18 Divided by What is 90? Solving the Equation
This article will guide you through solving the equation: 18 divided by what equals 90. We'll explore the mathematical process, show different ways to approach the problem, and offer some real-world applications.
Understanding the Problem
The question "18 divided by what is 90" can be written as a mathematical equation:
18 / x = 90
Where 'x' represents the unknown number we're trying to find. Our goal is to isolate 'x' and solve for its value.
Method 1: Algebraic Solution
To solve for 'x', we can use basic algebra:
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Multiply both sides by x: This eliminates 'x' from the denominator. The equation becomes: 18 = 90x
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Divide both sides by 90: This isolates 'x'. The equation becomes: x = 18 / 90
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Simplify the fraction: Reduce the fraction to its simplest form. Both 18 and 90 are divisible by 18. Therefore: x = 1/5
Therefore, 18 divided by 1/5 is 90.
Method 2: Thinking it Through
We can also approach this problem intuitively. If 18 divided by a number equals 90, that means the number must be significantly smaller than 18. Think about what fraction of 18 would result in 90 when inverted and multiplied. The answer is 1/5.
Method 3: Using a Calculator
For a quick solution, you can use a calculator. First, divide 18 by 90 (18 ÷ 90 = 0.2). This gives you the answer in decimal form. To convert this decimal to a fraction, you can use the calculator's fraction function or simply recognize that 0.2 is equivalent to 1/5.
Real-World Application
Understanding how to solve this type of equation has practical applications in various fields:
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Scaling recipes: If a recipe calls for 18 grams of sugar and you want to make a batch five times larger, you'd need 90 grams (18 x 5). This problem shows the inverse calculation – finding the scaling factor.
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Financial calculations: Proportion problems are common in finance. For example, figuring out the percentage change between two values or determining the appropriate investment to achieve a specific return.
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Engineering and Physics: Many engineering and physics problems involve ratios and proportions, where solving for an unknown factor is crucial.
Conclusion
The answer to "18 divided by what is 90?" is 1/5. We've shown several methods to arrive at this solution, highlighting the importance of understanding both algebraic methods and intuitive problem-solving approaches. This seemingly simple mathematical problem underscores the practical applications of basic algebraic principles in various fields. Remember to always check your work and consider the context of the problem to ensure the solution makes logical sense.
