Question

What would we do to both sides to solve this equation for m?
1/4m = 2 1/4

Answer 1

So, subtract 1/4 from both sides?

Answer 2

So, multiply by 1/4 on both sides?

Answer 3

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:
\[
m = 9
\]

Answer 4

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?

Answer 5

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!