Answer :
When comparing different quantities, it is helpful to express them as ratios. A ratio provides a way to express the relative size of two quantities. To create a ratio, both quantities must be in the same units. Let's convert as necessary and compare these quantities step-by-step.
(a) 50 cm, 1.3 m
First, convert meters to centimeters:
[tex]1 ext{ m} = 100 ext{ cm}[/tex]
[tex]1.3 ext{ m} = 1.3 imes 100 ext{ cm} = 130 ext{ cm}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{50 ext{ cm}}{130 ext{ cm}} = \frac{5}{13}[/tex]
(b) 8 weeks, 4 days
Convert weeks to days:
[tex]1 ext{ week} = 7 ext{ days}[/tex]
[tex]8 ext{ weeks} = 8 imes 7 = 56 ext{ days}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{56 ext{ days}}{4 ext{ days}} = \frac{14}{1}[/tex], or simply 14:1
(c) 500 g, 2 kg
Convert kilograms to grams:
[tex]1 ext{ kg} = 1000 ext{ g}[/tex]
[tex]2 ext{ kg} = 2 imes 1000 ext{ g} = 2000 ext{ g}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{500 ext{ g}}{2000 ext{ g}} = \frac{1}{4}[/tex]
(d) 5 hours, 50 minutes
Convert hours to minutes:
[tex]1 ext{ hour} = 60 ext{ minutes}[/tex]
[tex]5 ext{ hours} = 5 imes 60 ext{ minutes} = 300 ext{ minutes}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{300 ext{ minutes}}{50 ext{ minutes}} = \frac{6}{1}[/tex], or simply 6:1
(e) 2.5 l, 300 ml
Convert liters to milliliters:
[tex]1 ext{ l} = 1000 ext{ ml}[/tex]
[tex]2.5 ext{ l} = 2.5 imes 1000 ext{ ml} = 2500 ext{ ml}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{2500 ext{ ml}}{300 ext{ ml}} = \frac{25}{3}[/tex]
(f) 5.2 cm, 16 mm
Convert centimeters to millimeters:
[tex]1 ext{ cm} = 10 ext{ mm}[/tex]
[tex]5.2 ext{ cm} = 5.2 imes 10 ext{ mm} = 52 ext{ mm}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{52 ext{ mm}}{16 ext{ mm}} = \frac{13}{4}[/tex]
(g) 3 minutes, 45 seconds
Convert minutes to seconds:
[tex]1 ext{ minute} = 60 ext{ seconds}[/tex]
[tex]3 ext{ minutes} = 3 imes 60 ext{ seconds} = 180 ext{ seconds}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{180 ext{ seconds}}{45 ext{ seconds}} = \frac{4}{1}[/tex], or simply 4:1
(h) 6.4 t, 880 kg
Convert tons to kilograms:
[tex]1 ext{ ton} = 1000 ext{ kg}[/tex]
[tex]6.4 ext{ t} = 6.4 imes 1000 ext{ kg} = 6400 ext{ kg}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{6400 ext{ kg}}{880 ext{ kg}} = \frac{16}{2.2} = \frac{80}{11}[/tex]
(i) 1 hour 15 minutes, 50 minutes
Convert hours to minutes:
[tex]1 ext{ hour} = 60 ext{ minutes}[/tex]
[tex]1 ext{ hour 15 minutes} = 60 ext{ minutes} + 15 ext{ minutes} = 75 ext{ minutes}[/tex]
Now the ratio:
[tex]ext{Ratio} = \frac{75 ext{ minutes}}{50 ext{ minutes}} = \frac{3}{2}[/tex]
