To find the missing number in the pattern [tex]\( (12 \text { [3] 4) (20 [5] 10) } \)[/tex], we need to analyze the given relationships among the numbers.
### Step-by-step Analysis:
#### Observing [tex]\( 12 \text { [3] 4 } \)[/tex]:
1. Here, we have the numbers 12, 3, and 4.
2. Notice that if we divide 12 by 4, we get 3:
[tex]\[
\frac{12}{4} = 3
\][/tex]
Thus, 3 fits perfectly in the brackets from this division operation.
#### Observing [tex]\( 20 \text { [5] 10 } \)[/tex]:
1. Here, we have the numbers 20, 5, and 10.
2. When we divide 20 by 4, we get 5:
[tex]\[
\frac{20}{4} = 5
\][/tex]
This matches the pattern consistent with the first set of numbers.
### Applying the Pattern to the New Set of Numbers:
Given the pattern of dividing the first number by the third number to fit the number in the brackets, we express the relationship between these numbers as follows:
[tex]\[
\frac{A}{C} = B
\][/tex]
### Finding a Missing Number:
To consider another term in such a pattern that fits the similar consistent behavior:
Let's reuse similar variable structure:
[tex]\[
\frac{12}{4} = 3 \quad -> Verified \\
\frac{20}{4} = 5 \quad -> Verified
\][/tex]
To find another similar number set (a, b, c) that fits a plausible structure. Choose a straightforward numbers relationship such as `10`, we reflect:
#### Working Another Example:
Here consistency demands:
[tex]\[
\frac{p }{4 } \quad\Rightarrow p = (4 * 4.1666)
\][/tex]
Thus, the method verifies similarity:
[tex]\(
original number p = 16.666667 \implies \frac{16.7}{ 4 }
\)[/tex]
Finally, we'd have the consistent pair:
(3.0, 5.0, 16.6667)
So, based on this pattern, a rightly identified missing number to fit pairs relations:
[tex]\[ ( Correctly computed 16.666... \][/tex]
Thus represent result span :)
