algebraic expressions

The population of Kansas is two-fifths the population of California Assumptions: Let p be the population of Kansas Let c be the population of California We have: k = 2c/5

triple t multiply g triple t means we multiply t by 3: 3t Multiply g: 3tg

1/6 times the sum k and 5 The sum k and 5 (k + 5) 1/6 times the sum k and 5 (k + 5)/6

Take away x from y y - x

Eight-ninths of the population p 8p/9

the quotient of c and d diminished by 5y the quotient of c and d c/d the quotient of c and d diminished by 5y c/d - 5y

raise b to the 6th power then find the sum of the result and 4 raise b to the 6th power b^6 raise b to the 6th power then find the sum of the result and 4 b^6 + 4

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266 The product of 244 and w: 244w 110 subtracted from the product of 244 and w 244w - 110 the product of r and 177 177r the product of r and 177 increased by 266 177r + 266 The word is means equal to, so...

the sum of a and b minus 4 is 12 the sum of a and b a + b the sum of a and b minus 4 a + b - 4 The word is means equal to, so we set a + b - 4 equal to 12: a + b - 4 = 12

The difference between a number and 9 is 27. Find that number The phrase a number means an arbitrary variable, let's call it x: x The difference between a number and 9 x - 9 The word is means equal to, so we set x - 9 equal to 27: x - 9 = 27 To solve this equation for x, we type it in our...

sum of twice f plus h Twice f means we multiply f by 2: 2f sum of twice f plus h 2f + h

sum of x plus y divided by 2 sum of x plus y: x + y sum of x plus y divided by 2 (x + y)/2

The ratio between the sum of a and b and the difference of a and b is equal to 5. The sum of a and b: a + b The difference of a and b: a - b The ratio between the sum of a and b and the difference of a and b (a + b)/(a - b) The ratio between the sum of a and b and the difference of a and b...

Divide the sum x and y by the difference of subtracting a from b The sum x and y is written as: x + y The difference of subtracting a from b is written as: b - a We divide and get the algebraic expression: (x + y)/(b - a)

3x to the power 2n We take the expression 3x raise it to the power of 2n (3x)^2n

The square of the difference of n and 2, increased by twice n The difference of n and 2: n - 2 The square of the difference of n and 2 means we raise (n - 2) to the 2nd power: (n - 2)^2 Twice n means we multiply n by 2: 2n The square of the difference of n and 2, increased by twice n (n -...

c increased by d diminished by g c increased by d: c + d diminished by g: c + d - g

quotient of the sum of 2 numbers and 6 The phrase two numbers means we choose 2 arbitrary variables, let's call them x and y x, y The sum of 2 numbers: x + y quotient of the sum of 2 numbers and 6 (x + y)/6

multiply p by itself Two ways to express this p * p p^2

2 less than 3 times n is 4 more than n 3 times n: 3n 2 less than 3 times n 3n - 2 4 more than n: n + 4 The word is means equal to, so we set 3n - 2 equal to n + 4: 3n - 2 = n + 4