Final answer:
The correct number to replace the blank in the fraction equation (45/60 = 15/blank) is 20, as both sides simplify to the fraction 3/4.
Step-by-step explanation:
To replace the blank in ( frac{45}{60} = frac{15}{{blank}} ), we need to simplify the fraction on the left to its lowest terms to find the correct number that will replace the blank. Both 45 and 60 can be divided by 15. Dividing the numerator (45) by 15 gives us 3, and dividing the denominator (60) by 15 gives us 4. Therefore, the fraction frac{45}{60} simplifies to frac{3}{4}.
Now, we can observe that 15 (the numerator on the right side of the equation) must be multiplied by the same number to give us the simplified numerator of 3. To find this number, we divide 3 by 15, which equals 1/5. So, to keep the proportions the same, we multiply the denominator (blank) by 1/5 too. Hence, the correct number to fill in the blank is 4 * 5 = 20.
So the correct answer to fill in the blank is:
( frac{45}{60} = frac{15}{20} )