Translating English to Algebra Flashcards

Write an expression for the number of pencils in the box after removing two if p = the number of pencils in the box.

Answer: p - 2

When you 'remove' items from a quantity, it signifies a subtraction operation. If 'p' represents the initial number of pencils in the box and two are removed, the remaining number is found by subtracting 2 from 'p'. Therefore, the correct algebraic expression is p - 2.

Write an expression for the number of tables in a coffee shop after the management adds three more tables.

Answer: t + 3

When items are 'added' to an existing quantity, it indicates an addition operation. If 't' represents the initial number of tables in the coffee shop and three more are added, the new total is found by adding 3 to 't'. Thus, the correct algebraic expression is t + 3.

Write an expression for the amount of fat in a cookie with half the fat if g is the amount in a cookie.

Answer: 1/2 g

To find 'half' of a quantity, you can either divide that quantity by 2 or multiply it by 1/2. If 'g' represents the original amount of fat in a cookie, then half the fat can be expressed as g divided by 2 (g/2) or g multiplied by 1/2 (1/2 g). Both are equivalent and correctly represent taking half of the original amount.

Write an expression for the number of flowers in a bouquet that is half the size of f = the number in a bouquet.

Answer: 1/2 f

To find 'half the size' of a quantity 'f', you must either divide 'f' by 2 or multiply 'f' by 1/2. The expression 1/2 f correctly represents this operation. This indicates that the new bouquet has half the number of flowers as the original bouquet.

Which of the following scenarios could the term "8x + 5" be used to represent?

Answer: An application fee is $5 and each additional page cost $8

In the algebraic expression 8x + 5, the '5' represents a fixed, one-time cost, while '8x' represents a variable cost that depends on the quantity 'x'. In the scenario where an application fee is $5 and each additional page costs $8, the $5 is the fixed fee, and the $8 per page (where 'x' is the number of additional pages) is the variable cost. This perfectly matches the structure of the expression.

Exponent not to exceed 1

Answer: Linear

A linear equation or function is characterized by its variables having an exponent of 1 (or 0 for constants). For example, in the equation y = mx + b, the variable 'x' has an implicit exponent of 1. If an exponent exceeds 1 (e.g., x^2 for quadratic, x^3 for cubic), the equation would no longer be considered linear.

The rotation of the figure does not alter its size or shape.

Answer: Turn transformation

A turn transformation, also known as a rotation, is a type of geometric transformation that moves a figure around a fixed point without changing its dimensions or form. This means the figure's size and shape remain congruent to the original, only its orientation in space changes. Therefore, rotation does not alter the figure's size or shape.