Write an expression that is equivalent to 1/2a – 4
The correct answer and explanation is:
Equivalent Expression for 12a−4\frac{1}{2}a – 4
Correct Answer:
An equivalent expression is: a2−4\frac{a}{2} – 4
Explanation (300 words):
The expression given is: 12a−4\frac{1}{2}a – 4
This expression includes two terms:
- 12a\frac{1}{2}a – a multiplication term involving a fraction and a variable.
- −4-4 – a constant being subtracted.
Understanding 12a\frac{1}{2}a:
This is the same as saying “one-half of aa”, or aa divided by 2. In algebra, multiplication is commutative, which means the order of multiplication does not matter. So: 12a=a⋅12=a2\frac{1}{2}a = a \cdot \frac{1}{2} = \frac{a}{2}
Thus, the term 12a\frac{1}{2}a is equivalent to a2\frac{a}{2}.
Full Expression:
So now, replacing 12a\frac{1}{2}a with its equivalent form: 12a−4=a2−4\frac{1}{2}a – 4 = \frac{a}{2} – 4
Both expressions mean exactly the same thing—they represent a value that is half of aa, minus 4.
Why Write It as a2\frac{a}{2} Instead?
Sometimes a2\frac{a}{2} is preferred over 12a\frac{1}{2}a because it clearly shows that the variable aa is in the numerator, making it visually easier to see that the whole variable is being divided by 2.
This form is especially useful in more complex algebraic expressions or equations, where understanding the placement of variables and operations helps simplify or solve problems more efficiently.
Summary:
- 12a\frac{1}{2}a and a2\frac{a}{2} are the same.
- So the equivalent expression to 12a−4\frac{1}{2}a – 4 is a2−4\frac{a}{2} – 4.