2. • To use algebra as a problem solving technique,
you must learn how to translate words into
equations.
• Become familiar with how words translate
into mathematics.
3. Example Expression Explanation
A number increased x+4 Increased by means
by four add
Nine more than a more than means
r+9
number add
less than means
eight less than a y-8
subtract
number
eight decreased by 8-y decreased by means
a number to subtract
four times a times means to
4e
number multiply
a product is the answer to
the product of ten 10p
multiplication
and a number
a number divided m/5 divisor goes on the
by 5 bottom
4. Example Expression Explanation
Five divided by a number 5/n The unknown is the divisor
One-fourth of a number (1/4)s or s/4 Of means multiple; since
the numerator is 1, it is the
same as dividing by 4
A number raised to the r2 A second power is an
second power exponent of 2
The square root of a The symbol for square root
number is
5.
6. • 1. a number increased by nine
• 2. the product of seven and a number
• 3. Five times a number
• 4. the sum of a number and eight
• 5. a number minus ten
• 6. one less than a number
• 7. three divided by a number
• 8. a number decreased by twenty
• 9. a number divided by fifteen
• 10. a number plus one-half
• 11. a number divided by two
• 12. four more than a number
• 13. the square root of a number
• 14. a number raised to the third power
• 15. three-fifths of a number
7. Example Expression Explanation
Twice a number Twice means to multiply
2x + 4 or 4 + 2x
increased by four by two and increased by
means to add.
Twice the sum of a 2(x+4) The parentheses
number and four group the sum
together.
Five less than three 3a-5 Times means to
times a number multiply and less than
means to subtract
The sum of a number Sum means to add,
c + (1/3)c or c + c/3
and one-third of the and one third of
same number means to divide by
three or multiply by
one-third
Five divided into the
The fraction bar
sum of three and a (x+3)/5
groups x+3 together.
number
Find the sum, then
divide by five.
8. • Eight more than three times a number is
twenty. Find the number.
8 more than
means to add,
Step 1: Let x stand and three
for the unknown in times means
the phrase (a to multiply. Is
number).
-8 -8 means equals.
Step 2: Solve for x. 3x = 12
3 3
x= 4
9. • One-third of a number decreased by seven
equals four. Find the number.
One-third of
means to
Step 1: Let x stand either divide
for the unknown in by three or
the phrase (a multiply by
number). +7 +7 one-third.
Seven less
Step 2: Solve for x. than means to
= 11 subtract.
10. • 1. Half a number
decreased by five is six.
• 2. Three more than six
times a number is twelve.
• 3. Seven less than twice a
number equals the same
number increased by
three.
