NB TCN Numeracy cheat sheet

Place value: each position is 10 times the one to its right; 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000.

Order of operations: parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.

Sign rules: negative × negative = positive; negative × positive = negative; subtracting a negative equals adding its absolute value.

Divisibility: by 3 if digit sum is divisible by 3; by 4 if last two digits form a multiple of 4; by 9 if digit sum is divisible by 9.

Rounding: look at the digit one place right of the target; 5 or more rounds up, 4 or less keeps the digit.

Fraction-decimal conversions: 1/8 = 0.125, 1/4 = 0.25, 1/3 ≈ 0.333, 1/2 = 0.5, 2/3 ≈ 0.667, 3/4 = 0.75.

Absolute value is distance from zero: |−7| = 7, and |a − b| gives the distance between a and b on a number line.

Prime numbers below 20: 2, 3, 5, 7, 11, 13, 17, 19; 1 is neither prime nor composite.

Metric prefixes: kilo = 1000, centi = 0.01, milli = 0.001 of the base unit.

Metric conversions: 1 km = 1000 m, 1 m = 100 cm = 1000 mm, 1 kg = 1000 g, 1 L = 1000 mL.

Customary length: 1 ft = 12 in, 1 yd = 3 ft = 36 in, 1 mi = 5280 ft.

Customary capacity and weight: 1 cup = 8 fl oz, 1 pint = 2 cups, 1 quart = 2 pints, 1 gallon = 4 quarts; 1 lb = 16 oz.

Time: 1 min = 60 s, 1 h = 60 min, 1 day = 24 h; elapsed time = end time − start time.

Unit conversion method: multiply by a conversion fraction equal to 1 with the unwanted unit in the denominator so it cancels.

Perimeter sums edge lengths; area of a rectangle = length × width; volume of a rectangular prism = length × width × height, in cubic units.

Temperature: F = (9/5)C + 32 and C = (5/9)(F − 32); water freezes at 0 °C = 32 °F.

A ratio compares two quantities; a proportion states two ratios are equal, a/b = c/d, solved by cross-multiplication ad = bc.

Unit rate = quantity ÷ number of units; unit price = total cost ÷ number of items.

Percent means per hundred: p% = p/100, so 35% = 0.35 = 7/20.

Percent of a number: part = percent × whole, using the decimal or fraction form of the percent.

Find the whole when given a part: whole = part ÷ percent; find the percent: percent = part ÷ whole × 100.

Percent change = (new − old) ÷ old × 100; a positive result is an increase, a negative result a decrease.

Successive percent changes multiply, not add: a 20% rise then a 20% fall leaves 1.2 × 0.8 = 0.96 of the original.

Scale drawings use a ratio such as 1 cm : 5 m; set up a proportion to convert drawing length to actual length.

Direct proportion: quantities grow together at a constant ratio; inverse proportion: their product stays constant.

Mean = sum of values ÷ count; median = middle value of an ordered list (average the two middle values if the count is even).

Mode is the most frequent value; a data set can have no mode or more than one mode.

Range = maximum − minimum; it measures spread but ignores all interior values.

Outliers pull the mean toward them but barely affect the median, so the median is more resistant to extreme values.

A bar graph compares categories; a line graph shows change over time; a circle graph shows parts of a whole totaling 100%.

In a circle graph, a sector's angle = percent × 360°, so 25% corresponds to 90°.

Reading tables: check row and column headings and total rows before computing any statistic.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; probabilities range from 0 to 1.

To estimate a total from a sample, multiply the sample rate by the population size.

Evaluate an expression by substituting the given value for each variable and following order of operations.

Combine like terms: 3x + 5x = 8x; unlike terms such as 3x and 5 cannot be combined.

Distributive property: a(b + c) = ab + ac, used to expand and to factor expressions.

Solve a linear equation by performing the same operation on both sides until the variable is isolated.

Slope of a line through two points = (y2 − y1)/(x2 − x1); slope is rise over run.

Slope-intercept form y = mx + b, where m is the slope and b the y-intercept.

Arithmetic sequences add a constant difference d; nth term = a1 + (n − 1)d.

Geometric sequences multiply by a constant ratio r; nth term = a1 × r^(n−1).

Inequalities: multiplying or dividing both sides by a negative number reverses the inequality sign.

Angles: complementary pairs sum to 90°, supplementary pairs sum to 180°, and the three angles of any triangle sum to 180°.

Vertical angles are equal; angles on a straight line sum to 180°; angles around a point sum to 360°.

Rectangle area = length × width; triangle area = ½ × base × height; parallelogram area = base × height.

Trapezoid area = ½ × (base1 + base2) × height; circle area = πr², circumference = 2πr.

Pythagorean theorem: for a right triangle, a² + b² = c², where c is the hypotenuse.

Volume: rectangular prism = lwh; cylinder = πr²h; sphere = (4/3)πr³.

Similar figures have equal angles and proportional sides; scale factor k multiplies lengths, k² multiplies areas, k³ multiplies volumes.

A cube has 6 faces, 12 edges, and 8 vertices; surface area of a cube = 6s².

Coordinate plane: distance between points = √((x2 − x1)² + (y2 − y1)²); midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Identify the unknown first, assign it a variable, then translate each condition into an equation.

Estimate before computing: round to convenient numbers to check whether an exact answer is reasonable.

Work rate: combined rate = sum of individual rates; time together = 1 ÷ combined rate.

Average speed = total distance ÷ total time, not the average of the separate speeds.

Multi-step percent problems: apply discounts before tax, since tax is computed on the discounted price.

Check answers by substitution or by reversing the operation; a result that contradicts the units signals an error.

Dimensional analysis: keep units attached to numbers so mismatched units, such as hours and minutes, are caught.

Break complex word problems into stages and record intermediate results with their units.