Final answer:
To solve the proportion (4/12) = (a/27), cross-multiply to get 4 \(\times\) 27 = a \(\times\) 12, which simplifies to 108 = 12a. Dividing both sides by 12 yields a = 9.
Step-by-step explanation:
To find the value of a that makes the proportion (4/12) = (a/27) true, we need to apply cross-multiplication. Cross-multiplication is when we multiply the numerator of one fraction by the denominator of the other fraction and set the products equal to each other. Following this method:
Multiply 4 by 27 to get one product.
Multiply a by 12 to get the second product.
After cross-multiplication, our equation will look like this: 4 \(\times\) 27 = a \(\times\) 12.
Calculating the left side, we have 108 = a \(\times\) 12. To solve for a, divide both sides of the equation by 12, which gives us a = 108 / 12. After dividing, we find that a equals 9.
Therefore, the value that makes the proportion true is a = 9.