Add the fractions `5 3/8` and `5/16`

Options

A. `5 11/16`
B. `5 9/16`
C. `4 11/16`
D. `5 15/16`

Answer

To solve the problem of adding the fractions \(5 \frac{3}{8}\) and \(\frac{5}{16}\), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(5 \frac{3}{8}\) can be converted to an improper fraction. To do this, multiply the whole number (5) by the denominator (8) and add the numerator (3).

\[ 5 \frac{3}{8} = \frac{(5 \times 8) + 3}{8} = \frac{40 + 3}{8} = \frac{43}{8} \]

### Step 2: Write the second fraction
The second fraction is already given as \(\frac{5}{16}\).

### Step 3: Find a common denominator
To add the fractions \(\frac{43}{8}\) and \(\frac{5}{16}\), we need a common denominator. The least common multiple (LCM) of 8 and 16 is 16.

### Step 4: Convert the first fraction to the common denominator
We need to convert \(\frac{43}{8}\) to have a denominator of 16. To do this, multiply both the numerator and denominator by 2:

\[ \frac{43}{8} = \frac{43 \times 2}{8 \times 2} = \frac{86}{16} \]

### Step 5: Add the fractions
Now that both fractions have the same denominator, we can add them:

\[ \frac{86}{16} + \frac{5}{16} = \frac{86 + 5}{16} = \frac{91}{16} \]

### Step 6: Simplify if necessary
The fraction \(\frac{91}{16}\) is already in its simplest form, so we can leave it as is.

### Final Answer
The sum of \(5 \frac{3}{8}\) and \(\frac{5}{16}\) is \(\frac{91}{16}\).

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