Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Recognize compound units such as meters per second, dollars per hour, and grams per cubic centimeter as comparisons between two quantities. Translate “per,” “for each,” and “in every” into division and interpret what the resulting unit means.

Use what you learned in the previous lesson to solve real-world problems.

Compare quantities by checking their dimensions, such as length, time, area, volume, or money. Decide when an expression is impossible because it tries to add unlike things, such as meters plus seconds.

Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Use letters to stand for quantities whose values may change, and distinguish them from fixed numbers and constants. Read a formula by naming what each symbol measures before doing any calculation.

Use what you learned in the previous lesson to solve real-world problems.

Turn phrases like “5 more than x,” “3 times the distance,” and “half the cost” into expressions. Focus on choosing the operation that matches the relationship, not on solving an equation.

Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Build formulas from real-world rules such as “total cost is a fixed fee plus a charge per mile.” Identify which quantities are inputs, which quantity is being computed, and what units each term must have.

Use what you learned in the previous lesson to solve real-world problems.

Represent direct proportion with statements such as “y is 4 times x” or “cost is proportional to weight.” Use the constant of proportionality and its units to explain what one unit of the input produces.

Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Translate percent changes as multiplication, such as increasing by 8% means multiplying by 1.08 and decreasing by 8% means multiplying by 0.92. Separate “8% of a quantity” from “8 percentage points” in plain-language situations.

Use what you learned in the previous lesson to solve real-world problems.

Evaluate a formula by substituting values with their units and carrying the units through the arithmetic. Check that the numerical answer and final unit answer the question that was asked.

Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Rearrange simple formulas to isolate a named quantity when the algebra move is straightforward. Keep the meaning of the variables visible so the rearranged formula still describes the same relationship.

Use what you learned in the previous lesson to solve real-world problems.

Use parentheses to preserve meaning in phrases such as “three times the sum” or “the total divided equally.” Recognize when missing parentheses would change the real-world rule being modeled.

Use what you learned in the previous lesson to solve real-world problems.

Check what you understood with a short quiz.

Review this chapter with practice based on your mistakes.