Final answer:
The values of a and b when 1/3 × 1/4 = a/b are 1 and 12 respectively, giving us a fraction of 1/12. This is applied in scale measurements such as determining actual dimensions from a given scale.
Step-by-step explanation:
The question is asking to determine the values of a and b in the equation 1/3 × 1/4 = a/b. To find the values of a and b, we simply multiply the numerators (top numbers) of the fractions together to find the new numerator, and multiply the denominators (bottom numbers) together to find the new denominator.
Multiplying the numerators 1 × 1 gives us 1, and multiplying the denominators 3 × 4 gives us 12. Therefore, the product of the two fractions is 1/12, making the values of a and b equal to 1 and 12, respectively.
Let's look at an application with proportions:
If the scale dimension is 4, then to find the actual dimension using the proportion 1:2=4:x, we solve for x. By cross-multiplication, we get 1×x=2×4, which simplifies to x=8. Thus, the actual dimension corresponding to the scale dimension is 8.