Example Question - cross-multiply
Here are examples of questions we've helped users solve.
Solving an Equation with Incomplete Image Clarity
The image is not entirely clear, but I will provide the solution to the equation based on what is visible: Given: \[ \frac{1}{a} + \frac{1}{b} = \frac{1}{4.5} \] First, find the common denominator for \(\frac{1}{a}\) and \(\frac{1}{b}\), which is \(ab\). \[ \frac{b}{ab} + \frac{a}{ab} = \frac{1}{4.5} \] \[ \frac{a + b}{ab} = \frac{1}{4.5} \] Cross-multiply to solve for \(a + b\): \[ a + b = ab \cdot \frac{1}{4.5} \] Convert 4.5 to a fraction: \[ a + b = ab \cdot \frac{1}{\frac{9}{2}} \] Inverse the fraction: \[ a + b = ab \cdot \frac{2}{9} \] Divide both sides by ab to solve for \(\frac{1}{ab}\): \[ \frac{a+b}{ab} = \frac{2}{9} \] Therefore: \[ \frac{1}{ab} = \frac{2}{9(a+b)} \] The correct expression that represents \(\frac{1}{ab}\) is: \[ \frac{2}{9(a+b)} \] Looking at the options provided, the answer is: b) \(\frac{2}{9(a+b)}\)
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, \(x = 12\).
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