TRANSLATING ENGLISH TO MATH

• One of the major skills required in mathematics is the ability to translate a verbal statement into a mathematical variable expression or equation.. n and 2 Write the expression care

TRANSLATING

ENGLISH TO MATH

SJC ~ San Jacinto Campus

Math Center Workshop Series

Janice Levasseur

• One of the major skills required in

mathematics is the ability to translate a

verbal statement into a mathematical

(variable) expression or equation.

• This ability requires recognizing the verbal

phrases that translate into mathematical operations.

• Added to

• (the sum of)

• (the total of)

• Increased by

• Plus

• More than

Note: The sum is the answer to an addition

problem “The sum of x and y”  (x + y)

Note: The difference is the answer to a subtraction

“The difference between x and y”  (x – y)

Note: The product is the answer to a multiplication

problem “The product of x and y”  (x)(y)

• Divided by

• The quotient of

• The ratio of

Note: The quotient is the answer to a division

problem “The quotient of x and y”  x

y

• The square of exponent 2

• The cube of exponent 3

Translate the following verbal expressions into variable expressions:

Ex: y added to sixteen

What is the operation? Addition

What is being added? y and 16

Write the expression: y + 16

What is the operation?

Ex: the sum of b and eight

AdditionWhat is being added? b and 8Write the expression: (b + 8)

What is the operation?

Ex: the total of four and m

AdditionWhat is being added? 4 and mWrite the expression: (4 + m)

Ex: w increased by fifty-five

What is the operation? AdditionWhat is being added? w and 55Write the expression: w + 55

Ex: g plus twenty

What is the operation? AdditionWhat is being added? g and 20Write the expression: g + 20

Ex: nineteen more than K

What is the operation? AdditionWhat is being added? 19 and KWrite the expression: K + 19

19 + K Can also by written as:

Ex: n subtracted from two

What is the operation? Subtraction

What is being subtracted? n and 2

Write the expression (careful!): 2 – n

Subtraction does not possess

the commutative property so

order is important There is a difference between what goes

in front of the subtraction sign (the minuend) and what goes after (the subtrahend)

What is the operation?

Ex: the difference of q and three

Subtraction

What is being subtracted? q and 3

Write the expression (careful!): (q – 3)

Ex: r less twelve

What is the operation? Subtraction

What is being subtracted? r and 12

Write the expression (careful!): r – 12

Ex: seventeen decreased by m

What is the operation? Subtraction

What is being subtracted? 17 and m

Write the expression (careful!): 17 – m

Ex: w minus 3

What is the operation? Subtraction

What is being subtracted? w and 3

Write the expression (careful!): w – 3

Ex: nineteen less than d

What is the operation? Subtraction

What is being subtracted? 19 and d

Write the expression (careful!): d – 19

Subtraction does not possess

the commutative property so

order is important There is a difference between what goes

in front of the subtraction sign (the minuend) and what goes after (the subtrahend)

Ex: nine times c

What is the operation? Multiplication

What is being multiplied? 9 and c

What is the operation?

Ex: the product of negative six and b

Multiplication

What is being multiplied? -6 and b

Write the expression: -6b

Ex: five multiplied by a number

What is the operation? Multiplication

What is being multiplied? 5 and n

Ex: fifteen precent of the selling price

What is the operation? Multiplication

What is being multiplied? 15% and p

Write the expression: .15p

Ex: twice a number

What is the operation? Multiplication

What is being multiplied? 2 and n

Write the expression: 2n

Ex: the square of a number

What is the operation? Multiplication

What is being multiplied? n and n

Write the expression: n2

Ex: the cube of a number

What is the operation? Multiplication

What is being multiplied? n and n and n

Write the expression: n3

Ex: four divided by y

What is the operation? Division

What is being divided? 4 and y

Write the expression (careful!): 4

y

What is the operation?

Ex: the quotient of the opposite of n and nine

Division

What is being divided? -n and 9

Write the expression (careful!): -n

9

What is the operation?

