Number: Fractions, Decimals, Percent, Ratio, and Rate
Fractions, decimals, percents, ratios, and rates are five ways to describe the same kinds of comparisons, and Grade 7 expects you to convert among them freely and choose the efficient form.
For fractions, build equivalent fractions with a common denominator before adding or subtracting; never add the denominators. To multiply, multiply numerators and multiply denominators, then simplify. To divide, multiply by the reciprocal.
Decimals either terminate or repeat. Convert a fraction to a decimal by dividing, and a decimal to a percent by multiplying by 100. Percent means "per hundred," so 18% of 250 = 0.18 × 250 = 45. Percent change compares the change to the original amount: change ÷ original × 100.
A ratio compares quantities. Keep straight whether it is part-to-part (boys : girls) or part-to-whole (boys : students). A rate compares quantities with different units, and a unit rate gives the amount per one unit - the basis for unit price and "best buy" questions. Set up proportions with matching units in matching positions.
Traps: adding denominators (1/2 + 1/3 is not 2/5); forgetting to flip when dividing by a fraction; applying a percent increase to the new amount instead of the original; and comparing prices without converting to the same unit first.
Worked example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Rule of thumb: rewrite every division by a fraction as multiplication by its reciprocal before calculating, then simplify before multiplying when possible.