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TRANSLATING ENGLISH TO MATH
TRANSLATING ENGLISH TO MATH
One of the major skills required in mathematics is the ability to
One of the major skills required in mathematics is the ability to
Addition
Addition
Subtraction
Subtraction
Multiplication
Multiplication
Division
Division
Power
Power
Power
Power
Power
Power
Translate the following verbal expressions into variable expressions:
Translate the following verbal expressions into variable expressions:
Ex: n subtracted from two
Ex: n subtracted from two
Back to the example: Ex: The sum of two numbers is 18
Back to the example: Ex: The sum of two numbers is 18
Ex: A college employs a total of 600 teaching assistants (TA) and
Ex: A college employs a total of 600 teaching assistants (TA) and
Ex: A wire 12 ft long is cut into two pieces
Ex: A wire 12 ft long is cut into two pieces
TRANSLATING ENGLISH TO MATH
TRANSLATING ENGLISH TO MATH
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TRANSLATING ENGLISH TO MATH

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1TRANSLATING ENGLISH TO MATH. SJC ~ San 31a. a. +. 13.
Jacinto Campus Math Center Workshop Series 32Ex: the quotient of nine less than x
Janice Levasseur. and twice x. Division & Subtraction
2One of the major skills required in & Multiplication. What operation(s)?
mathematics is the ability to translate a Take it word for word to translate: the
verbal statement into a mathematical quotient of. 9 less than x and. twice x.
(variable) expression or equation. This x. -. 9. 2. x.
ability requires recognizing the verbal 33Translate into a variable expression
phrases that translate into mathematical and then simplify. Identify any variables
operations. used. Ex: a number added to the product of
3Addition. Added to (the sum of) (the five and the number. “a number”, “the
total of) Increased by Plus More than. number” ? let n = a number. What
Note: The sum is the answer to an addition operation(s)? Addition and Multiplication.
problem. “The sum of x and y” ? (x + y). a number. added to. the product of. 5 and.
4Subtraction. Subtracted from (the the number. n. +. ( )( ). 5. n. = 6n when
difference between) Less Decreased by simplified (combine like terms).
Minus Less than. Note: The difference is 34Ex: a number minus the sum of the
the answer to a subtraction. “The number and fourteen. let n = a number. “a
difference between x and y” ? (x – y). number”, “the number” ? What operation(s)?
5Multiplication. Times The product of Subtraction and Addition. a number. minus.
Multiplied by Of Twice. Note: The product the sum of. the number and. 14. ( + ). n.
is the answer to a multiplication problem. 14. n. _. = n – n – 14 (removing
“The product of x and y” ? (x)(y). parentheses). = – 14 (combining like
6Division. Divided by The quotient of terms).
The ratio of. Note: The quotient is the 35Ex: Twice the quotient of four times a
answer to a division problem. “The number and eight. “a number” ? let n = a
quotient of x and y” ? x . y. number. What operation(s)? Multiplication
7Power. Equals. The square of exponent and Division. twice. the quotient of. 4
2 The cube of exponent 3. Equals times a number and. 8. 2. 4. n. 8.
Is/Are/Was/Were Amounts to. Note: These (Simplifying). = n (Simplifying).
lists are not complete. 36Equals. Equals Is/Are/Was/Were Amounts
8Translate the following verbal to The results is To obtain. Note: These
expressions into variable expressions: Ex: lists are not complete.
y added to sixteen. What is the operation? 37Write a variable expression. Identify
Addition. What is being added? y and 16. any variables used. Ex: The sum of two
Write the expression: y + 16. numbers is 18. Express the numbers in
9Ex: the sum of b and eight. What is terms of the same variable. * If the sum
the operation? Addition. What is being of two numbers is 9 and the first number
added? b and 8. Write the expression: (b + is 5, what is the second? 4. How did you
8). get that? Subtract: 9 – 5 = 4. * If the
10Ex: the total of four and m. What is sum of two numbers is 17 and the first
the operation? Addition. What is being number is 12, what is the second? 5. How
added? 4 and m. Write the expression: (4 + did you get that? Subtract: 17 – 12 = 5.
m). 38Back to the example: Ex: The sum of
11Ex: w increased by fifty-five. What is two numbers is 18. Let n = first number.
the operation? Addition. What is being Then the second number is found by
added? w and 55. Write the expression: w + subtracting: 18 – n = second number Check:
55. Do n and 18 – n sum to 18? n + (18 – n) =
12Ex: g plus twenty. What is the n + 18 – n = 18.
operation? Addition. What is being added? 39Translate the English sentences into
g and 20. Write the expression: g + 20. equations and solve. Identify any
13Ex: nineteen more than K. What is the variables used. Ex: The sum of five and a
operation? Addition. What is being added? number is three. Find the number. What are
19 and K. Write the expression: K + 19. we looking for? The number = n. Translate
Can also by written as: 19 + K. word-for-word: The sum of. a number. is.
14Ex: n subtracted from two. What is the 3. 5 and. =. 3. (__ + __). 5. n. Now solve
operation? Subtraction. What is being 5 + n = 3 by subtracting 5 from both sides
subtracted? n and 2. Write the expression -5 -5 n = - 2.
