[Mathematic course] Master the Fundamentals of Algebra

Discover how to simplify a fraction by finding the greatest possible common number between the numerator and denominator, then divide by that number to reach the simplest form.

Master how to simplify fractions by dividing numerator and denominator by the greatest common factor to reach the simplest form, using examples like 3/6, 6/9, and 8/24.

Learn to simplify fractions with the greatest common factor. Follow four steps: write factors, find the largest common factor, divide, and write the reduced fraction (12/24 becomes 1/2).

Learn to find the greatest (or highest) common factor, identify common factors, and simplify fractions such as 42/84, 54/72, and 18/24.

Explore prime numbers as numbers with exactly two factors, one and themselves, starting from 2, 3, 5, 7, and 11, and learn why 2 is the only even prime.

Explore equivalent fractions, which have the same value regardless of numerators and denominators, and learn to obtain them by multiplying or dividing both numerator and denominator by the same number.

Explore finding equivalent fractions by multiplying or dividing numerator and denominator by the same number, identify simplest forms, and compare examples like 1/3 and 5/10.

Identify equivalent fractions by multiplying the numerator of one by the denominator of the other and vice versa, then compare products for equality.

Multiply or divide the numerator and denominator by the same number to find many equivalent fractions, such as 1/2 and 2/4. Simplify 75/100 to 3/4 and continue.

Master algebra basics: compare fractions with the same denominator or same numerator. The larger numerator wins with a common denominator; the smaller denominator wins with a common numerator.

Master the fundamentals of algebra by learning to compare fractions using same denominator or same numerator rules, and work through examples like five over three versus five over four.

Master the fundamentals of algebra by learning to compare fractions with different numerators and denominators: simplify, handle equal numerators or denominators, and use the lowest common multiple to compare.

Find the lowest common multiple using prime factorization to create a common denominator for comparing fractions. Apply this with 3/4 and 1/3 by converting to 9/12 and 4/12 to compare.

Define multiples as products of a number with another, and factors as numbers multiplied to obtain results, illustrated by 6 × 3 = 18 and 5 × 4 = 20.

Decompose numbers into prime factors, list factors by their maximum frequency, and multiply them to find the lowest common multiple. See a step-by-step example with 12 and 8, yielding 24.

Learn the easy way to find the lowest common multiple by listing multiples, then select the smallest number appearing on all lists, with examples like 12 and 8 producing 24.

Distinguish proper fractions, where the numerator is less than the denominator (1/5), from improper fractions, where the numerator is greater than or equal to the denominator (7/4).

Explore mixed fractions, proper and improper fractions, and learn to convert between improper fractions and mixed numbers using division and multiplication steps, with examples like 46/7 and 4 1/2.

Explore the three types of fractions: proper fractions, mixed numbers, and improper fractions. Proper fractions are less than one; improper fractions have a numerator greater than denominator and exceed one.

Revise the types of fractions by distinguishing proper fractions from improper fractions, noting that proper fractions are less than one and improper fractions are greater than or equal to one.

Define exponentiation as multiplying a base by itself a specified number of times, written as b to the power of n, as in 2 to the 5th power.

Define exponent concepts, identify the base and exponent, and show how powers are formed by multiplying a number by itself, with exponent form, expanded form, and standard form.

Learn how to add and subtract exponents by ensuring the bases are the same, then combine coefficients and keep the common exponent, with practical power examples.

Explore the laws of exponents, including the product, quotient, power, zero, and negative exponent rules, with detailed explanations to master exponents.

Master the product law for exponents: multiply like bases, keep the base, and add exponents; when bases differ, multiply the bases first and then apply the exponent.

Explore the quotient rule as the opposite of the product rule for exponents, with multiplication adding exponents and division subtracting them; keep the base the same.

Master how the power of a power rule works by multiplying exponents when raising a power to another power, and apply it to solve equations with nested powers.

Master the power of a product rule by distributing an exponent to each factor, producing a^n b^n, with worked examples illustrating the rule.

Explore the power of the quotient rule by distributing exponents to every term inside brackets.

Master the zero exponent rule: any non-zero number raised to the power of zero equals one, so x^0 = 1 for any non-zero x.

Explore the negative exponent rule and learn to convert negative exponents to positive by taking reciprocals and placing the number in the denominator.

Learn exponent rules for algebra: multiply powers with the same base by adding exponents, divide by subtracting exponents, and convert negative exponents to reciprocals, including exponent of an exponent.

Explore the power of ten by understanding exponents and writing numbers as one followed by zeros, with examples such as ten to the two, three, and beyond.