Use your calculator to check your 1. Write each of these tatios in its simplest form. c) \( 7: 21: 35 \) a) \( 15 ; 20 \) b) \( 200: 180 \) f) 9 min 000 s d) \( 102: 99: 87 \) e) \( 75 \mathrm{~m}: 125 \mathrm{~cm} \) Write each of these as a rate. Use the units given In brackets. a) Mpho buys four dozen eggs for R48. (R/dozen) b) Dan can eat three bananas in 90 seconds. (bananas/min) c) A cartravels 616 km on 56 litres of petrol. ( \( \mathrm{km} / \mathrm{\ell} \) ) d) A snail crawls 150 cm in 2 hours. ( \( \mathrm{cm} / \mathrm{min} \) ) Which is faster: \( 1 \mathrm{~m} / \mathrm{s} \) or \( 1 \mathrm{~km} / \mathrm{h} \) ? Pat is knitting a scarf. On average she can knit 2 cm in 35 minutes. a) Express this as a rate in \( \mathrm{min} / \mathrm{cm} \). b) Express this as a rate in \( \mathrm{mm} / \mathrm{min} \). c) How long will it take her to knit a scarf that is 160 cm long?

Sure, let's work through each of your questions step by step. --- ### **1. Simplifying Ratios** **a) \(15 : 20\)** - **Find the Greatest Common Divisor (GCD):** The GCD of 15 and 20 is 5. - **Simplify:** \[ \frac{15}{5} : \frac{20}{5} = 3 : 4 \] - **Simplest Form:** \(3 : 4\) --- **b) \(200 : 180\)** - **Find the GCD:** The GCD of 200 and 180 is 20. - **Simplify:** \[ \frac{200}{20} : \frac{180}{20} = 10 : 9 \] - **Simplest Form:** \(10 : 9\) --- **c) \(7 : 21 : 35\)** - **Find the GCD:** The GCD of 7, 21, and 35 is 7. - **Simplify:** \[ \frac{7}{7} : \frac{21}{7} : \frac{35}{7} = 1 : 3 : 5 \] - **Simplest Form:** \(1 : 3 : 5\) --- **d) \(102 : 99 : 87\)** - **Find the GCD:** The GCD of 102, 99, and 87 is 3. - **Simplify:** \[ \frac{102}{3} : \frac{99}{3} : \frac{87}{3} = 34 : 33 : 29 \] - **Simplest Form:** \(34 : 33 : 29\) --- **e) \(75\, \text{m} : 125\, \text{cm}\)** - **Convert Units:** \[ 75\, \text{m} = 7500\, \text{cm} \] - **Form the Ratio:** \(7500 : 125\) - **Find the GCD:** The GCD of 7500 and 125 is 25. - **Simplify:** \[ \frac{7500}{25} : \frac{125}{25} = 300 : 5 \] - **Further Simplify:** \[ \frac{300}{5} : \frac{5}{5} = 60 : 1 \] - **Simplest Form:** \(60 : 1\) --- **f) \(9\, \text{min} : 000\, \text{s}\)** - It seems there's a typo here. If it's intended to be \(9\, \text{min} : 0\, \text{s}\), the ratio is undefined because division by zero is not possible. --- ### **2. Writing as Rates** **a) Mpho buys four dozen eggs for R48. (R/dozen)** - **Calculate Rate:** \[ \text{Rate} = \frac{48\, \text{R}}{4\, \text{dozen}} = 12\, \text{R/dozen} \] - **Rate:** **R12/dozen** --- **b) Dan can eat three bananas in 90 seconds. (bananas/min)** - **Convert Seconds to Minutes:** \[ 90\, \text{seconds} = 1.5\, \text{minutes} \] - **Calculate Rate:** \[ \frac{3\, \text{bananas}}{1.5\, \text{minutes}} = 2\, \text{bananas/min} \] - **Rate:** **2 bananas/min** --- **c) A car travels 616 km on 56 litres of petrol. (\( \mathrm{km} / \mathrm{\ell} \))** - **Calculate Rate:** \[ \frac{616\, \text{km}}{56\, \text{ℓ}} = 11\, \text{km/ℓ} \] - **Rate:** **11 km/ℓ** --- **d) A snail crawls 150 cm in 2 hours. (\( \mathrm{cm} / \mathrm{min} \))** - **Convert Hours to Minutes:** \[ 2\, \text{hours} = 120\, \text{minutes} \] - **Calculate Rate:** \[ \frac{150\, \text{cm}}{120\, \text{minutes}} = 1.25\, \text{cm/min} \] - **Rate:** **1.25 cm/min** --- ### **3. Comparing Speeds** **Which is faster: \(1\, \text{m/s}\) or \(1\, \text{km/h}\)?** - **Convert \(1\, \text{km/h}\) to m/s:** \[ 1\, \text{km/h} = \frac{1000\, \text{m}}{3600\, \text{s}} \approx 0.2778\, \text{m/s} \] - **Comparison:** \[ 1\, \text{m/s} > 0.2778\, \text{m/s} \] - **Conclusion:** **\(1\, \text{m/s}\) is faster.** --- ### **4. Pat’s Knitting Rate** **Pat can knit 2 cm in 35 minutes.** **a) Express this as a rate in \(\mathrm{min/cm}\).** - **Calculate Rate:** \[ \frac{35\, \text{min}}{2\, \text{cm}} = 17.5\, \text{min/cm} \] - **Rate:** **17.5 min/cm** --- **b) Express this as a rate in \(\mathrm{mm/min}\).** - **Convert cm to mm:** \[ 2\, \text{cm} = 20\, \text{mm} \] - **Calculate Rate:** \[ \frac{20\, \text{mm}}{35\, \text{min}} \approx 0.571\, \text{mm/min} \] - **Rate:** **≈0.571 mm/min** --- **c) How long will it take her to knit a scarf that is 160 cm long?** - **Using the Rate \(17.5\, \text{min/cm}\):** \[ 160\, \text{cm} \times 17.5\, \text{min/cm} = 2800\, \text{minutes} \] - **Convert to Hours and Minutes (optional):** \[ 2800\, \text{minutes} = 46\, \text{hours} \, 40\, \text{minutes} \] - **Time Required:** **2800 minutes** (or **46 hours and 40 minutes**) --- If you have any further questions or need more detailed explanations on any of these steps, feel free to ask!