Perfect Your Math Fundamentals (Pre-Algebra)

Explore integers as the building blocks of operations, including positive, negative, and zero; learn to read the number line, compare values, and arrange integers in ascending order.

Learn to add and subtract integers by applying sign rules, subtracting smaller from larger, and grouping positives and negatives, with multiple-number examples.

Explore multiplication and division of integers by applying sign rules: same signs yield positive results, different signs yield negative results, with even or odd counts determining the final sign.

Master the consecutive signs rule for integers in pre-algebra: if signs are the same, result is positive; if different, result is negative, with steps to convert to a single sign.

Apply powers on integers: negative bases with odd exponents stay negative; even exponents make them positive; positive bases stay positive. Illustrate with -3^3 = -27 and 2^5 = 32.

Master divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11 using last digits and the sum of digits to check divisibility.

Apply divisibility tests for composite numbers using coprime prime factors, such as three and four for twelve, seven and two for fourteen, and nine and two for eighteen.

Learn prime factorization by dividing a number by successive primes from two to express it as a product of prime factors. Explore factors and divisibility with examples like 12.

Discover how to find multiples and the lowest common multiple using listing multiples and prime factorization, with practical examples.

Learn how to find the lcm using the division method by repeatedly dividing by the smallest prime factor, then multiplying the prime factors to obtain the lcm.

Learn to solve word problems with least common multiples, using the division method to compute LCMs for numbers like 3, 7, 12, and 14 and predict when events ring together.

Learn to find the highest common factor using the division method to solve word problems, such as largest tile size, longest measuring tape, and tin capacities.

Explore fractions by defining numerator and denominator, classify them as proper, improper, mixed, unity fractions, and decimal and vulgar fractions, with circle, square, and triangle examples.

Master equivalent fractions by multiplying or dividing the numerator and denominator by the same number to keep the value unchanged, and reduce to lowest form.

Learn how to convert unlike fractions to like fractions using the least common multiple of denominators, then compare fractions with cross-multiplication and rules for positive and negative values.

Add and subtract fractions by converting to like fractions, finding common denominators, and reducing to lowest terms; convert improper fractions to mixed numbers and back.

Learn how to multiply and divide fractions by converting mixed numbers to improper fractions, canceling common factors, multiplying numerators and denominators, and using reciprocals for division.

Demonstrates how to find fractions of quantities, such as three quarters of four hundred pounds, by dividing a whole into equal parts and applying simple calculations.

Learn to write decimal numbers in expanded form and read decimals by identifying place values before and after the decimal, including tenths, hundredths, and thousandths.

Convert numbers from expanded form to decimal form, practicing reading decimals such as 5.63, 13.146, and 0.562 (or 562 thousandths), and reinforcing place value across hundreds, thousands, and decimals.

Learn to convert decimals to fractions and mixed numbers, placing zeros for decimal places, and reducing to lowest terms.

Differentiate like decimals from unlike decimals by the digits after the decimal. Convert to like decimals by adding zeros to match the decimal places for easier addition, subtraction, and comparison.

Learn to compare and order decimal numbers by first comparing whole number parts, then decimal digits, converting to like decimals when needed, and arranging values in ascending or descending order.

Learn to add and subtract decimal numbers by aligning decimal points, placing numbers in the same vertical line, and converting to like decimals when needed.

Learn how to multiply decimal numbers by aligning decimal places, counting total decimal digits, and shifting the decimal point, with practical examples.

Master the order of operations by applying PEMDAS: compute inside parentheses first, evaluate exponents, then handle multiplication and division from left to right, followed by addition and subtraction.

Practice problems on nested parentheses and innermost expressions, using the order of operations. Solve with brackets and square brackets, prioritizing multiplication and division, then exponent and decimals.

Master the order of operations with bodmas by solving nested brackets, exponents, and left-to-right multiplication, division, addition, and subtraction through step-by-step practice problems.

Explore solving expressions with BODMAS, tackling brackets of various types and applying left-to-right rules for division, multiplication, addition, and subtraction.

Identify whether numbers are rational or irrational by applying identities and simplifying expressions with pi, square roots, and decimals to reveal rationality or irrationality.

Explore the difference between rational and irrational numbers and how to find rationals between 4 and 6. Show that rational times irrational is irrational; two irrationals can be rational.

Explore terminating decimals with a finite number of digits after the decimal and non-terminating recurring decimals with infinite repeating blocks, including dot notation to mark the repeating sequence.

Learn to convert terminating decimals to fractions by counting decimal places, forming a fraction with a power of ten in the denominator, and simplifying to lowest terms.

Learn how rounding makes calculations easier and helps estimates. See examples like 862 rounded to 60, 99, and 2000, and learn about repeating and irrational decimals.

Master rounding techniques by using place value, target digit, and the next-digit rule to decide rounding down or up, replacing smaller places with zeros.

Learn rounding to units, tens, hundreds, and thousands by applying the next digit rule: keep or raise the target and zero trailing digits, e.g., 257 becomes 260.

Master rounding to significant figures by identifying the first significant digit, counting zeros between digits, and applying rules for decimals and whole numbers to achieve precise estimates.