The Complete Course On Math Fundamentals

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Learn to simplify expressions by treating a lone variable as having an invisible coefficient of 1 and by combining like terms, using a van diagram to visualize patterns and coefficients.

Identify natural numbers, whole numbers, integers, rational and irrational numbers, fractions, mixed numbers, decimals, even and odd numbers, primes, composites, and absolute value with examples.

Explore the properties of numbers, including commutative and associative laws for addition and multiplication, plus identity and multiplicative inverse, with practical examples.

Explore commutative and associative properties of addition and multiplication, identify the identity property, and learn multiplicative inverses through examples like 2+5=5+2 and reciprocal concepts.

Explore basic division with a guided long division worksheet, solving problems step-by-step through subtraction until the remainder is zero, including 25 divided by 5 and 100 divided by 25.

Explore the distributive property with practice problems and video solutions, applying outside multiplication to terms inside parentheses and simplifying expressions with like and unlike terms.

master the least common multiple using backward thinking, the bigger of the given numbers, and factor trees with natural numbers, plus a worksheet and video solution.

Explore divisibility rules for 2 to 10, using last-digit tests for 2 and 5, digit-sum tests for 3 and 9, and checks for 4, 8, 6, 7, and 10.

Explore solving chapter two problems by finding the least common multiple and greatest common factor, then apply the order of operations with parentheses, exponents, and multiplication/division and addition/subtraction.

Explore how to classify decimals as terminating, nonterminating, or repeating using a guided worksheet and video solution, with examples like 8.7, 2, pi, and 3/4.

Master converting fractions to decimals through step-by-step long division, learn decimal placement and repeating versus terminating decimals.

Convert decimals to fractions by using digits after the decimal as the numerator and a power of ten as the denominator, then simplify with the greatest common factor.

Convert percent to fractions through guided worksheet video solutions and practice examples, converting 25, 10, 50 and more percent, and simplify using the greatest common factor.

Master the most frequently used fractions, decimals, and percentages from the handout for quick test solutions. Convert fractions like one fourth to 0.25 and decimals to percentages to save time.

master percent word problems by setting up proportions, applying cross products to find the missing value, and converting between decimals and percent values.

Classify fractions as proper, improper, or mixed numbers by comparing numerator and denominator; learn to identify and form proper fractions, improper fractions, and mixed numbers with provided examples.

Explore equivalent fractions by visualizing one half and its equivalents, such as 1/2 = 2/4 = 3/6. Verify equality by multiplying top and bottom by the same number.

Use the cross product to compare fractions and determine which is greater, then find the lowest common denominator and convert to that denominator, identifying equivalent fractions, numerators, and decimals.

Develop skills in subtracting fractions by finding the lowest common denominator, performing the subtraction on the numerators, and simplifying results, including converting to mixed numbers when needed.

Multiply fractions by cross-multiplying numerators and denominators, whether denominators are the same or different, then simplify the result using the greatest common factor.

Practice multiplying fractions using cross multiplication, diagonal simplification, and pre-multiplication reduction on a fractions worksheet, applying greatest common factor and the identity property to produce simplified results.

Discover how to divide fractions by keeping the first term, flipping the second term, and turning division into multiplication; apply the method to any denominators with examples.

Solve chapter five quiz problems by adding, subtracting, and dividing fractions and simplifying to lowest terms. Find the lowest common denominator and apply reciprocal multiplication for division.

Multiply mixed numbers by converting to improper fractions, multiply numerators and denominators, then convert back to a mixed number, using greatest common factor to simplify.

Convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator, and convert improper fractions to mixed numbers via division, then simplify.

Convert mixed numbers to improper fractions, divide by multiplying by the reciprocal, and simplify results, using same-denominator addition and final mixed-number forms.

Learn to compare decimals by place value, determining greater than, less than, or equal to, using ones, tenths, hundredths, and thousandths, including negative numbers, with number-line reasoning.

Learn how to round numbers to the nearest thousand by examining the hundreds digit, applying the five-or-higher rule, and setting subsequent digits to zero, with worked examples.

Learn to add integers with different signs using the number line, absolute value, and sign rules, with examples like -8 + 2 and -10 + 4.

Master adding integers using a number line and sign-reassignment techniques to simplify problems. The lesson includes a worksheet, video solution, and answer key.

Learn to subtract integers with the same signs by adding magnitudes and keeping the sign. See examples like 6 minus 4 and 6 minus 8, plus a number line visualization.

The lecture teaches multiplying integers by counting negative terms: an even number of negatives yields a positive product, while an odd number yields a negative one, shown with several examples.

Multiply integers by signs: count the negative terms; even negatives yield positive, odd negatives yield negative, then multiply the magnitudes.

Develop skill in dividing integers by counting negative terms to determine sign, using even or odd negatives to decide positive or negative quotients, with step-by-step and shortcuts.