Translate Phrases into Math Expressions I
Name ___________________________
Translate the following phrases into mathematical expressions.
1.
The sum of a number and ten.
1.
2.
Eighteen more than a number.
2.
3.
Five less than a number.
3.
4.
The product of a number and three.
4.
5.
The difference of a number and seven.
5.
6.
The difference of seven and a number.
6.
7.
Two more than a number.
7.
8.
Sixteen less than twice a number.
8.
9.
Five times the sum of a number and four.
9.
10.
Three times the difference of a number and one.
10.
11.
The quotient of a number and six.
11.
12.
Two-thirds of a number.
12.
13.
Eight more than a twice a number.
13.
14.
The difference of a number and eight, divided by ten.
14.
15.
Three more than the sum of a number and four.
15.
16.
Double the difference of a number and seven.
16.
17.
Nine less than the product of a number and two.
17.
18.
The quotient of two and three more than a number.
18.
19.
The product of triple a number and five.
19.
20.
Sixteen less than the sum of three and a number.
20.
Translate Phrases into Math Expressions II
Translate the following phrases into mathematical expressions.
1.
The sum of a number and five.
1.
2.
Eighteen less than a number.
2.
3.
The product of a number and eight is two.
3.
4.
Three times the sum of a number and four.
4.
5.
The quotient of twice a number and six.
5.
6.
Two-thirds of a number is eighteen.
6.
7.
Eight more than a number.
7.
8.
The difference of a number and eight, divided by ten.
8.
9.
Two numbers have a sum of fifteen. One of the numbers
is x . Find an expression for the other number.
9.
10.
One of the angles of two complementary angles measures x .
Find an expression for the other angle.
10.
11.
Joan has fourteen books. Suppose that she donates x books
to the library. How many books does she have left?
11.
12.
Ed is x years old now. How old will he be in five years?
12.
13.
Movie tickets cost x dollars for an adult and y dollars
13.
for a child. Find the total cost for two adults and four children.
14.
Ted is x years old now. How old was he last year?
14.
15.
One of the angles of two supplementary angles measures x .
Find an expression for the other angle.
15.
16.
Let x represent the first of three consecutive integers.
16.
Find a variable expression for the next two consecutive integers.
17.
Let x represent the first of three consecutive EVEN integers.
Find a variable expression for the next two even integers.
17.
18.
Let x represent the first of three consecutive ODD integers.
Find a variable expression for the next two odd integers.
18.
TRANSLATING ENGLISH PHRASES INTO ALGEBRAIC EXPRESSIONS
ENGLISH PHRASES
ALGEBRAIC EXPRESSIONS
Ten more than a number ................................................................................................................................................. x + 10
A number added to five..................................................................................................................................................... 5 + x
A number increased by thirteen ...................................................................................................................................... x + 13
Four less than ten ............................................................................................................................................................ 10 − 4
Six less than a number ...................................................................................................................................................... x − 6
A number decreased by seven ........................................................................................................................................... x − 7
The difference between a number and three ..................................................................................................................... x − 3
The difference between three and a number ..................................................................................................................... 3 − x
Twice a number..................................................................................................................................................................... 2x
Half (of) a number ...................................................................................................................................................
1
x
x or
2
2
A number squared or the square of a number ........................................................................................................................ x2
The square of five more than a number ........................................................................................................................ (x + 5)2
Five more than the square of a number or the square of a number, increased by five..................................................... x2 + 5
Ten percent of a number .................................................................................................................................................. 0.10x
Ten times a number ............................................................................................................................................................. 10x
Quotient of a number and three.............................................................................................................................................
x
3
Quotient of three and a number.............................................................................................................................................
3
x
Five times the sum of a number and two ......................................................................................................................5(x + 2)
Five times the difference of a number and four ............................................................................................................5(x − 4)
Five is three more than a number ................................................................................................................................ 5 = x + 3
The product of two and a number is ten........................................................................................................................ 2x = 10
One half (of) a number is ten .....................................................................................................................................
