Question

What is the missing number in this simplified exponential expression: 7?÷75=712
7
?
÷
7
5
=
7
12
?(1 point)

Answer 1

To solve the equation given in the format \( \frac{7?}{75} = \frac{7}{12} \), we can set \( 7? \) as \( 7x \), where \( x \) is the missing digit we need to find.

Starting from the equation:

\[
\frac{7x}{75} = \frac{7}{12}
\]

We can cross multiply to eliminate the fractions:

\[
7x \cdot 12 = 7 \cdot 75
\]

This simplifies to:

\[
84x = 525
\]

Now, we can solve for \( x \):

\[
x = \frac{525}{84}
\]

Calculating the right-hand side:

\[
x = 6.25
\]

Since \( x \) must be a single digit (as it's part of the integer \( 7? \)), this doesn't work. Let's approach it differently by simplifying our equation step by step correctly.

Let's isolate \( x \):

1. Start with the equation:
\[
7? = \frac{7}{12} \cdot 75
\]

2. Simplifying the right side:
\[
75 ÷ 12 = 6.25 \quad \text{(but we don't need to divide, multiply instead)}
\]
\[
7 × 75 = 525
\]

Thus, we find that \( 7? = 525 ÷ 12 \)

This means we need to further analyze:

The number on the left is actually not clear; let’s focus again:

Given \( \frac{7x}{75} = \frac{7}{12} \), canceling the 7:

\[
\frac{x}{75} = \frac{1}{12}
\]

Cross-multiplying gives us:

\[
12x = 75
\]

Dividing both sides by 12:

\[
x = \frac{75}{12}
\]

Calculating gives us \( x = 6.25\), not valid again for digit 0-9.

Thus we have stayed at:

To find \( ?: 7x = 525 \)

Where \( ? = 6 \)

Finally,

\[
The missing number ? is 6.
\]