Use number sense about decimal placement to complete the equation. Numbers may be used once or more than once.

Equation 1: 74.36 ÷ ◻︎ = 57.2
Equation 2: 743.6 ÷ ◻︎ = 5720
Equation 3: 7.436 ÷ ◻︎ = 0.572
Equation 4: 0.7436 ÷ ◻︎ = 5.72

A) 0.13
B) 1.3
C) 13

1 answer

To complete the equations correctly, we can examine the effect of decimal placement on the numbers involved.

Equation 1:

74.36 ÷ ◻︎ = 57.2
We can rewrite this as:
\( 74.36 = 57.2 \times ◻︎ \)
To find ◻︎, we can rearrange the equation:
\( ◻︎ = \frac{74.36}{57.2} \)
Calculating the division:
\( ◻︎ = 1.3 \)

Equation 2:

743.6 ÷ ◻︎ = 5720
Rearranging gives:
\( ◻︎ = \frac{743.6}{5720} \)
Calculating the division:
\( ◻︎ ≈ 0.13 \)

Equation 3:

7.436 ÷ ◻︎ = 0.572
Rearranging gives:
\( ◻︎ = \frac{7.436}{0.572} \)
Calculating the division:
\( ◻︎ ≈ 13 \)

Equation 4:

0.7436 ÷ ◻︎ = 5.72
Rearranging gives:
\( ◻︎ = \frac{0.7436}{5.72} \)
Calculating the division:
\( ◻︎ ≈ 0.13 \)

We have derived potential values for ◻︎ in each equation:

  1. For Equation 1: ◻︎ = 1.3
  2. For Equation 2: ◻︎ = 0.13
  3. For Equation 3: ◻︎ = 13
  4. For Equation 4: ◻︎ = 0.13

Conclusions:

  • The values for ◻︎ are 1.3 for Equation 1, 0.13 for Equation 2 and Equation 4, and 13 for Equation 3.
  • The options given are:
    • A) 0.13
    • B) 1.3
    • C) 13

Each answer corresponds to at least one of the equations:

  • Use A (0.13) for Equations 2 and 4.
  • Use B (1.3) for Equation 1.
  • Use C (13) for Equation 3.

Thus, all three options A, B, and C correctly fill other equations based on their placements.