Grade 7 Mathematics: Ratios, Proportions, and Rational Numbers
Core Concepts
Grade 7 math centers on proportional reasoning and operations with rational numbers. You must be able to compute unit rates, including rates with fractions (e.g., 3/4 mile in 1/2 hour gives 3/2 miles per hour), decide whether two quantities are proportional, and solve proportions with cross-multiplication. You also need fluency with adding, subtracting, multiplying, and dividing integers and fractions, applying the rules that a negative times a negative is positive and that dividing by a fraction means multiplying by its reciprocal. Expect percent problems (tax, tip, discount, percent increase and decrease), expressions and equations (combining like terms, the distributive property, solving two-step equations), and geometry involving scale drawings and circles.
Traps That Cost Points
- Sign errors: Subtracting a negative, as in 5 − (−3) = 8, is the most common slip.
- Wrong base in percent change: A price rising from 20 to 25 is a 25% increase, not 5%, because the change is divided by the original value.
- Mixing up part and whole: In "15 is what percent of 60?" the whole is 60, so divide 15 by 60.
- Forgetting to distribute to every term: 3(x + 4) = 3x + 12, not 3x + 4.
- Scale factor direction: A scale of 1 cm : 5 m means multiply by 5 to go from drawing to reality.
Rule of Thumb: Set Up a Ratio Table
Write the two quantities in labeled columns, then find the multiplier between rows. Labeling units prevents upside-down proportions.
Worked Example
A jacket costs $80 and is discounted 25%, then taxed 8% on the sale price. Sale price: 80 × 0.75 = $60. Tax: 60 × 0.08 = $4.80. Total: $64.80. Note the trap: applying the 8% to the original $80 gives the wrong answer.