Calculating half of a mixed number like 1 3⁄4 might seem tricky at first, but with a bit of breakdown, it becomes a straightforward process. Let’s walk through the steps to find the answer efficiently.
Step 1: Convert the Mixed Number to an Improper Fraction
A mixed number consists of a whole number and a fraction. To convert 1 3⁄4 into an improper fraction:
[ 1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} ]
Step 2: Calculate Half of the Improper Fraction
Finding half of a fraction involves multiplying it by 1⁄2. So, for 7⁄4:
[ \frac{1}{2} \times \frac{7}{4} = \frac{1 \times 7}{2 \times 4} = \frac{7}{8} ]
Step 3: Simplify (if necessary)
In this case, 7⁄8 is already in its simplest form.
Final Answer:
Half of 1 3⁄4 is 7⁄8.
Key Takeaway: To find half of a mixed number, first convert it to an improper fraction, then multiply by 1/2. The result for 1 3/4 is 7/8.
Why This Works
Breaking down the mixed number into an improper fraction makes it easier to perform operations like multiplication. Multiplying by 1⁄2 is the same as dividing by 2, which directly gives you half of the original value.
Practical Application
This method is useful in cooking, construction, or any scenario where you need to divide measurements or quantities equally. For example, if a recipe calls for 1 3⁄4 cups of flour and you only need half, you’d use 7⁄8 cups.
Can I convert the result back to a mixed number?
+Since 7/8 is less than 1, it cannot be expressed as a mixed number. It remains as the proper fraction 7/8.
What if I need to find a quarter of 1 3/4 instead?
+Multiply 7/4 by 1/4:
\[
\frac{1}{4} \times \frac{7}{4} = \frac{7}{16}
\]
So, a quarter of 1 3/4 is 7/16.
How does this apply to real-world scenarios?
+This calculation is useful in situations like dividing ingredients, sharing resources, or measuring materials where precision is important.
By following these steps, you can confidently calculate half of any mixed number, ensuring accuracy and efficiency in your mathematical tasks.
