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Ratios Made Easy: Concepts, Tricks & Applications

Understand ratios. Learn useful shortcuts. Solve real problems.

6 Units27 MissionsAbout 6 hoursCourse map

Complete the Course to Earn a Certificate and Join the Hall of Fame

A bright workbench has two clear measuring cups, a round bead and a star. It shows the course theme. It does not give answers to a question.
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Equal-part bars and a clock. These connect ratio comparisons with sharing and rates.

A CLOSER LOOK

See the comparison

Mix the right amounts, compare fairly and solve everyday problems. Understand why a shortcut works before using it.

See it. Try it. Make it yours.

  1. See the comparison

  2. Keep the same mix

  3. Make ratios visible

Beginners aged 10 and above, including learners with limited English. · What to know before you start

Bring with you: Count whole objects. Add, subtract, multiply and divide small whole numbers. Read simple English with support if needed. Recognise a half as one of two equal parts. All ratio notation, decimal notation used here, percentages, units and graph conventions are taught in the course.

Mix the right amounts, compare fairly and solve everyday problems. Understand why a shortcut works before using it.

A complete beginner route from counting comparisons to equivalent ratios, visual models, sharing, scale, rates and percentages. Explain why methods work, spot false shortcuts and solve unfamiliar mixed problems.

By the end, you can…

  • Count two kinds of objects. Compare parts with the whole.
  • Make bigger and smaller amounts. Keep the same ratio.
  • Use tables, number lines, bars and graphs.
  • Share amounts. Find missing amounts. Use drawing scales.
  • Compare prices and speeds. Change units.
  • Use percentages. Choose a method for mixed problems.

For another Course

  • Formal algebraic proofs, negative ratios and inverse proportion.
  • Compound interest, percentage change chains, trigonometry, area and volume scale factors.
  • No claim of fluent English or advanced fraction arithmetic. Fractional work uses halves and quarters, explicitly explained here.

YOUR LEARNING PATH

One idea leads to the next.

0 of 27 Missions completed or proven
Unit 1

See the comparison

Count two kinds of objects. Compare parts with the whole.

  1. Two amounts, one comparisonMission 1 of 27Locked. Count two kinds of objects and say what a ratio compares.
  2. Order mattersMission 2 of 27Locked. Write ratios in the right order. Swap the order when the question changes.
  3. Parts and the wholeMission 3 of 27Locked. Compare one part with another part, or with the whole group.
  4. For every groupMission 4 of 27Locked. Repeat complete groups and find which totals fit the pattern.
Unit 2

Keep the same mix

Make bigger and smaller amounts. Keep the same ratio.

  1. Make a bigger mixMission 5 of 27Locked. Make a bigger mix by multiplying both amounts by the same number.
  2. Make a smaller mixMission 6 of 27Locked. Make a smaller mix by dividing both amounts by the same number.
  3. Find the simplest ratioMission 7 of 27Locked. Write a ratio with the smallest whole numbers that keep the same comparison.
  4. Ratios with halves and decimalsMission 8 of 27Locked. Turn half-cups and quarter-cups into whole-number ratios.
Unit 3

Make ratios visible

Use tables, number lines, bars and graphs.

  1. Build a ratio tableMission 9 of 27Locked. Complete and check tables that keep the same ratio.
  2. Two number lines, one storyMission 10 of 27Locked. Use two matching number lines to find amounts, including points between marks.
  3. Draw equal partsMission 11 of 27Locked. Use equal boxes to find amounts from a total or a difference.
  4. Which mix is stronger?Mission 12 of 27Locked. Compare two mixes by making one amount the same in both.
  5. Put ratio pairs on a graphMission 13 of 27Locked. Read points on a graph and check whether they show the same ratio.
Unit 4

Solve real ratio problems

Share amounts. Find missing amounts. Use drawing scales.

  1. Share a total fairlyMission 14 of 27Locked. Share a total in a ratio. Check the shares and the total.
  2. Three parts togetherMission 15 of 27Locked. Keep all three parts in order when sharing and comparing.
  3. Find a missing amountMission 16 of 27Locked. Find a missing amount. Explain which number you divide by and why.
  4. When the ratio changesMission 17 of 27Locked. Find a new ratio when one amount changes. Find how much to add or remove.
  5. Ratios on maps and modelsMission 18 of 27Locked. Use a drawing to find real lengths. Change the units when needed.
Unit 5

Find the amount for one

Compare prices and speeds. Change units.

  1. A rate tells how much for oneMission 19 of 27Locked. Find how much there is for one. Keep the names and units clear.
  2. Compare prices fairlyMission 20 of 27Locked. Compare prices for one item. Find the cheapest way to buy what you need.
  3. Distance, time and speedMission 21 of 27Locked. Use distance and time to find speed. Check whether the speed stays the same.
  4. Keep the units honestMission 22 of 27Locked. Change liquid and time units to compare rates and find filling times.
Unit 6

Connect ratios and percentages

Use percentages. Choose a method for mixed problems.

  1. Percent means out of 100Mission 23 of 27Locked. Understand percent as an amount out of 100 equal parts.
  2. Find a percent of an amountMission 24 of 27Locked. Find a percent of an amount using equal parts and useful shortcuts.
  3. Find the whole or the percentageMission 25 of 27Locked. Find the whole or the percentage. Start by naming what is missing.
  4. Know when a shortcut failsMission 26 of 27Locked. Check whether a ratio method fits the question and its rules.
  5. Run the Ratio StudioMission 27 of 27Locked. Choose ratio methods for an event plan. Explain your choices and check the rules.Mastery Challenge

A Debsie Course · Beginners aged 10 and above, including learners with limited English.