Master Fundamentals of Ratio & Proportion

Explore the language of ratios by comparing quantities, mastering order and writing ratios in fraction or word form with practical examples from cooking, gaming, and daily life.

Learn to simplify ratios by dividing both numbers by their greatest common factor, converting decimals and fractions to whole numbers, and ensuring units are aligned to reveal the same relationship.

Compare two parts within the same group using part-to-part ratios, and distinguish them from simple ratios across different groups, illustrated with apples, boys and girls, and blue and pink candies.

Discover how to find and create equivalent ratios using multiplication or division, verify them with cross multiplication, and apply ratio tables to real life problems like recipes and maps.

Master the part-to-whole ratio by identifying the part and whole, calculating totals, writing the ratio, and simplifying, with examples like apples and classroom populations.

Learn how rates differ from ratios by using different units, and how unit rates express 'per one' in examples like 30 km in 3 hours.

Explore scale ratio: learn to convert measurements from maps and blueprints to real sizes using models, including 1 to 100, 1 to 50, and 1 to 30.

See how proportion creates balance by matching sizes and amounts in two ratios. Write a proportion by placing any two equivalent ratios in an equation, like 1/2 and 3/6.

Master solving proportion by using cross-multiplication to test equivalent ratios, form fractions with consistent positions, and solve for unknowns in real world scenarios like coins and scaled drawings.

Identify common mistakes in proportion by confirming that equal ratios exist, not just similar looking fractions. Simplify ratios and use cross multiplying to verify equality, keeping correct order.

Understand direct proportion by examining how increasing chocolates raises money and decreasing chocolates lowers it. See that y is directly proportional to x, with pens and cost as practical examples.

Explore direct proportion through practical examples such as notebooks and cost, distance and time, and flour and cookies, using fraction form, cross-multiplication, and solving for the unknown x.

Identify and fix the three common errors in direct proportion problems: misplacing quantities in the fractions, performing incorrect cross multiplication, and mixing incompatible units.

Explore inverse proportion, where one quantity rises as another falls, shown by pizza slices and workers-days. Use x proportional to 1/y and a constant product to verify this relation.

Solve inverse proportion by using a constant product of workers and days, and of speed and time, as shown in 4 workers 12 days and 6 workers x days.

Solve inverse proportion problems by applying the constant-product rule to scenarios like chairs rearranged into fewer rows, printers with varying speeds, brick loading times, and tanks emptied by multiple pipes.

Master inverse proportion by avoiding direct-proportion methods and always checking if quantities move in opposite directions. Organize data in tables and verify units to correctly apply the inverse relationship.

Identify inverse proportion quickly by checking opposite-direction changes, and apply the constant product rule to verify answers in exam problems.