Level 4: Fractions, Decimals, and Percentages in Everyday Math
Level 4 introduces parts of a whole: fractions, decimals, and percentages, usually in shopping, measurement, or scheduling contexts. You need to move fluidly among the three forms and apply them to a base amount.
Concepts to know
- Equivalent forms: 1/4 = 0.25 = 25%; 1/5 = 0.20 = 20%; 3/4 = 0.75 = 75%. Memorize the common eighths, fifths, and tenths.
- Percent of a number: convert the percent to a decimal and multiply. 15% of 80 = 0.15 × 80 = 12.
- Finding the whole from a part: if 20% of a total is 14, the total is 14 ÷ 0.20 = 70.
- Adding and subtracting fractions requires a common denominator; multiplying fractions does not.
- Unit price comparisons: divide price by quantity to compare.
Traps to watch
- Percent increase vs. percent of. A 20% markup on $50 is $10, giving $60 - not $50 × 20. Always multiply by the decimal, then add or subtract.
- Percent off then percent off. Two successive 10% discounts are not 20% off; the second discount applies to the reduced price.
- Mixing forms. Convert everything to decimals before comparing or computing.
- Denominator errors when adding fractions - never add denominators.
Rule of thumb
For any percent problem, write the relationship as part = percent × whole, fill in the two values you know, and solve for the third. This one equation handles "what is 30% of 90," "18 is what percent of 90," and "18 is 30% of what number."
Worked example
A jacket costs $80 and is marked 25% off. Discount = 0.25 × 80 = $20, so the sale price is $60. A 6% sales tax adds 0.06 × 60 = $3.60, for a total of $63.60.
Level 6: Measurement, Geometry, and Data Interpretation
Level 6 questions apply arithmetic to measurement and to information given in tables, charts, or short word problems. Expect area, perimeter, volume, unit conversion, and simple statistics.
Concepts to know
- Perimeter = distance around; area of a rectangle = length × width; volume of a rectangular solid = length × width × height.
- Unit conversions: 12 inches = 1 foot; 3 feet = 1 yard; 16 ounces = 1 pound; 60 minutes = 1 hour; 1,000 milliliters = 1 liter.
- Mean, median, mode, range: mean = total ÷ count; median = middle value when ordered; mode = most frequent; range = highest − lowest.
- Reading tables: identify the row and column labels before pulling a number.
Traps to watch
- Area vs. perimeter. Painting a wall needs area; fencing a yard needs perimeter.
- Squared and cubic units. An area answer is in square feet; a volume answer is in cubic feet.
- Conversion before computation. Convert all measurements to the same unit before multiplying.
- Median with an even count. Average the two middle values.
- Chart scales. Check whether a bar chart's axis starts at zero; a truncated axis exaggerates differences.
Rule of thumb
Before computing, write the formula and the target unit. If your formula output does not carry the right unit, you have chosen the wrong formula.
Worked example
A room is 12 feet by 15 feet with 8-foot ceilings. Floor area = 12 × 15 = 180 sq ft. Volume = 180 × 8 = 1,440 cubic feet. If carpet costs $3 per square foot, carpeting costs 180 × 3 = $540.