Unit 03 Ratios and Rates Notes

Unit 03 Ratios and Rates

  • Ratios and rates help us compare things like sizes and costs.

  • We use them for maps, money, and finding the best deals.

3.01 Ratios

  • Ratio: Compares two amounts.

    • Example: 1:3 (like 1 apple for every 3 bananas).

  • Equivalent Ratios: Ratios that are the same.

    • Make them by multiplying or dividing both sides by the same number.

    • Example: 1:3 = 2:6 (multiply both by 2).

  • Simplify Ratios: Make the numbers as small as possible.

    • Divide both sides by the same number.

    • Example: 5:15 = 1:3 (divide both by 5).

  • Same Units: If the units are different, change them to be the same.

  • Finding a Quantity:

    • If you know a ratio and one amount, you can find the other.

    • Example: Recipe with 3 parts oats and 4 parts flour. If you use 180g of oats, find the flour amount.

    • One part: 180÷3=60g180 ÷ 3 = 60g

    • Flour (4 parts): 4Imes60=240g4 Imes 60 = 240 g

    • Formula: Amount of flour = (43Imes180g=240g)(\frac{4}{3} Imes 180g = 240g)

  • Divide by Ratio:

    • Unitary Method: Find what one part is worth, then find each share.

    • Fraction Method: Divide each side of the ratio by the total number of parts.

  • Three Quantities:

    • Ratios can compare three things like a: b: c.

    • Example: Sharing $50 in a 1:3 ratio.

    • 1 part + 3 parts = 4 parts

    • Each part: $50/4=$12.50\$50/4 = \$12.50

3.02 Maps and Scale

  • Scale Ratios: Maps use ratios to show real sizes.

  • If the scale is 1:1000, real life is 1000 times bigger than the map.

  • Scale Factor: The number you multiply by (like 1000).

    • Map to real life: multiply by the scale factor.

    • Real life to map: divide by the scale factor.

  • Example: Map scale 1:100. Two points are 12cm apart on the map.

    • Real distance: 12Imes100=1200cm=12M12 Imes 100 = 1200 cm = 12 M

  • Scale Bars: Use the same units to write as a ratio.

3.03 Rates

  • Rate: Compares amounts with different units.

    • Example: $6 for 3 kgs.

  • Unit Rate: Rate for one unit.

    • Example: $2 per kg.

  • Apply Rates:

    • Change to a unit rate first, then multiply.

  • Convert Rates:

    • Change one unit at a time.

3.04 Financial Rates

  • Simple Interest: Interest on a loan or investment.

    • Formula: I=PRTI=PRT

    • I = Interest amount

    • P = Principal (start amount)

    • R = Interest rate per year

    • T = Time in years

  • Example: $3000 loan at 17% per year for 2 years.

    • I=3000×17×2100=$1020I = \frac{3000 \times 17 \times 2}{100} = \$1020

  • Taxation Rates:

    • Income tax and Medicare levy (2% of income).

    • Total tax = Income tax + Medicare levy

    • Net income = Income - Total tax

  • Exchange Rates:

    • How much one country's money is worth in another.

    • AUD to other currency: multiply by the exchange rate.

    • Other currency to AUD: divide by the exchange rate.

  • Example: 1 AUD = 0.55 USD. 79 AUD = 0.55×79=43.45USD0.55 \times 79 = 43.45 USD

3.05 Best Buys

  • Best Buy: Getting the most for your money.

  • Unit Price: Cost per unit (like per kg or litre).

  • Example: Apple juice $13.76 for 3.2 L, orange juice $6.30 for 2.1 L.

    • Apple juice: \frac{$13.76}{3.2 L} = \$4.30/L

    • Orange juice: \frac{$6.30}{$2.12} = \$3/L

    • Orange juice is cheaper per litre.

  • Discounts:

    • Sale price = Original price - (Original price*Discount)

3.06 Distance Time Graphs

  • Shows how distance changes over time.

  • Speed = DistanceTime\frac{Distance}{Time}

  • Average Speed = $$\