Evaluate the expression `6 1/4 xx 0.25 + 0.75 - 0.3125`

Options

A. `5.9375`
B. `4.2968`
C. `2.1250`
D. 2

Answer

To evaluate the expression \( 6 \frac{1}{4} \times 0.25 + 0.75 - 0.3125 \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 6 \frac{1}{4} \) can be converted to an improper fraction:
\[ 6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

### Step 2: Convert \( 0.25 \) to a fraction
The decimal \( 0.25 \) can be expressed as:
\[ 0.25 = \frac{25}{100} = \frac{1}{4} \]

**Hint:** To convert a decimal to a fraction, write it over its place value (e.g., 0.25 is 25 over 100) and simplify if possible.

### Step 3: Multiply the fractions
Now we can multiply the fractions:
\[ \frac{25}{4} \times \frac{1}{4} = \frac{25 \times 1}{4 \times 4} = \frac{25}{16} \]

**Hint:** When multiplying fractions, multiply the numerators together and the denominators together.

### Step 4: Convert \( 0.75 \) to a fraction
The decimal \( 0.75 \) can be expressed as:
\[ 0.75 = \frac{75}{100} = \frac{3}{4} \]

**Hint:** Similar to step 2, convert the decimal to a fraction by writing it over its place value and simplifying.

### Step 5: Convert \( 0.3125 \) to a fraction
The decimal \( 0.3125 \) can be expressed as:
\[ 0.3125 = \frac{3125}{10000} \]
This can be simplified to:
\[ 0.3125 = \frac{5}{16} \]

**Hint:** To convert a decimal with four decimal places to a fraction, write it over \( 10^4 \) (which is 10000) and simplify.

### Step 6: Combine the expression
Now we can rewrite the expression:
\[ \frac{25}{16} + \frac{3}{4} - \frac{5}{16} \]

### Step 7: Find a common denominator
The common denominator for \( 16 \) and \( 4 \) is \( 16 \). Convert \( \frac{3}{4} \) to have a denominator of \( 16 \):
\[ \frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \]

### Step 8: Combine the fractions
Now we can combine the fractions:
\[ \frac{25}{16} + \frac{12}{16} - \frac{5}{16} = \frac{25 + 12 - 5}{16} = \frac{32}{16} \]

### Step 9: Simplify the result
Now simplify \( \frac{32}{16} \):
\[ \frac{32}{16} = 2 \]

### Final Answer
Thus, the value of the expression \( 6 \frac{1}{4} \times 0.25 + 0.75 - 0.3125 \) is \( 2 \).

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