Integers, Fractions, Decimals, Rounding, Ratios, Averages, and Business Graphs
What this domain tests
This area bundles the arithmetic every later topic depends on: signed integers, fractions, decimals, rounding, ratios, averages, and business graphs. Items are short word problems plus graph-reading questions in which the data must be extracted from a described chart.
Core rules
- Signs and order of operations: parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Subtracting a negative adds: 14 − (−6) = 20. A negative times a negative is positive.
- Fractions: multiply straight across; divide by inverting the second fraction and multiplying. Add or subtract only after building a common denominator. Reduce by dividing numerator and denominator by their greatest common factor.
- Decimals and rounding: align decimal points when adding. To round to a place, look at the single digit to its right - 5 or more rounds up. Money answers are reported to the cent, but keep unrounded values in intermediate steps.
- Ratios: a ratio compares parts. In a 3:2 mix the whole is 5 parts, so the first quantity is 3/5 of the total, not 3/2 of it. Simplify by dividing both terms by a common factor.
- Unit price: total cost ÷ number of units; compare unit prices to judge the better buy.
- Averages: mean = sum ÷ count. When groups differ in size, use a weighted average: multiply each value by its weight, sum, then divide by the total weight.
- Business graphs: a line graph shows trend over time, a bar chart compares categories, and a pie chart shows parts of a whole, where each slice percentage × total gives its value. Check the axis scale - a broken axis exaggerates change.
Worked example
A salesperson's commissions for four months were $1,250, $980, $1,505, and $1,765. Find the average monthly commission. Sum = 1,250 + 980 + 1,505 + 1,765 = 5,500. Average = 5,500 ÷ 4 = $1,375.
Traps that cost marks
- Rounding at every step instead of only at the end, which shifts the final cent.
- Treating a part-to-part ratio as a fraction of the whole.
- Averaging percentages from groups of different sizes without weighting them.
- Reading a pie slice percentage as a dollar amount.
- Misreading a graph scale that starts above zero.