what is half of 7 3/4
The correct answer and explanation is:
Correct Answer:
Half of 7 3/4 is 3 7/8.
Step-by-Step Explanation (with 300-word explanation):
To find half of 7 3/4, we need to divide the number by 2. First, convert the mixed number into an improper fraction:
Step 1: Convert 7 3/4 to an improper fraction.
A mixed number combines a whole number and a fraction. To convert it: 734=(7×4)+34=28+34=3147 \frac{3}{4} = \frac{(7 \times 4) + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4}
Step 2: Divide by 2.
Dividing by 2 is the same as multiplying by 1/2: 314÷2=314×12=31×14×2=318\frac{31}{4} \div 2 = \frac{31}{4} \times \frac{1}{2} = \frac{31 \times 1}{4 \times 2} = \frac{31}{8}
Step 3: Convert the improper fraction back to a mixed number. 318=3 remainder 7⇒378\frac{31}{8} = 3 \text{ remainder } 7 \Rightarrow 3 \frac{7}{8}
So, half of 7 3/4 is 3 7/8.
Why This Method Works:
Dividing mixed numbers like 7 3/4 requires accuracy. Converting to an improper fraction simplifies the operation. Once it’s in that form, multiplication or division becomes a matter of multiplying numerators and denominators.
Why divide by 2? Taking “half” means you’re equally splitting a quantity into two parts. So if you think of 7 3/4 as a total quantity (like 7.75 gallons of water), dividing by 2 tells you how much is in each half.
Lastly, converting back to a mixed number helps visualize the answer more intuitively. Most people find “3 7/8” easier to understand in practical terms than “31/8.”
This approach works with any fraction or mixed number and is a fundamental skill in arithmetic.