Answer:
To find the number that completes the pattern, we need to identify the algebraic equation that applies to both rows.
Given rows:
1. 9 1 6 4
2. 4 5 7 2
Let's examine possible equations:
### Row 1: 9 1 6 4
### Row 2: 4 5 7 2
The pattern should fit the format \( f(a, b, c) = d \), where \(a, b, c, d\) are the numbers in the row.
One possible way to approach this is to consider an equation involving basic arithmetic operations.
Let's look at possible equations for each row:
#### Row 1:
9 (a), 1 (b), 6 (c), 4 (d)
\[ f(a, b, c) = d \]
\[ 9 - 1 - 6 = 2 \neq 4 \]
\[ 9 / 1 + 6 = 15 \neq 4 \]
\[ 9 - 1 * 6 = 3 \neq 4 \]
\[ (9 - 1) / 2 = 4 \] (This fits, let's check for Row 2)
#### Row 2:
4 (a), 5 (b), 7 (c), 2 (d)
\[ f(a, b, c) = d \]
\[ (4 - 5) / 7 = -1/7 \neq 2 \]
The pattern does not hold. Let's reconsider.
Another possible pattern is \(a - b - c = d\):
#### Row 1:
\[ 9 - 1 - 6 = 2 \neq 4 \]
\[ 9 - (1 + 6) = 2 \neq 4 \]
Let's try another operation.
Another equation could be \(a \times b + c = d\):
#### Row 1:
\[ 9 \times 1 + 6 = 15 \neq 4 \]
\[ 9 + 1 \times 6 = 15 \neq 4 \]
Let's try another.
#### Checking addition and subtraction sequences:
Considering \( a - b = d - c \):
For Row 1:
\[ 9 - 1 = 8 \]
\[ 4 - 6 = -2 \] (Doesn't match)
For Row 2:
\[ 4 - 5 = -1 \]
\[ 2 - 7 = -5 \] (Doesn't match)
If we consider \( a + b - c = d \):
For Row 1:
\[ 9 + 1 - 6 = 4 \] (Matches)
For Row 2:
\[ 4 + 5 - 7 = 2 \] (Matches)
Thus, the pattern might be \( a + b - c = d \).
#### Now applying the same to find the missing number:
### Row 3: 7 8 ? 13
Given \( 7 + 8 - ? = 13 \):
\[ 7 + 8 - ? = 13 \]
\[ 15 - ? = 13 \]
\[ ? = 15 - 13 \]
\[ ? = 2 \]
Therefore, the number that completes the pattern is **2**.
