Adding a Fraction to Reach a Whole Number: A Simple Mathematical Problem Solved

When faced with the challenge of finding what should be added to a fraction to reach a whole number, the process can be both satisfying and insightful. In today's article, we will delve into the problem of finding the exact fraction that, when added to 21/5, results in 5. This involves solving a simple equation, understanding the concept of fractions and equivalence, and applying the principles of algebra.

Introduction to the Problem

Let's consider the problem at hand: to find what should be added to 21/5 to make 5. This problem can be represented with the equation:

x 21/5 5

Step-by-Step Solution

First, we need to isolate the unknown variable, x. We can do this by subtracting 21/5 from both sides of the equation:

x 5 - 21/5

Next, we should convert the whole number 5 into a fraction with the same denominator as 21/5 to facilitate the subtraction. We know that 5 can be expressed as 25/5:

x 25/5 - 21/5

Since the denominators are the same, we can subtract the numerators directly:

x (25 - 21)/5 4/5

Thus, the fraction that needs to be added to 21/5 to make it equal to 5 is 4/5.

Alternative Methods

There are several ways to approach this problem, and let's explore a few to ensure a comprehensive understanding:

First, we can solve it directly by subtracting 21/5 from 5. By expressing 5 as a fraction with the same denominator, we get:

5 - 21/5 (25/5) - (21/5) (25 - 21)/5 4/5

Alternatively, we can use algebra. Let's set up the equation 21/5 X 5. By moving 21/5 to the RHS, we get:

X 5 - 21/5

Expressing 5 as 25/5, we get:

X (25/5) - (21/5) (25 - 21)/5 4/5

Another approach is to use cross multiplication. Starting with the equation:

(21/5)X 5

Through cross multiplication, we get:

(21/5) * (x/1) 5

Multiplying through, we get:

(21X/5) 5

Multiplying both sides by 5, we get:

21X 25

Subtract 21 from 25, we get:

5X 25 - 21 4

Dividing both sides by 5, we get:

X 4/5

A simpler way to think about it is to directly subtract 21/5 from 5. Expressing 5 as 25/5, we get:

5 - 21/5 25/5 - 21/5 (25 - 21)/5 4/5

Conclusion

Addition of fractions to achieve a whole number is a fundamental concept in mathematics. Understanding how to manipulate fractions and algebraic equations opens up a world of mathematical problem-solving. Whether through direct subtraction, algebraic manipulation, or cross multiplication, the key is to convert the whole number into a fraction with the same denominator to facilitate the calculation.

By mastering these techniques, you can approach similar problems with confidence, enhancing your problem-solving skills and deepening your understanding of mathematical concepts.