TRANSLATING ENGLISH TO MATH Math Center Workshop Series

TRANSLATING ENGLISH TO MATH Math Center Workshop Series By 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.

Addition • • • 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)

Subtraction • • • Subtracted from (the difference between) Less Decreased by Minus Less than Note: The difference is the answer to a subtraction. “The difference between x and y” (x – y)

Multiplication • • • Times The product of Multiplied by Of Twice Note: The product is the answer to a multiplication problem. “The product of x and y” (x)(y)

Division • 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

Power • The square of • The cube of exponent 2 exponent 3 Equals • Is/Are/Was/Were • Amounts to Note: These lists are not complete.

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

Ex: the sum of b and eight What is the operation? Addition What is being added? b and 8 Write the expression: (b + 8)

Ex: the total of four and m What is the operation? Addition What is being added? 4 and m Write the expression: (4 + m)

Ex: w increased by fifty-five What is the operation? Addition What is being added? w and 55 Write the expression: w + 55

Ex: g plus twenty What is the operation? Addition What is being added? g and 20 Write the expression: g + 20

Ex: nineteen more than K What is the operation? Addition What is being added? 19 and K Write the expression: K + 19 Can also be written as: 19 + K

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).

Ex: the difference of q and three What is the operation? 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 Write the expression: 9 c

Ex: the product of negative six and b What is the operation? Multiplication What is being multiplied? -6 and b Write the expression: -6 b

Ex: five multiplied by a number What is the operation? Multiplication What is being multiplied? 5 and n Write the expression: 5 n

Ex: fifteen percent of the selling price What is the operation? What is being multiplied? Write the expression: Multiplication 15% and p . 15 p

Ex: twice a number What is the operation? What is being multiplied? Write the expression: Multiplication 2 and n 2 n

Ex: the square of a number What is the operation? Multiplication What is being multiplied? n and n Write the expression: n 2

Ex: the cube of a number What is the operation? Multiplication What is being multiplied? n and n Write the expression: n 3

Ex: four divided by y What is the operation? Division What is being divided? 4 and y Write the expression (careful!): 4 y

Ex: the quotient of the opposite of n and nine What is the operation? Division What is being divided? -n and 9 Write the expression (careful!): -n 9

Ex: the ratio of eleven and p What is the operation? 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 9 + t 5 of t and five

Ex: the product of a and the sum of a and thirteen What operation(s)? Multiplication and Addition Take it word for word to translate: The product of a and the sum of a and thirteen ( a )( a + 13 )

Ex: the quotient of nine less than x and twice x What operation(s)? Division & Subtraction & Multiplication Take it word for word to translate: the quotient of 9 less than x and twice x x - 9 2 x

Equals • • • Equals Is/Are/Was/Were Amounts to The results is To obtain Note: These lists are not complete.