Add the missing terms so that these quantities are in proportion.

_:11:_and 11:121:11. And this one

26:52:13 and _: _:1

For the first one, divide each term by 11.

For the second one, divide each term by 13.

To find the missing terms in the given proportions, we need to understand the concept of proportionality. In a proportion, the ratio of the corresponding terms in two sets of numbers is equal.

Let's begin with the first proportion, _:11:_ and 11:121:11. Here, we need to find the missing terms indicated by "_".

To determine the missing terms, we can set up an equation using the ratio concept. The ratio of the first set is _:11:_ which means the first term is unknown, the second term is 11, and the third term is also unknown. Similarly, the ratio of the second set is 11:121:11, indicating that the first term is 11, the second term is 121, and the third term is 11.

Based on the concept of proportionality, we can set up the equation:

Unknown term / 11 = 11 / Unknown term

To solve for the unknown terms, we can cross-multiply:

Unknown term * Unknown term = 11 * 11
Unknown term² = 121

Taking the square root of both sides:

Unknown term = √121
Unknown term = 11

Therefore, the missing terms are 11:11:11.

Now, let's move on to the second proportion, 26:52:13 and _: _:1. Here, we need to find the missing terms indicated by "_".

Again, we can set up an equation using the ratio concept. The first set has a ratio of 26:52:13, which means the first term is 26, the second term is 52, and the third term is 13. For the second set, the ratio is _: _:1, where the first two terms are unknown, and the last term is 1.

Using the concept of proportionality, we can set up the equation:

Unknown term / Unknown term = 26 / 52

Cross-multiplying:

Unknown term * (Unknown term) = 26 * 52
Unknown term² = 1352

Taking the square root of both sides:

Unknown term ≈ √1352
Unknown term ≈ 36.8 (rounded to one decimal place)

Therefore, the missing terms are approximately 36.8:36.8:1.