This course turns arithmetic into a tool for everyday problems. It starts with ratios: what they mean, how to simplify them and how to share an amount in a given ratio. Proportion and the unitary method lead to direct and inverse proportion, used for costs, work and food supplies. Percentages come next, with increase and decrease, then profit, loss, discount and markup. The course closes with averages, speed, distance and time, trains and relative speed, and simple and compound interest. Every topic is worked step by step with examples and practice questions with answers.
Primary Years
Arithmetic Applications (Level 1)
Ratio and proportion, the unitary method, direct and inverse proportion, percentages, profit and loss, averages, speed, distance and time, and simple and compound interest.
- 19 lessons
Overview
Lessons
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What a ratio is
Comparing two quantities of the same kind by dividing: same units first, the terms of a ratio, simplest form and equal ratios.
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Dividing a quantity in a given ratio
Sharing an amount in a ratio into two or three parts, by the fraction way and the k way, with the reason each rule works.
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Problems on ratios
Word problems on salaries, comparing ratios, books, students, alloys, matches, fields, prices and mixing two mixtures.
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Proportion
Equal ratios, means and extremes, fourth, third and mean proportional, the properties of a proportion, and finding a missing term.
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Unitary method and direct proportion
Finding the value of one unit first, then direct proportion: when one quantity grows the other grows in the same ratio.
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Inverse proportion
When one quantity goes up the other comes down: men and days, pumps and time, and food that lasts longer or shorter.
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Percentages, fractions and decimals
What per cent means, the fractions to know by heart, the pattern in sevenths, and changing between percentages, fractions, ratios and decimals.
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Finding percentages
Finding a percentage of a number, writing one number as a percentage of another, finding an unknown number, and an election problem.
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Percentage increase and decrease
New values after a percentage change, percentage change itself, shortcut results for comparing and for price and use, and population growth.
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Profit, loss and discount
Cost price, selling price and marked price, with the formulas for profit, loss, discount and the cost price from the marked price.
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Equal selling prices and false weights
Two results with proofs: equal profit and loss on the same selling price always means a loss, and a false weight brings a gain.
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Problems on profit and loss
Twelve worked problems: chocolates, commission, profit equal to loss, chairs, oranges, eggs, sugar, wheat, a television and apples.
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Marked price and markup
Markup on the cost price, markup and discount together, and harder problems that work back from the selling price.
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Average
The average or mean, the x̄ and sigma notation, sum equals number times average, and what happens when every number is changed.
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Problems on averages
Ages, parts of a list, visitors in a month, raising a batting average, run rates and one person replacing another.
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Speed, distance and time
Speed equals distance over time, changing km/h and m/s, average speed for equal distances, and speed and time for the same distance.
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Trains and relative speed
How far a train goes to pass a pole or a platform, relative speed in the same and opposite directions, and other journey problems.
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Simple interest
Principal, rate, time and amount, simple and compound interest compared, and the formula S.I. = PRT/100 used to find any one of them.
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Compound interest
The compound interest formula, interest added more than once a year, population growth and decrease, and different rates in different years.
Practice papers
Ten question papers that follow the lessons in order. Each has 20 questions for 50 marks (1 hour 30 minutes), with a key sheet and worked solutions.
MCQ tests
Ten tests of 25 multiple-choice questions (30 minutes each). Answer them on the page and check your score, or download the PDF with its key and solutions.
Class notes
Arithmetic Applications (Level 1)
Typed from the teacher's handwritten class slides, 58 pages.
Download the notes (PDF, 1.8 MB)