Write an expression that represents 72 divided by n plus 4
The Correct Answer and Explanation is:
Expression:72n+4\frac{72}{n + 4}n+472
Explanation
The expression 72n+4\frac{72}{n + 4}n+472 represents the mathematical operation of dividing the number 72 by the sum of a variable nnn and the constant 4. Here’s how this works step by step:
In mathematics, a fraction like ab\frac{a}{b}ba means “a divided by b.” So in our case, the numerator (top part) is 72, and the denominator (bottom part) is n+4n + 4n+4. This means we are not simply dividing 72 by nnn, but rather by the entire expression n+4n + 4n+4. It’s important to include the parentheses around n+4n + 4n+4 to show that the entire sum is in the denominator.
If you were to write this expression without using a fraction, it could also be written as:
scssCopyEdit72 ÷ (n + 4)
This means that before performing the division, you must first add 4 to nnn, and then divide 72 by the result. For example, if n=2n = 2n=2, then n+4=6n + 4 = 6n+4=6, and the expression becomes 726\frac{72}{6}672, which equals 12. This illustrates the importance of order of operations in mathematics. According to these rules, parentheses must be evaluated first before division.
A common mistake is to forget the parentheses and misinterpret the expression as 72n+4\frac{72}{n} + 4n72+4, which changes the meaning entirely. In that version, you would first divide 72 by nnn, then add 4 afterward. But our original expression keeps the addition inside the denominator, so it all affects the divisor before the division happens.
This expression is useful in many real-world contexts, such as calculating average rates, dividing resources among a group, or solving algebraic problems. Understanding how to correctly interpret and manipulate algebraic expressions like this helps build a solid foundation for more advanced math.