UpStudy Free Solution:

To find what number times 8 equals 36, you can set up the equation:

\[8 \times x = 36\]

To solve for \(x\), divide both sides of the equation by 8:

\[x = \frac { 36} { 8} \]

Simplify the fraction:

\[x = 4.5\]

So, \(4.5\) times 8 equals 36.

Supplemental Knowledge

Solving linear equations often involves isolating the variable to determine its value. Here are some additional concepts and steps that can help in understanding this process better:

1. Setting Up the Equation:

- Identify the relationship described in the problem and express it as an equation. For example, "what number times 8 equals 36" translates to \(8 \times x = 36\).

2. Isolating the Variable:

- To find \(x\), you need to isolate it on one side of the equation. This typically involves using inverse operations.

3. Inverse Operations:

- Division is the inverse operation of multiplication. If a variable is multiplied by a number, you can isolate it by dividing both sides of the equation by that number.

4. Simplifying Fractions:

- Once you have isolated the variable, simplify any fractions if possible to find the most reduced form of your answer.

5. Verification:

- Substitute your solution back into the original equation to verify that it satisfies the equation.

6. Example Problem for Practice:

- Suppose you need to find what number times 5 equals 25.

- Set up the equation: \(5 \times y = 25\)

- Divide both sides by 5: \(y = \frac { 25} { 5} \)

- Simplify: \(y = 5\)

- Verify: \(5 \times 5 = 25\), which confirms that \(y = 5\) is correct.

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