Mathematical Expression Evaluation and X Calculation
I'll help you solve each question individually.
For question 2:
To make the expression \(2 \times 3 + 3 = 3\) correct, we need to insert brackets in such a way that it respects the order of operations and the equation balances. We can insert the brackets around "3 + 3":
\(2 \times (3 + 3) = 3\)
Now, let's evaluate the expression inside the brackets:
\(2 \times 6 = 3\)
But this equation \(2 \times 6 = 3\) is not correct since \(2 \times 6\) equals \(12\), not \(3\). Therefore, there's no way to insert brackets to make the original expression correct. It's possible that there's a typo or the exercise intends to challenge the student's understanding that some expressions with incorrect relationships cannot be made correct merely with bracket placement.
For question 3:
a. \(\frac{3}{36} = \frac{x}{36}\)
To solve for \(x\), we can cross-multiply:
\(36 \times x = 3 \times 36\)
\(36x = 108\)
Divide both sides by 36:
\(x = \frac{108}{36}\)
Simplify the fraction:
\(x = 3\)
b. \(3 = \frac{36}{x}\)
To solve for \(x\), multiply both sides by \(x\) and divide both sides by 3:
\(3x = 36\)
Divide by 3:
\(x = \frac{36}{3}\)
\(x = 12\)
Therefore, \(x = 12\).
