Question

Find the correct answer \( \frac{2}{9} \times \frac{3}{4} = \text{?} \)

• A. \(5/13 \)
• B. \(1/6 \)
• C. \(5/36 \)
• D. \(6/13 \)

Hint:

To minimize calculation mistakes, simplify the terms by canceling cross-multiples before multiplying them out! For example, simplify 2 with 4 to get 1 and 2, and 3 with 9 to get 1 and 3. Then simply calculate \(\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}\).

Answer 1

The Correct Option is B

Concept: When multiplying two fractions together, we multiply the numerators directly across to determine the new numerator, and multiply the denominators directly across to determine the new denominator. The general structural rule is written as: \[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \] Once the resulting product is obtained, it is brought down to its simplest irreducible form by dividing out the highest common factor (HCF) shared between the numerator and denominator.

Step 1: Set up and perform the multiplication across the numerators and denominators.
We are given the following fraction multiplication expression to evaluate: \[ \text{Expression} = \frac{2}{9} \times \frac{3}{4} \] Multiplying the terms across the top and bottom explicitly gives: \[ \text{Expression} = \frac{2 \times 3}{9 \times 4} \] Calculating the products: \[ 2 \times 3 = 6 \] \[ 9 \times 4 = 36 \] Substituting these product values back into our fraction yields: \[ \text{Expression} = \frac{6}{36} \]

Step 2: Reduce the fraction to its simplest terms.
To reduce \(\frac{6}{36}\), we find the Greatest Common Divisor (GCD) of the numerator 6 and the denominator 36. Since 36 is an exact multiple of 6 (\(6 \times 6 = 36\)), the GCD is 6. We now divide both the top and the bottom numbers by 6: \[ \text{Numerator} = \frac{6}{6} = 1 \] \[ \text{Denominator} = \frac{36}{6} = 6 \] Putting it back together gives the simplified value: \[ \text{Expression} = \frac{1}{6} \] This matches perfectly with Option (B).