1-4: Translating Words and Sentences into Symbols
I can translate phrases into variable expressions.
Write down all the words you can think of that mean each operation.
Addition
Subtraction
Multiplication
Division
Phrase
Translation
Addition
The sum of 8 and x.
A number increased by 7.
5 more than a number.
8+x
n+7
n+5
Subtraction
The difference between a number and 4.
A number decreased by 8.
5 less than a number.
6 minus a number.
n–4
n–8
n–5
6–n
The product of 5 and a number.
Seven times a number.
One third of a number.
5 * n or 5n
7 * n or 7n
𝟏
n
𝟑
The quotient of a number and 8.
A number divided by 10.
𝒏
𝟖
𝒏
𝟏𝟎
Multiplication
Division
CAUTION: Be careful with phrases involving subtraction.
The phrase “5 less than x” is translated to x – 5, not 5 – x.
Example 1) Translate each phrase into a variable expression.
a) 3 less than half of x
½x–3
b) Half the difference between x and 3
½ (x – 3)
A = lw
P = 2l + 2w
D = rt
C = np
Here are four Formulas commonly used in Algebra:
Area of a rectangle equals the length of the rectangle times the width of the rectangle.
Perimeter of the rectangle equals two times the length plus two times the width.
Distance traveled equals the rate times the time traveled.
Cost equals the number of items times the price per item.
Example 2) Find the area and perimeter of a rectangle with length 10 and width w.
Area: 10w
Perimeter: 2(10) + 2w = 20 + 2w
Example 3) Twice the sum of a number and four is ten.
2 ( n + 4) = 10
2n + 8 = 10
n=1
Example 4) When a number is multiplied by four, the result is decreased by 6, the final
result is 10.
4n – 6 = 10
4n = 16
n=4
Guided Practice
Translate each phrase into a variable expression. Use n for the variable.
1. Eight times a number.
8n
2. The product of three and a number.
3n
3. Five more than a number.
n+5
4. One fourth of a number.
1/4n
5. A number decreased by four.
n–4
6. A number divided by five.
n/5
7. Nine less than half a number.
½n-9
8. Nine more than twice a number.
2n + 9
Complete each statement with a variable expression.
9. A rectangle has width 6 units and length x units. The area is ___6x__ square units.
10. You travel for (t – 2) hours at 75 km/h. You traveled __75 (t – 2) _______ km.
11. Al earns (p + 3) dollars per hour. In 8 hours, he earns ____8 ( p + 3)____ dollars.
12. The Golden Gate Bridge was built n years ago. Three years from now it will be
standing __n + 3____ years.
13. Nine years from now Fenway Park will be g years old. It is now __g – 9 _ years old.
14. Workers on an assembly like produce (x + 10) cars each day. In 5 days they
produce ___5 (x + 10)____ cars.
Translate each sentence into an equation.
15. One third a number is seven. 1/3 n = 7
16. Six less than a number is twelve. n - 6 = 12
17. Half of the sum of three and a number is four. ½ (3 + n) = 4
18. Four less than twice a number is nine. 2n – 4 = 9
19. Twice a number is 18 more than five times a number. 2n = 18 + 5n
20. A number is 9 more than one third of itself. n = 9 + 1/3 n
21. Eleven less than twice n is seven more than n. 2n – 11 = 7 + n
22. Ten times x is twice the sum of x and eight.
10x = 2(x + 8)