1.5 Rates, Ratio, Proportions and Percentages

• Rates and fractions
• Comparing ratios
• Increase and decrease of quantities
• Percentage change of given quantities
• Direct and indirect proportions

• identify rates in different situations
• work out rates in real-life situations
• express fractions as ratios in real-life situations
• compare two or more ratios in different situations
• divide quantities in given ratios in real-life situations
• work out ratios in different situations
• work out increase and decrease of quantities using ratios in real-life situations
• work out percentage change of given quantities in real-life situations
• identify direct and indirect proportions in real-life situations
• work out direct and indirect proportions in real-life situations
• promote use of ratios and proportions in real life

“How do we use rates in real-life situations?”

“How do we use ratios in daily activities?”

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1. What a rate is
   40 min · 1 practice tasks · quiz
   A rate as a comparison of two different kinds of quantity, its units, and how it differs from a ratio.
2. Working out and comparing rates
   40 min · 1 practice tasks · quiz
   Using rates to compare two offers, and why the cheaper rate is not always the cheaper deal.
3. Expressing fractions as ratios
   40 min · 1 practice tasks · quiz
   The difference between comparing a part with the whole and comparing one part with another, and moving between the two.
4. Simplifying ratios
   40 min · 1 practice tasks · quiz
   Reducing a ratio to whole numbers with nothing in common, and matching the units before you start.
5. Comparing two or more ratios
   40 min · 1 practice tasks · quiz
   Turning ratios into fractions or decimals so that they can be ranked, and why the bigger numbers do not win.
6. Dividing a quantity in a ratio
   40 min · 1 practice tasks · quiz
   Sharing a total into unequal parts using the total-parts method, and checking that the shares add back.
7. Increase and decrease in a ratio
   40 min · 1 practice tasks · quiz
   Scaling a quantity up or down by multiplying by a ratio written as a fraction, and checking the direction.
8. Percentage increase
   40 min · 1 practice tasks · quiz
   Working out how big a rise is compared with what you started with, and why the original is always the divisor.
9. Percentage decrease and discount
   40 min · 1 practice tasks · quiz
   Working out a fall as a percentage, calculating a discount, and the one-step method for what you actually pay.
10. Percentage change in real life
    40 min · 1 practice tasks · quiz
    Applying percentage change to fares, marks, prices and populations, and why percentages make different changes comparable.
11. Direct proportion
    40 min · 1 practice tasks · quiz
    When more of one thing means proportionally more of another, and the find-one-first method that solves it.
12. Indirect proportion
    40 min · 1 practice tasks · quiz
    When more of one thing means less of another, and why the product stays constant instead of the quotient.
13. Telling the two proportions apart
    40 min · 1 practice tasks · quiz
    The doubling test that decides whether a problem is direct or indirect, and what to do once you know.
14. Ratios and proportions in real life
    40 min · 1 practice tasks · quiz
    Recipes, concrete, map scales, shares, dilution and fuel mixes, and why the ratio must survive a change of size.