MATHEMATICS- SUPER BASICS, EASY TRICKS

Introduction to divisibility tests, and which tests we study and why, covering tests for 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 20, and 25.

Identify divisibility by 2, 5, and 10 using the last-digit rule; recognize even and odd numbers and apply unit-digit checks to judge divisibility, with examples.

Learn divisibility tests for three and nine using the digit sum method; numbers divisible by nine are divisible by three, but not all divisible by three are divisible by nine.

Explore divisibility tests for four and eight using last two digits and last three digits, with examples and the rule that odd numbers are not divisible by even numbers.

master divisibility tests for 6, 12, and 15 by combining 2, 3, 4, and 5 rules, using last digits for 2 and 5, and digit sums for 3.

Learn the divisibility test for 11 by splitting a number into two sets of alternate digits, summing each, and checking whether the difference is zero or a multiple of 11.

Master divisibility tests for 20 and 25 by checking the last two digits, using the 20 rule (00, 20, 40, 60, 80) and the 25 rule (00, 25, 50, 75).

Learn to apply divisibility tests efficiently to reduce fractions to lowest form, identify common factors, and determine equivalent fractions quickly using tests for 5, 3, 9, 11, and 25.

Explore a concise chart of 13 divisibility tests, with last-digit rules for 2,5,10 and last-two-digit, digit-sum, or alternate-digit tests for others to speed up problem solving.

Explore the basics of factorization by defining factors, primes, and composites, clarify common confusions between prime and composite numbers, and use divisibility to speed up factorization.

Learn the meaning of factors and multiples, how numbers divide evenly, and that every number is a factor and a multiple of itself, with finite factors and infinite multiples.

Explore prime and composite numbers, including definitions, examples, and key rules such as two is the only even prime and one is neither prime nor composite, with divisibility insights.

Master the factorization technique by breaking numbers into prime factors using divisibility tests, starting with even numbers and progressing to larger factors to reach a product of primes.

Explore prime and coprime numbers, their factors, and the key property that numbers divisible by two and nine are divisible by 18.

Learn to create divisibility tests using coprime numbers and prime factors. Apply factorization to test numbers quickly and improve speed through practice.

Explore the basics of hcf and lcm, including highest common factor and greatest common factor, and how to find factors, common factors, and the least common multiple.

Explore how to find the HCF and LCM using the prime-factorization method, by factoring numbers, identifying common bases and least powers, with practical examples.

Master eight quick tricks to find hcf and lcm orally in seconds, including least-factor checks, descending-factor tests, ignoring multiples, and prime-factorization as a fallback.

Learn to compute hcf and lcm of fractions and decimals, reduce fractions to the lowest form before applying the formulas, and align decimal places to obtain correct results.

Learn to compute the HCF and LCM of algebraic terms and numerical coefficients using prime factorization, identifying common and uncommon bases and raising powers to the lowest or highest.

Learn to solve hcf and lcm word problems using prime factorization and data interpretation. Apply gcd and lcm to rope cuts, signals, juices, and chocolate packets, noting greatest and minimum.

Explore part two of hcf-lcm word problems, applying prime factorization, divisibility tricks, and remainder methods to find the least common multiple and greatest common factor.

Master the basics of fractions and decimals, including how fractions form proper, improper, and mixed types, convert between fractions and decimals, and visualize parts with simple examples.

Master how proper fractions stay below one and improper fractions exceed one. Convert them to mixed numbers with a whole part and a remainder.

Learn how to convert decimals to fractions by shifting the decimal point, forming fractions such as 0.7 to 7/10 and 0.07 to 7/1000, then reduce to lowest terms using divisibility.

Convert fractions to decimals using the denominator rule for ten, hundred, thousand, ten thousand, or apply long division for other cases, including terminating and recurring decimals.

Learn how recurring decimals form and convert to fractions, using bar notation to denote repetition and step-by-step examples, including converting mixed numbers and recurring decimals to fractions.

Explore quick methods for adding and subtracting fractions and mixed fractions, using shortcuts for common denominators, the least common multiple, and splitting mixed numbers into whole and fractional parts.

Multiply and divide fractions and mixed fractions using factorization, divisibility tests, and reciprocal techniques, converting mixed fractions to improper forms for quick, accurate cancellation.

Learn addition and subtraction of decimals by aligning the decimal point under decimal points and equalizing decimal places with zeros, using carry forward.

Master multiplication and division of decimals by shifting decimal points, counting decimal places, and converting between fractions and decimals through practical examples and step-by-step rules.

Explore tricks for ranking fractions by ascending or descending order using cross multiplication and denominator cues to identify the highest and lowest fractions.

Learn the cross multiplication trick to compare two fractions by multiplying a numerator by the other fraction's denominator to determine which is larger, with limitations for multiple fractions.

Learn how to compare multiple fractions by concentrating on denominators, use a common denominator when possible, and order by numerators to determine ascending or descending sequences.

Focus on numerators to compare fractions using three tricks for ascending and descending order, including cross multiplication. When numerators are equal, the lowest denominator yields the highest value.

Learn a trick for comparing proper fractions that share a common difference between numerator and denominator, then order them by the smallest or largest numerator for ascending or descending results.

Learn trick five for comparing improper fractions by using a common difference between numerators and denominators to arrange fractions in ascending or descending order, with practical examples and twists.

Convert fractions to decimals to compare quickly, especially with small denominators. Arrange in ascending or descending order, and use reciprocals for difficult proper fractions to determine highest and lowest.

Explore what percentage means and how to convert fractions to percent, using a common base of 100 to compare scores. Practice quick, word-problem applications for exam-ready percent calculations.

Convert fractions to percentages by multiplying by 100 and keeping the denominator, using decimal shifts and cross-multiplication as needed. Master practical fraction-to-percent conversions through varied examples.

Learn to convert percent to fraction, reduce to simplest form, and solve exam-style examples. Explore conversion between fractions, decimals, and percentages, including numbers over 100 percent.

Use the percentage chart and a quick shortcut to turn percent into fractions for exam problems. Memorize base values like 1/2, 1/4, 1/7, and 1/11 to derive others.

Master percentage increase and decrease using a base of 100, applying simple multipliers (120, 80) to solve word problems and student count scenarios.

Solve percent-based word problems from basic to medium difficulty, including percent of totals, difference in counts, mango and fruit distributions, revenue changes, and successive discounts, using three solving methods.

Explore the basics of ratio and proportion, comparing two quantities with A is to B and A over B. Apply cross multiplication and common multiples to solve examples.

Learn how to combine two or three ratios to form a single ratio, eliminate intermediate terms, and use multiplication, cancellation, and reciprocals to find the desired relation.

Learn to convert fractional ratios to simple whole-number ratios by multiplying both terms by a common factor, using reciprocal methods, and reducing to lowest form for easy calculations.

Learn mean proportional, third proportional, and fourth proportional in ratios with clear rules, cross-multiplication, and square roots, illustrated by practical examples.

Learn two practical methods to solve ratio and proportion word problems: use a common multiple for shares, or split the total by the sum of the ratio parts, with examples.

Discover how the number line places zero at the center, marks positive and negative numbers, including fractions, and guides addition to the right and subtraction to the left.

Learn how to multiply and divide with negative and positive numbers, apply the even-negatives rule for positive results, handle fractions and reciprocals, and build fluency with examples.

Learn simple rules for adding and subtracting negative and positive numbers and fractions, using magnitude, sign of the larger number, and a number line to build fluency through practice.

Congratulate students on completing the course and building math basics through steady practice and puzzles. Focus on consistency, confidence, and group study to master divisibility, factorization, fractions, and decimals.