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What would we do to both sides to solve this equation for m?

1/4m = 2 1/4

5 answers

To solve the equation \( \frac{1}{4}m = 2 \frac{1}{4} \), we can follow these steps:

  1. First, convert the mixed number \( 2 \frac{1}{4} \) into an improper fraction.

    • To do this, multiply the whole number (2) by the denominator (4) and add the numerator (1): \[ 2 \times 4 + 1 = 8 + 1 = 9 \]
    • Thus, \( 2 \frac{1}{4} = \frac{9}{4} \).

  2. Now, we rewrite the equation with the improper fraction: \[ \frac{1}{4}m = \frac{9}{4} \]

  3. To isolate \( m \), multiply both sides of the equation by 4: \[ 4 \cdot \frac{1}{4}m = 4 \cdot \frac{9}{4} \]

  4. Simplify both sides:

    • On the left side: \[ m = \frac{9}{1} = 9 \]

So, the solution to the equation is: \[ m = 9 \]

So, subtract 1/4 from both sides?

It seems like there might be a misunderstanding regarding the steps needed to solve the equation. To clarify, here’s the correct way to solve the equation \( \frac{1}{4}m = 2 \frac{1}{4} \) without initially thinking of subtraction:

  1. Convert the mixed number: As previously mentioned, convert \( 2 \frac{1}{4} \) to an improper fraction: \[ 2 \frac{1}{4} = \frac{9}{4} \]

  2. Set up the equation: Now the equation is: \[ \frac{1}{4}m = \frac{9}{4} \]

  3. Multiply both sides by 4: Instead of subtracting from both sides, to isolate \( m \), multiply both sides of the equation by 4: \[ 4 \cdot \frac{1}{4}m = 4 \cdot \frac{9}{4} \]

  4. Simplify: This results in: \[ m = 9 \]

So, subtracting \( \frac{1}{4} \) from both sides is not the correct approach in this case. Instead, to isolate \( m \), you multiply both sides by 4. The final answer remains \( m = 9 \). Is there anything else you would like to clarify or ask about?

So, multiply by 1/4 on both sides?

To isolate \( m \) in the equation \( \frac{1}{4}m = 2 \frac{1}{4} \), you would not multiply by \( \frac{1}{4} \) on both sides, because that would make the equation more complicated. Instead, to eliminate \( \frac{1}{4} \) from the left side, you should multiply by the reciprocal of \( \frac{1}{4} \), which is \( 4 \).

Here's a clearer breakdown:

  1. Starting Equation: \[ \frac{1}{4}m = 2 \frac{1}{4} \]

  2. Convert the Mixed Number: Convert \( 2 \frac{1}{4} \) into an improper fraction: \[ 2 \frac{1}{4} = \frac{9}{4} \] So the equation becomes: \[ \frac{1}{4}m = \frac{9}{4} \]

  3. Multiply by the Reciprocal: To eliminate \( \frac{1}{4} \), multiply both sides by \( 4 \): \[ 4 \cdot \frac{1}{4}m = 4 \cdot \frac{9}{4} \]

  4. Simplify: This results in: \[ m = 9 \]

So, to clarify: instead of multiplying by \( \frac{1}{4} \), multiplying by \( 4 \) (the reciprocal of \( \frac{1}{4} \)) is the appropriate step to solve for \( m \). Thus, the final result is \( m = 9 \). Let me know if you need further assistance!