Question

for problems 6–19, write an algebraic expression that represents the description. all variables are nonzero numbers.

1. triple the value of a number n
2. the quotient of t and 8.2
3. twice as much as n
4. a number x divided by $2\frac{1}{2}$
5. a number p squared
6. $\frac{1}{4}$ of f
7. a number m split evenly into 3 groups
8. one - half of the product of 2 and a number g
9. the quotient of r cubed and 4
10. the product of 5 and w divided by 10
11. 14 subtracted from the product of 5 and d
12. a number a divided by the sum of b and 2
13. 18 less than the product of 4 and b
14. y plus the difference of d and 6

for problems 24–27, evaluate

1. $\frac{ab}{2}$
2. $\frac{b^3}{25}$

remember
for problems 28–

1. $47.25\times0.6$

Explanation:

Let's solve some of these algebraic expression problems. We'll take problem 6 first:

Problem 6: Triple the value of a number \( n \)

Step 1: Understand "triple" means multiply by 3.

To triple a number \( n \), we multiply \( n \) by 3.
So the algebraic expression is \( 3 \times n \), which can be written as \( 3n \).

Step 1: Recall that "quotient" means division.

The quotient of \( t \) and \( 8.2 \) means \( t \) divided by \( 8.2 \).
So the algebraic expression is \( \frac{t}{8.2} \).

Step 1: "Twice" means multiply by 2.

To find twice \( n \), we multiply \( n \) by 2.
So the algebraic expression is \( 2 \times n \), or \( 2n \).

Answer:

\( 3n \)

Problem 7: The quotient of \( t \) and \( 8.2 \)