1
x = 10
2
Ten less than eight times a number is five more than the number .................................................................... 8x − 10 = x + 5
The sum of five times a number and ten is equal to the product of 15 and the number ..................................... 5x + 10 = 15x
The sum of two consecutive integers ......................................................................................................................... x+ (x + 1)
The sum of two consecutive even integers ................................................................................................................ x+ (x + 2)
The sum of two consecutive odd integers .................................................................................................................. x+ (x + 2)
The sum of the squares of two consecutive integers .............................................................................................. x2 + (x + 1)2
The sum of the cubes of two consecutive integers................................................................................................. x3 + (x + 1)3
VC DEPARTMENT OF MATHEMATICS
REVISED FALL 2014
TRANSLATING ENGLISH TERMS INTO ALGEBRAIC OPERATORS
Accumulate ................................. +
Add, add up, added to, addition,
additional..................................... +
Alike............................................ =
Also ............................................. +
Altogether ................................... +
Amounts to .................................. =
Amplify, amplified by ................. ×
And.............................................. +
Appreciate ................................... +
Are (equal) .................................. =
Area ............................................. ×
Balances ...................................... =
Bigger (than) ............................... +
Coincides (with) .......................... =
Combine(d) ................................. +
Corresponds (to).......................... =
Cut (by) ....................................... −
Cut by a factor of ........................ ÷
Decline, declined by.................... −
Decline(d) by a factor of ............. ÷
Decrease(d) by, decrement.......... −
Decrease(d) by a factor of ........... ÷
Deduct, deducted from ................ −
Depreciate ................................... −
Difference (of) ............................ −
Diminished (by) .......................... −
Diminished by a factor of............ ÷
Divide, divided by, divided into.. ÷
Double(d) .................................... ×
Dropped by.................................. −
Dropped by a factor of ................ ÷
Dwindle ....................................... −
Equal, equals ............................... =
Equivalent (to) ............................ =
Exceeds ....................................... >
Exceeds by .................................. +
Factors ......................................... ×
Fall .............................................. −
Farther ......................................... +
Fewer than................................... −
VC DEPARTMENT OF MATHEMATICS
Find the total............................... +
Fraction....................................... ÷
Fraction of .................................. ×
Gain ..................................... × or +
Gives (a result of), giving ........... =
Go (went) up............................... +
Go (went) up by a factor of ....... ×
Greater (than) ............................. +
Grew by, grow by ....................... +
Halved ........................................ ÷
Identical to .................................. =
In addition (to) ............................ +
In all............................................ +
In excess ..................................... +
Increased (by), increment ........... +
Increase(d) by a factor of............ ×
Intensified by .............................. ×
Interest on ................................... ×
Is (equal) ..................................... =
Is greater (than) .......................... >
Is less (than)................................ <
Less (than) .................................. −
Larger (than) ............................... +
Lengthen (by), longer (than)....... +
Lower, lowered by ...................... −
Matches ...................................... =
Magnified by .............................. ×
Minus .......................................... −
More (than) ................................. +
Multiple, multiply, multiplied by ×
Narrower (than) .......................... −
Net .............................................. +
Of [usually in connection with
fractions]..................................... ×
Older (than) ............................... +
On top of..................................... +
Per............................................... ÷
Percent (of) ................................. ×
Perimeter .................................... +
Plus ............................................. +
Product (of)................................. ×
Quadruple(d) ............................... ×
Quarter ........................................ ÷
Quantity ................................. (…)
Quotient (of) ............................... ÷
Raise, raised by, rise ................... +
Ratio (of) ..................................... ÷
Reciprocal (of) ............................ ÷
Reduce, reduce(d) by .................. −
Reduce(d) by a factor of ............. ÷
Represents ................................... =
Result (is), results (are), results in=
Same (result) as........................... =
Smaller (than) ............................. −
Smaller by a factor of.................. ÷
Shorten (by), shorter (than) ......... −
Subdivide .................................... ÷
Subtract, subtracted from ............ −
Sum (of), summation .................. +
Take away, take from.................. −
Tally (up) .................................... +
Thrice .......................................... ×
Times, times as much, times
larger, times more, times older ... ×
Times less, times smaller, times
younger ....................................... ÷
Together ...................................... +
Total (is)...................................... =
Total of........................................ +
Triple(d) ...................................... ×
Twice .......................................... ×
Volume........................................ ×
Was (equal), were (equal) ........... =
Wider (than) ................................ +
Will be (equal) ............................ =
… Years older (than) .................. +
Yields .......................................... =
REVISED FALL 2014