(careful!): 2 – n. Subtraction does not 40Ex: The difference between five and
possess the commutative property so order twice a number is one. Find the number.
is important. There is a difference What are we looking for? The number = n.
between what goes in front of the Translate word-for-word: The difference
subtraction sign (the minuend) and what between. 5 and. twice a number. is. 1.
goes after (the subtrahend). (______ – ______). 5. 2. n. =. 1. Now
15Ex: the difference of q and three. solve 5 – 2n = 1. Subtract 5 from both
What is the operation? Subtraction. What sides. – 2n = - 4. Divide both sides by -
is being subtracted? q and 3. Write the 2. n = 2.
expression (careful!): (q – 3). 41What are we looking for? The number =
16Ex: r less twelve. What is the n. Translate word-for-word: Four times a
operation? Subtraction. What is being number. is. three times. the difference
subtracted? r and 12. Write the expression between. 35 and. the number. n. 35. (
(careful!): r – 12. _____ - _____). 4n. =. 3. Solve 4n = 3(35
17Ex: seventeen decreased by m. What is – n). Simplify – distribute 3. 4n = 105 –
the operation? Subtraction. What is being 3n. Collect like terms (add 3n to both
subtracted? 17 and m. Write the expression sides). 7n = 105. Divide both sides by 7.
(careful!): 17 – m. n = 15. Ex: Four times a number is three
18Ex: w minus 3. What is the operation? times the difference between thirty-five
Subtraction. What is being subtracted? w and the number. Find the number.
and 3. Write the expression (careful!): w 42Ex: The sum of two numbers is two. The
– 3. difference between eight and twice the
19Ex: nineteen less than d. What is the smaller number is two less than four times
operation? Subtraction. What is being the larger. Find the two numbers. What are
subtracted? 19 and d. Write the expression we looking for? Two numbers: Let s =
(careful!): d – 19. Subtraction does not smaller number. Then 2 – s = larger
possess the commutative property so order number. The difference between. 8 and.
is important. There is a difference twice the smaller. is. two less than. four
between what goes in front of the times. the larger. 8. 2. s. 4. (2 – s). (
subtraction sign (the minuend) and what ______ - ______ ). =. _________ - 2.
goes after (the subtrahend). 43Solve 8 – 2s = 4(2 – s) – 2. 8 – 2s =
20Ex: nine times c. What is the 8 – 4s – 2. Collect like terms (add 4s to
operation? Multiplication. What is being both sides). 8 – 2s = 6 – 4s. Collect like
multiplied? 9 and c. Write the expression: terms (subtract 8 from both sides). 8 + 2s
9c. = 6. 2s = - 2. Simplify. Combine like
21Ex: the product of negative six and b. terms. Divide both sides by 2. s = - 1 ?
What is the operation? Multiplication. smaller number is -1. Therefore, 2 – s = 2
What is being multiplied? -6 and b. Write – ( - 1) = 3. the larger number is 3.
the expression: -6b. 44Ex: A college employs a total of 600
22Ex: five multiplied by a number. What teaching assistants (TA) and research
is the operation? Multiplication. What is assistants (RA). There are three times as
being multiplied? 5 and n. Write the many TAs as RAs. Find the number of RAs
expression: 5n. employed by the university. What are we
23.15p. Ex: fifteen precent of the looking for? The number of RAs = r. The
selling price. What is the operation? number of TAs =. 600 - r.
Multiplication. What is being multiplied? 45600 = 4r. 150 = r ? 150 RAs. There are
15% and p. Write the expression: three times as many TAs as RAs. So are
24Ex: twice a number. What is the there more TAs or RAs? TAs. 600 – r. How
operation? Multiplication. What is being many TAs? The number of TAs. is. 3 times
multiplied? 2 and n. Write the expression: the number of RAs. 600 - r. =. r. 3. Solve
2n. 600 – r = 3r. (add r to both sides).
25Ex: the square of a number. What is (divide both sides by 4). and 3r = 3(150).
the operation? Multiplication. What is = 450 TAs.
being multiplied? n and n. Write the 46Ex: A wire 12 ft long is cut into two
expression: n2. pieces. Each piece is bent into the shape
26Ex: the cube of a number. What is the of a square. The perimeter of the larger
operation? Multiplication. What is being square is twice the perimeter of the
multiplied? n and n and n. Write the smaller square. Find the perimeter of the
expression: n3. larger square.
27Ex: four divided by y. What is the 47What are we looking for? The perimeter
operation? Division. What is being of the larger square. What do we know? We
divided? 4 and y. Write the expression will form 2 squares using 2 pieces of
(careful!): 4 y. wire. The pieces are from cutting a single
28Ex: the quotient of the opposite of n piece in two: How long is each piece of
and nine. What is the operation? Division. wire? Let s = length of the shorter piece
What is being divided? -n and 9. Write the ? Then, 12 – s = length of the longer
expression (careful!): -n 9. piece since we start with a 12 ft wire.
29Ex: the ratio of eleven and p. What is 48Now, take the smaller wire and bend it
the operation? Division. 11 and p. What is into a square. What is the perimeter of
being divided? 11 p. Write the expression the smaller square? s since the shorter
(careful!): Division does not possess the piece is of length s. What is the
commutative property so order is perimeter of the larger square? 12 – s
important. There is a difference between since the longer piece is of length 12 -
what goes in front of the division sign/on s. Now what? Use the information,
top (the dividend) and what goes after the translate into an equation: perimeter of
division sign /on the bottom (the the larger square. is. twice the perimeter
divisor). of the smaller square. 12 – s. =. 2. s.
30Ex: nine increased by the quotient of 49Solve 12 – s = 2s. Add s to both
t and five. What operation(s)? Addition sides. Divide both sides by 3. 12 = 3s. 4
and Division. Take it word for word to = s. Therefore the shorter piece is 4 ft ?
translate: nine. increased by. the the smaller square has perimeter 4 ft.
quotient. of t and five. 9. +. t. 5. Have we answered the question asked? No.
31Ex: the product of a and the sum of a We want to find the perimeter of the
and thirteen. What operation(s)? larger square. So, 12 – s = 12 – 4 = 8. 8
Multiplication and Addition. Take it word ft is the perimeter of the larger square.
for word to translate: The product of. a 50
and. the sum of. a and. thirteen. ( )( ).
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