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1 | TRANSLATING ENGLISH TO MATH. SJC ~ San | 31 | a. a. +. 13. |
Jacinto Campus Math Center Workshop Series | 32 | Ex: the quotient of nine less than x | |
Janice Levasseur. | and twice x. Division & Subtraction | ||
2 | One 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 | 33 | Translate 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 | ||
3 | Addition. 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. | ||
4 | Subtraction. 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 | 34 | Ex: 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)? | ||
5 | Multiplication. 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 | ||
6 | Division. Divided by The quotient of | terms). | |
The ratio of. Note: The quotient is the | 35 | Ex: 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 | ||
7 | Power. 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. | 36 | Equals. Equals Is/Are/Was/Were Amounts | |
8 | Translate 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? | 37 | Write 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 | ||
9 | Ex: 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 | ||
10 | Ex: 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). | 38 | Back to the example: Ex: The sum of | |
11 | Ex: 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) = | ||
12 | Ex: g plus twenty. What is the | n + 18 – n = 18. | |
operation? Addition. What is being added? | 39 | Translate the English sentences into | |
g and 20. Write the expression: g + 20. | equations and solve. Identify any | ||
13 | Ex: 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. | ||
14 | Ex: 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 | 40 | Ex: 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 | ||
15 | Ex: 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). | 41 | What are we looking for? The number = | |
16 | Ex: 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 | ||
17 | Ex: 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 | ||
18 | Ex: 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 | 42 | Ex: The sum of two numbers is two. The | |
– 3. | difference between eight and twice the | ||
19 | Ex: 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). | 43 | Solve 8 – 2s = 4(2 – s) – 2. 8 – 2s = | |
20 | Ex: 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 | ||
21 | Ex: 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. | 44 | Ex: A college employs a total of 600 | |
22 | Ex: 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? | 45 | 600 = 4r. 150 = r ? 150 RAs. There are | |
15% and p. Write the expression: | three times as many TAs as RAs. So are | ||
24 | Ex: 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). | ||
25 | Ex: 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 | 46 | Ex: A wire 12 ft long is cut into two | |
expression: n2. | pieces. Each piece is bent into the shape | ||
26 | Ex: 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. | ||
27 | Ex: four divided by y. What is the | 47 | What 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 | ||
28 | Ex: 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. | ||
29 | Ex: the ratio of eleven and p. What is | 48 | Now, 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. | ||
30 | Ex: nine increased by the quotient of | 49 | Solve 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. | ||
31 | Ex: 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. ( )( ). | |||
TRANSLATING ENGLISH TO MATH.ppt |
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