Ex: the ratio of eleven and p

Division

What is being divided? 11 and p

Write the expression (careful!): 11

p

Division does not possess the

commutative property so order is

important There is a difference between what goes in front of the division sign/on top ( the dividend ) and what goes after the division sign /on the bottom ( the divisor ).

Ex: nine increased by the quotient of t and

five

What operation(s)? Addition and Division

Take it word for word to translate:

nine increased by the quotient

5

Ex: the product of a and the sum of a and

Ex: the quotient of nine less than x and

Translate into a variable expression and

then simplify

Identify any variables used.

Ex: a number added to the product of five and

Ex: a number minus the sum of the number

Ex: Twice the quotient of four times a number

Write a variable expression

Identify any variables used.

Ex: The sum of two numbers is 18

Express the numbers in terms of the same

variable.

* If the sum of two numbers is 9 and the first

number is 5, what is the second?

4 How did you get that? Subtract: 9 – 5 = 4

* If the sum of two numbers is 17 and the first

number is 12, what is the second?

5 How did you get that? Subtract: 17 – 12 = 5

Back to the example:

Ex: The sum of two numbers is 18

Let n = first number

Then the second number is found by subtracting:

Translate the English sentences into equations

and solve Identify any variables used.

Ex: The sum of five and a number is three

Find the number.

What are we looking for? The number = n

Ex: The difference between five and twice a

number is one Find the number.

What are we looking for? The number = n

Ex: Four times a number is three times the difference

between thirty-five and the number Find the number.

What are we looking for? The number = n

Solve 4n = 3(35 – n) Simplify – distribute 3

4n = 105 – 3n Collect like terms (add 3n to both sides)7n = 105 Divide both sides by 7

n = 15

Ex: The sum of two numbers is two The

difference between eight and twice the smaller number is two less than four times the larger Find the two numbers.

What are we looking for? Two numbers:

Let s = smaller number Then 2 – s = larger number

The difference between 8 and twice the smaller

is two less than four times

s = _ - 24 (2 – s)

the larger

Solve 8 – 2s = 4(2 – s) – 2 Simplify

8 – 2s = 8 – 4s – 2 Combine like terms

8 – 2s = 6 – 4s Collect like terms

(add 4s to both sides)

8 + 2s = 6 Collect like terms

(subtract 8 from both sides)2s = - 2 Divide both sides by 2

s = - 1  smaller number is -1

Therefore, 2 – s = 2 – ( - 1) = 3 the larger number is 3

Ex: A college employs a total of

600 teaching assistants (TA) and research assistants (RA) There are three times as many TAs as RAs Find the number of RAs employed by the university.

What are we looking for? The number of RAs = r

The number of TAs = 600 - r

There are three times as many TAs as RAs

So are there more TAs or RAs? TAs

How many TAs?

The number of TAs is 3 times the number of RAs

600 - r = 3 r

600 = 4r

150 = r  150 RAs and 3r = 3(150)

Solve 600 – r = 3r

(divide both sides by 4)

(add r to both sides)

= 450 TAs

600 – r

Ex: A wire 12 ft long is cut into

two pieces Each piece is bent into the shape of a square The perimeter of the larger square is

twice the perimeter of the

smaller square Find the perimeter of the larger square.

What are we looking for?

The perimeter of the larger squareWhat do we know?

We will form 2 squares using 2 pieces of wireHow long is each piece of wire?

The pieces are from cutting a single piece in two:

Let s = length of the shorter piece 

Then, 12 – s = length of the longer piece

since we start with a 12 ft wire

Now, take the smaller wire and bend it into a square What is the perimeter of the smaller square?

s since the shorter piece is of length s

What is the perimeter of the larger square?

12 – s since the longer piece is of length 12 - s

Now what?

Use the information, translate into an equation:

perimeter of the larger square is

twice the perimeter of the smaller square

12 – s = 2 s

Solve 12 – s = 2s Add s to both sides

12 = 3s Divide both sides by 3

Therefore the shorter piece is 4 ft  the smaller square has perimeter 4 ft

4 = s

Have we answered the question asked?

No We want to find the perimeter of the larger square So, 12 – s = 12 – 4 = 8

8 ft is the perimeter

of the larger square