91Ó°ÊÓ

One of the first steps in solving a math problem is understanding how to convert the words into a mathematical equation.
This process can sometimes feel challenging, but with practice, it becomes easier. Let's break it down.
In the given problem, we read that three-tenths of a number is 15.
Here’s how we break this down:
- 'Three-tenths' refers to the fraction \frac{3}{10}\ of the number.
- 'Of a number' is represented by the variable \(x\).
- 'Is' translates to an equals sign.
- '15' is simply 15.
Combining these elements, we get the equation \frac{3}{10}x = 15\.
By mastering this step, you will be able to transform any word problem into an equation, which is crucial for finding a solution.

Once you have your equation, the next step is to isolate the variable.
This means getting the variable by itself on one side of the equation.
The variable in our equation is \(x\).
Right now, \frac{3}{10}x = 15\.
We need to get \(x\) alone on one side of the equation.
To do this, we will use the reciprocal of \frac{3}{10}\, which is \frac{10}{3}\.
By multiplying both sides of the equation by \frac{10}{3}\, we cancel out the fraction:
\frac{3}{10}x \times \frac{10}{3} = 15 \times \frac{10}{3}.
This simplifies to: \x = 15 \times \frac{10}{3}\.
Now we have \(x\) isolated on one side.

Multiplying by the reciprocal is a common method to solve equations involving fractions.
The reciprocal of a fraction is simply the fraction flipped.
For example, the reciprocal of \frac{3}{10}\ is \frac{10}{3}\.
By multiplying \frac{3}{10}x \times \frac{10}{3}\, the fractions cancel out, leaving just \(x\) on one side:
\frac{3}{10} \times \frac{10}{3} = 1\.
This leaves us with \(x\) on one side:
\x = 15 \times \frac{10}{3}.
When you simplify the multiplication:
\x = \frac{150}{3} = 50\.
Now we know that \(x = 50\).
Using the reciprocal is a powerful tool in algebra that helps simplify and solve equations efficiently.