How to Ace Arithmetic

Explore the introduction to percentages, including how to use a common base of 100 for comparison and to convert between fractions, decimals, and percentages.

Master fractions and their equal percentages, memorize common values like one-half equals 50 percent and one-twelfth equals 8.33 percent, and learn quick conversions and their multiples of two hundred percent.

Learn the four basic concepts of percentages—what percentage of a quantity, what percentage a quantity is of another, and how to compare increases and decreases—using absolute differences and reference values.

Practice questions on basic percentage concepts using a data table of students' math, physics, and chemistry scores. Analyze percent of a score, percent differences, and comparisons.

master percentage increase and decrease, compute absolute increases, compare final value to the initial value, and apply compounding across years for true growth.

Learn to calculate percentage increases and decreases from a base value with practical examples, including 20 percent rises and the growth formula x plus xy over 100.

Explore percentage more and percentage less concepts through three approaches, with examples like 25% more than B, 40% less, and formulas to restore original values.

Learn to distinguish percentage points from percentages by measuring the difference in magnitude between two percent values, with basis points guidance and practical examples.

Analyze how price and quantity changes affect revenue by the product of two quantities, covering three approaches and the successful growth formula.

Explore how percentage concepts drive mensuration: compute area and perimeter changes for squares and rectangles, and volume changes for cylinders using percentage growth and range reasoning.

Master basic concepts of profit, loss, and discount by comparing cost price, market price, and selling price, with discounts calculated on market price to determine final selling price.

Explore basic concepts of profit, loss, and discount through practical questions that show how selling price relates to cost price, and how discounts affect profit percentages.

examine how two articles with the same cost price produce an overall profit or loss, using 10%/−10% and 20%/10% examples and the (profit−loss)/2 rule.

Two articles with the same selling price can yield an overall loss, explained through cost price, selling price, and a shortcut formula for total profit or loss.

Explore successive sales by calculating cost price across multiple trades using profit and loss, percentage growth, and the successful growth formula, with examples of 20 percent and 10 percent profits.

Learn to compute the overall price under successive discounts, using market price, selling price, and single-discount equivalence with 20% and 10% examples.

Master quantity-based profit and loss problems by treating quantity as the pricing criterion. Apply the basic concept, a shortcut formula, and examples with articles and mangoes to compute profit percentages.

Explore how dishonest traders inflate profits by weight and price in milk and goods, calculating profit percentage from cost price and selling price with weight deception examples.

Learn how partnership profits are shared by the ratio of capital investments, time in business, and the product of both when time varies.

Apply partnership concepts to calculate profit shares from investment ratios and time periods in practical examples, determining total profit and per-partner shares.

Discover how stocks and shares illustrate ownership, calculate rate of return on face value versus market value, and distinguish corporate stocks from government bonds.

Explore practical stocks and shares problems, calculating income from face value with premiums, determining number of shares, and comparing rate of return to choose the best investment option.

Explore basic concepts of simple interest, including principal, rate per annum, and time, and learn the formula for interest and total amount.

Explore simple interest concepts through practice questions, applying the simple interest formula to determine principal, rate, time, and interest, and compare total amounts.

Illustrate practice questions on basic concepts of simple interest, with two parts at different rates; compute equal interests, find the difference, and determine the effective rate.

Explore simple interest, where interest accrues on the principal, so the total amount becomes multiples like double or triple. Use two shortcuts to find years for k-times growth.

Explore simple interest installments by tracking principal and accrued interest, comparing repayment from principal versus total due, and deriving installment formulas with a 10 percent rate example.

Explore compound interest basics, contrast it with simple interest, and see how principal grows as interest accrues on the previous year, forming a geometric progression.

Explore the basic concepts of compound interest through formula, component method, and effective growth, with practice questions and annual compounding examples.

Explore how compound interest varies with different intervals, including half-yearly, quarterly, and monthly, by applying the applicable period rate and the compounding frequency to compute future value.

Explore compound interest problems where a sum becomes n times itself, using the formula and geometric progression, with examples like doubling in five years and twenty-seven times in eighteen years.

Calculate installments in compound interest using multiple methods, including equal annual installments and present-value approaches, illustrated with a 10% rate, 10,000 principal, yearly repayments, and compare with simple interest installments.

Explain the difference between compound interest and simple interest with practical examples, basic concepts, and a shortcut formula for a 15,000 principal at annual rates.