How many one-fourths need to be added to `2 1/4` to make 5?

Options

A. 11
B. 18
C. 9
D. 2

Answer

To solve the problem of how many one-fourths need to be added to \(2 \frac{1}{4}\) to make 5, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \(2 \frac{1}{4}\) can be converted to an improper fraction.

\[ 2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]

### Step 2: Set up the equation.
Let \(x\) be the number of one-fourths we need to add. Since one-fourth can be represented as \(\frac{1}{4}\), we can express the equation as:

\[ x \cdot \frac{1}{4} + \frac{9}{4} = 5 \]

### Step 3: Convert 5 into a fraction with a denominator of 4.
To make calculations easier, we convert 5 into a fraction with a denominator of 4:

\[ 5 = \frac{5 \times 4}{1 \times 4} = \frac{20}{4} \]

### Step 4: Substitute and simplify the equation.
Now, substitute \(\frac{20}{4}\) into the equation:

\[ \frac{x}{4} + \frac{9}{4} = \frac{20}{4} \]

### Step 5: Combine the fractions.
Since all fractions have the same denominator, we can combine them:

\[ \frac{x + 9}{4} = \frac{20}{4} \]

### Step 6: Eliminate the denominator.
To eliminate the denominator, multiply both sides of the equation by 4:

\[ x + 9 = 20 \]

### Step 7: Solve for \(x\).
Now, subtract 9 from both sides to find \(x\):

\[ x = 20 - 9 = 11 \]

### Conclusion:
Thus, the number of one-fourths that need to be added to \(2 \frac{1}{4}\) to make 5 is \(11\).

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