Math101 · Independent Ontario learning library
01 · Subject library
Foundations
Numbers, fractions, decimals, ratios, and the arithmetic that everything else rests on.
Start with Absolute Value →36 complete · 36 total lessons
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01Absolute ValueThe absolute value $|x|$ is the distance from the real number $x$ to $0$ on a number line. Distance is never negative, so $|5|=5$, $|-5|=5$, and $|0|=0$.Full lesson + sheet02Adding FractionsAdd fractions by expressing them in equal-sized parts, combining the numerators, and simplifying.Full lesson + sheet03AnnuitiesAn annuity is a sequence of equal payments at regular intervals whose value depends on compounding and payment timing.Full lesson + sheet04BudgetingA budget is a realistic plan for income, spending, saving, debt, and irregular costs over a defined period.Full lesson + sheet05Compound InterestCompound interest applies growth to a changing balance, creating exponential saving and borrowing models.Full lesson + sheet06DecimalsDecimals use base-ten place value to represent whole and fractional quantities.Full lesson + sheet07Dividing FractionsDividing by a fraction asks how many groups of that fractional size fit in a quantity.Full lesson + sheet08Equivalent FractionsEquivalent fractions name the same number using different-sized unit parts. Multiplying or dividing numerator and denominator by the same nonzero number preserves value because it multiplies the fraction by $k/k=1$.Full lesson + sheet09EstimationEstimation uses rounding, compatible numbers, benchmarks, and bounds to produce useful approximate values and check exact work.Full lesson + sheet10ExponentsExponents record repeated multiplication and provide a compact language for powers, roots, scientific notation, algebra, and growth.Full lesson + sheet11Factors and MultiplesA factor divides a whole number with no remainder; a multiple is the result of multiplying that number by an integer.Full lesson + sheet12FractionsFractions represent division, parts of a whole, ratios, and points on the number line.Full lesson + sheet13Greatest Common FactorThe greatest common factor (GCF) of two or more nonzero whole numbers is the largest positive integer dividing every number exactly.Full lesson + sheet14IntegersIntegers extend whole numbers to include negative values, opposites, and directed change.Full lesson + sheet15Irrational NumbersAn irrational number is a real number that cannot be written as a ratio $a/b$ of integers with $b\ne0$. Its decimal expansion neither terminates nor repeats a fixed block.Full lesson + sheet16Least Common MultipleThe least common multiple (LCM) of positive integers is the smallest positive number that is a multiple of each.Full lesson + sheet17MeasurementMeasurement compares a quantity with a chosen unit and reports a value, unit, and appropriate precision.Full lesson + sheet18Multiplying FractionsMultiplying fractions finds a fraction **of** another quantity. The product $\frac ab\cdot\frac cd=\frac{ac}{bd}$ follows from taking $a/b$ of $c/d$ of one whole.Full lesson + sheet19Natural NumbersNatural numbers are the counting numbers. Many texts define $\mathbb N=\{1,2,3,\ldots\}$, while others include $0$.Full lesson + sheet20Number LineA number line represents real numbers as points ordered from left to right. Equal distances represent equal numerical differences, zero sets the origin, and a chosen unit fixes scale.Full lesson + sheet21Order of OperationsOrder of operations is a convention for reading an unparenthesized expression consistently.Full lesson + sheet22PercentPercent describes a quantity out of one hundred and connects fractions, decimals, rates, discounts, taxes, interest, and data.Full lesson + sheet23Prime FactorizationPrime factorization expresses an integer greater than $1$ as a product of prime numbers. Apart from the order of factors, this product is unique—the Fundamental Theorem of Arithmetic.Full lesson + sheet24Prime NumbersA prime number is a whole number greater than $1$ with exactly two positive factors: $1$ and itself. A composite number greater than $1$ has more than two positive factors.Full lesson + sheet25Proportional ReasoningProportional reasoning recognizes and uses constant multiplicative relationships across tables, graphs, equations, rates, and scale.Full lesson + sheet26ProportionsA proportion states that two ratios are equal and can solve scale, percent, rate, and similarity problems.Full lesson + sheet27RatesRates compare quantities with different units and make speed, price, density, productivity, and proportional change measurable.Full lesson + sheet28Rational NumbersRational numbers are ratios of integers and include fractions, integers, terminating decimals, and repeating decimals.Full lesson + sheet29RatiosRatios compare quantities multiplicatively and power proportions, scale drawings, mixtures, probability, rates, and percent.Full lesson + sheet30Real NumbersReal numbers fill the number line and include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.Full lesson + sheet31Scientific NotationScientific notation expresses extremely large or small values as a number from 1 to 10 multiplied by a power of ten.Full lesson + sheet32Simple InterestSimple interest calculates interest only on the original principal and makes borrowing, saving, time, and rate relationships transparent.Full lesson + sheet33Square RootsFor $a\ge0$, the principal square root $\sqrt a$ is the unique nonnegative number whose square is $a$. Thus $\sqrt{49}=7$, not $\pm7$.Full lesson + sheet34Subtracting FractionsFractions can be subtracted only after they describe pieces of the same size. For $\frac ab-\frac cd$, rewrite both with a common nonzero denominator, then subtract numerators while preserving the common denominator.Full lesson + sheet35Unit ConversionUnit conversion multiplies by equivalence ratios equal to one so a quantity changes form without changing size.Full lesson + sheet36Whole NumbersWhole numbers describe zero and positive counting quantities through place value, operations, factors, and estimation.Full lesson + sheet
