numerator and denominator by their GCF, which is 2:

4/2 = 2/1 = 2

Decimals

Decimals are another important concept in arithmetic. They are a way of representing parts of a whole, just like fractions. However, instead of having a numerator and denominator, decimals use a decimal point to represent the position of a number in relation to the whole. Each digit to the right of the decimal point represents a fractional part of a whole, with the place value decreasing by a factor of 10 from right to left.

Let's look at an example to illustrate decimals:

0.5 + 0.25

To add these decimals, we simply line up the decimal points and add the digits:

0.5

0.25
0.75

Multiplying decimals can be a bit trickier, but the process is essentially the same as multiplying whole numbers. We just need to be careful to line up the decimal points correctly:

1.5 x 0.25

First, we can ignore the decimal points and multiply as we normally would:

15 x 25 = 375

Next, we count the total number of digits to the right of the decimal points in both numbers (2 in this case) and place the decimal point in the product so that there are the same number of digits to the right of the decimal point:

1.5 x 0.25 = 0.375

Dividing decimals follows a similar process, but we need to be even more careful with the placement of the decimal point:

0.6 ÷ 0.2

We can convert this division problem into a multiplication problem by multiplying the first number by the reciprocal (or inverse) of the second number:

0.6 x 5 = 3

We can count the total number of digits to the right of the decimal points in both numbers (1 in this case) and place the decimal point in the product so that there is 1 digit to the right of the decimal point:

0.6 ÷ 0.2 = 3

Percentages

Percentages are a way of expressing a part of a whole as a fraction of 100. We can convert a percentage to a decimal by dividing by 100, or we can convert a decimal to a percentage by multiplying by 100.

Let's look at some examples to illustrate percentages:

Converting a percentage to a decimal:

25% = 0.25

Converting a decimal to a percentage:

0.75 = 75%

We can also use percentages to calculate percentages of a whole. To do this, we simply multiply the percentage (as a decimal) by the whole:

What is 20% of 50?

20% = 0.20
50 x 0.20 = 10

Therefore, 20% of 50 is 10.

Conclusion

In conclusion, arithmetic is a fundamental branch of mathematics that involves the manipulation of numbers through basic operations such as addition, subtraction, multiplication, and division. The order of operations is an important concept that tells us the sequence in which to perform these operations. Fractions, decimals, and percentages are also important concepts in arithmetic that involve the representation of parts of a whole. By understanding these concepts and practicing with examples, anyone can become comfortable with doing arithmetic and gain confidence in their math skills.