Download TC Worksheet #1

Translating Words into Math
The four basic operations used to combine numbers can be expressed in various ways. Below
are some equivalent words can be useful in translating the written word into mathematical
symbols:
Addition:
Synonym
more than
sum
plus
increased by
Example
3 more than 5
the sum of 2 and 6
6 plus 9
7 increased by 3
Translation
5+3
2+6
6+9
7+3
Subtraction:
Synonym
less than
difference
minus
decreased by
Example
3 less than 5
difference of 6 and 2
9 minus 6
7 decreased by 3
Translation
5–3
6–2
9–6
7–3
Multiplication:
Note: The symbol * is used for multiplication to avoid confusion with the variable x.
Synonym
Example
Translation
times
3 times 5
3*5
product
product of 2 and 6
2*6
of
one-half of 8
½*8
Division:
Note: The symbol / is used for division. If either the numerator or denominator of a fraction
contains more than one term or factor, it must be enclosed in a set of parentheses for grouping.
Synonym
Example
Translation
per, a
gas is $3 per gallon
$3/gallon
gas is $3 a gallon
ratio, quotient
ratio of 7 and 3
7/3
Quotient of 7 and 3
Equals:
Synonym
is, gives, yields
Example
3 times x is 5
3 times x gives 5
3 times x yields 5
Translation
3x = 5
Translating Words into Math
Examples
(Solutions provided at bottom of page)
Write each of the following algebraic expressions symbolically.
1. 9 is added to m
2. 5 times the sum of 8 and b
3. Four-fifths of the sum of 5 and d
4. 3 less than 5 times d
5. 4 times m
6. y divided by 5
7. Subtract one-third from 5 times w
8. Five-sixths of h is added to 5
9. Product of 4 and b
10. 7 minus f
Write each of the following equations symbolically.
11. One-third of the sum of x and 5 is 3 times the sum of 2 and m.
12. b minus 3 is n added to 6.
13. 6 times x is three-fifths of the sum of 7 and f.
14. Subtracting 8 from 4 times x gives 5 divided by m.
15. Subtracting four-fifths from 9 times m yields the difference of one-sixth of b and 2
Solutions:
1.
4.
7.
10.
13.
9+m
5d – 3
5w – 1/3
7–f
6x = 3/5(7 + f)
2.
5.
8.
11.
14.
5(8 + b)
4m
5/6h + 5
1/3(x + 5) = 3(2 + m)
4x – 8 = 5/m
3.
6.
9.
12.
15.
4/5(5 + d)
y/5
4b
b–3=n+6
9m – 4/5 = 1/6b – 2
Worksheet 1
Algebraic Expressions
Write each of the following algebraic expressions symbolically.
1. 4 is subtracted from one-half of f
2. 8 divided by b
3. Add 9 to 2 times f
4. Five-sixths of b is added to 7
5. Product of 8 and c
Write each of the following equations symbolically.
6. The sum of h and 5 is equal to 8 less than 6 times y.
7. One-sixth of the sum of x and 5 is 4 minus y.
8. 7 divided by x is 5 less than 8 times y.
9. The sum of 9 and w is the sum of 3 and 7 times h.
10. The product of 7 and w is 8 times the sum of 2 and x.