Which is equivalent to 16 3/4x ?
The correct answer and explanation is:
Correct Answer:
The expression 16 3/4x is equivalent to:
(67/4)x
300-Word Explanation:
To find an equivalent expression for 16 3/4x, we must first convert the mixed number (16 3/4) into an improper fraction, and then multiply it by x.
Step 1: Convert the Mixed Number to an Improper Fraction
A mixed number like 16 3/4 includes a whole number (16) and a fraction (3/4). To convert it into an improper fraction: 1634=(16×4+3)/4=64+34=67416 \frac{3}{4} = \left(16 \times 4 + 3\right) / 4 = \frac{64 + 3}{4} = \frac{67}{4}
Step 2: Multiply by x
Now that we have the improper fraction: 1634x=674×16 \frac{3}{4}x = \frac{67}{4}x
So, 16 3/4x is equivalent to (67/4)x.
Why This Matters:
Converting mixed numbers to improper fractions is important in algebra because it simplifies the process of combining like terms, solving equations, or performing other operations. For example, it is much easier to handle fractions like 67/4 in equations than dealing with a mixed number.
Real-World Example:
Imagine you work 16 3/4 hours and earn x dollars per hour. To calculate your earnings, you’d multiply the hours by x: Earnings=1634×x=674x\text{Earnings} = 16 \frac{3}{4} \times x = \frac{67}{4}x
This makes it clearer how much you earned.
Conclusion:
Thus, 16 3/4x is best written as (67/4)x for clarity and ease of calculation. Always convert mixed numbers into improper fractions before multiplying in algebraic expressions.