Question

algebra i | translating words into symbols
mathforlove.com
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

page 1 of 6

Explanation:

Step1: Define variable for unknowns

Let \( n \) represent "a number" where not specified.

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. \( 5(n + 4) \)