To translate the phrase "Four times a number is thirty-two" into an equation, we can define the unknown number as \( m \). The phrase can be represented as:
\[ 4m = 32 \]
Now, let's solve the equation:
- Divide both sides of the equation by 4 to isolate \( m \): \[ m = \frac{32}{4} \]
- This simplifies to: \[ m = 8 \]
Next, we check the solution by substituting \( m = 8 \) back into the original context of the problem:
Four times the number \( 8 \): \[ 4 \times 8 = 32 \]
Since this statement is true, the solution is verified.
Now, let's evaluate the statements given:
- This is a multiplication problem. - True (because it involves multiplying a number by 4).
- To solve the equation, multiply both sides by 4. - False (we actually divide both sides by 4).
- The correct equation is \( m4=32 \). - False (the correct equation should be written as \( 4m = 32 \)).
- The correct equation is \( m \) over 4 is equal to 32. - False (this would imply \(\frac{m}{4} = 32\), which is incorrect).
- This is a division problem. - False (the setup involves multiplication; however, the method of solving involves division).
- To solve the equation, divide both sides by 4. - True (we divide by 4 to isolate \( m \)).
- The correct equation is \( 4m=32 \). - True (this is the correct representation of the problem).
So, the three true statements are:
- This is a multiplication problem.
- To solve the equation, divide both sides by 4.
- The correct equation is \( 4m=32 \).