Question

algebra 1 | translating words into symbols
translate each phrase into a variable expression.

1. 5 more than a number
2. six times a number
3. a number decreased by 9
4. the sum of 7 and a number
5. one third of a number
6. a number increased by 12
7. the quotient of 20 and k
8. a number divided by 5
9. the product of 15 and z
10. the difference between a number and 4
11. 8 more than three times x
12. 2 less than four times a number
13. 3 less than a quarter of m
14. 9 more than one half of a number
15. 7 plus the quotient of a number and 3
16. 5 times the sum of a number and 4

Explanation:

Step1: Define variable for unknown

Let $n$ represent the unknown number (unless a specific variable is given).

Step2: Translate phrase 1

"5 more than a number" means add 5 to $n$:
$n + 5$

Step3: Translate phrase 2

"Six times a number" means multiply 6 and $n$:
$6n$

Step4: Translate phrase 3

"A number decreased by 9" means subtract 9 from $n$:
$n - 9$

Step5: Translate phrase 4

"The sum of 7 and a number" means add 7 and $n$:
$7 + n$

Step6: Translate phrase 5

"One third of a number" means multiply $n$ by $\frac{1}{3}$:
$\frac{1}{3}n$

Step7: Translate phrase 6

"A number increased by 12" means add 12 to $n$:
$n + 12$

Step8: Translate phrase 7

"The quotient of 20 and $k$" means divide 20 by $k$:
$\frac{20}{k}$

Step9: Translate phrase 8

"A number divided by 5" means divide $n$ by 5:
$\frac{n}{5}$

Step10: Translate phrase 9

"The product of 15 and $z$" means multiply 15 and $z$:
$15z$

Step11: Translate phrase 10

"The difference between a number and 4" means subtract 4 from $n$:
$n - 4$

Step12: Translate phrase 11

"8 more than three times $x$" means add 8 to $3x$:
$3x + 8$

Step13: Translate phrase 12

"2 less than four times a number" means subtract 2 from $4n$:
$4n - 2$

Step14: Translate phrase 13

"3 less than a quarter of $m$" means subtract 3 from $\frac{1}{4}m$:
$\frac{1}{4}m - 3$

Step15: Translate phrase 14

"9 more than one half of a number" means add 9 to $\frac{1}{2}n$:
$\frac{1}{2}n + 9$

Step16: Translate phrase 15

"7 plus the quotient of a number and 3" means add 7 to $\frac{n}{3}$:
$7 + \frac{n}{3}$

Step17: Translate phrase 16

"5 times the sum of a number and 4" means multiply 5 by $(n+4)$:
$5(n + 4)$

Answer:

1. $n + 5$
2. $6n$
3. $n - 9$
4. $7 + n$
5. $\frac{1}{3}n$
6. $n + 12$
7. $\frac{20}{k}$
8. $\frac{n}{5}$
9. $15z$
10. $n - 4$
11. $3x + 8$
12. $4n - 2$
13. $\frac{1}{4}m - 3$
14. $\frac{1}{2}n + 9$
15. $7 + \frac{n}{3}$
16. $5(n + 4)$