Solving Mathematical Problems: 9/5 Plus 8/2

In the realm of mathematics, solving problems involving fractions can be both challenging and rewarding. In this article, we will delve into the solution of the mathematical problem: 9/5 plus 8/2. This guide aims to offer a step-by-step approach not only to solve this particular problem but to also enhance your understanding of fractions, including improper and mixed fractions.

Understanding the Problem and Solution

The problem at hand is 9/5 plus 8/2. Let's break down the solution step-by-step, starting with the basics.

Step 1: Identifying the Fractions

We are given two fractions: 9/5 and 8/2. The first step in solving this problem is to identify these fractions. Whenever dealing with fractions, it's essential to understand what they represent before moving forward.

Step 2: Finding a Common Denominator

The next step is to find a common denominator for the fractions. The least common denominator (LCD) is the smallest number that can be evenly divided by both denominators. For 9/5 and 8/2, the denominators are 5 and 2. The smallest number that can be divided by both 5 and 2 without a remainder is 10. Therefore, the common denominator is 10.

Step 3: Converting the Fractions

Next, we need to convert the given fractions to equivalent fractions with the common denominator of 10. This involves multiplying the numerator and the denominator of each fraction by the appropriate factor to achieve the common denominator.

For 9/5, multiply both the numerator and the denominator by 2:

9/5 (9*2)/(5*2) 18/10

For 8/2, multiply both the numerator and the denominator by 5:

8/2 (8*5)/(2*5) 40/10

Step 4: Adding the Fractions

Now that both fractions have the same denominator, we can add them together by adding the numerators and keeping the denominator the same:

18/10 40/10 (18 40)/10 58/10

Step 5: Simplifying the Result

The final step is to simplify the fraction. 58/10 can be simplified by dividing the numerator and the denominator by 2:

58/10 (58/2)/(10/2) 29/5

Alternatively, we can express this as a mixed fraction. 29/5 can be broken down into 5 (full units) and 4/5 (the remainder), resulting in 5 4/5.

Step 6: Expressing as a Decimal

To express the result as a decimal, divide the numerator by the denominator:

29/5 5.8

Practice Problems for Greater Understanding

Now that you understand the process, it's time to practice! Here are some additional problems for you to solve:

1. Solve 7/4 3/2

2. Calculate 11/6 5/3

3. Find the sum of 3/8 12/4

Additional Tips for Solving Fraction Problems

Always identify the problem and the fractions involved. Find the least common denominator (LCD) for the fractions. Convert the fractions to have a common denominator. Add or subtract the numerators while keeping the denominator the same. Simplify the result if possible. Express the result as a mixed fraction if it's more appropriate. Convert the result to a decimal for a numerical understanding.

By following these steps and practicing regularly, you can become proficient in solving fraction problems and any related mathematical challenges with ease. Stay curious and continue to explore the vast world of mathematics!