Simplify the following ratios: a. \( 57: 342 \) b. \( 81: 3 \) d. \( 48: 36: 240 \) e. \( 250 \mathrm{~g}: 5 \mathrm{~kg} \) f. \( 800 \mathrm{~mm}: 24 \mathrm{~m} \)
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To simplify the given ratios, we will find the greatest common divisor (GCD) of each pair and divide the numbers accordingly. a. For \( 57: 342 \), the GCD is 57. Dividing both terms by 57 gives us \( 1: 6 \). b. For \( 81: 3 \), the GCD is 3. Dividing both terms by 3 gives us \( 27: 1 \). d. For \( 48: 36: 240 \), we first find the GCD of all three, which is 12. Dividing each term by 12 gives us \( 4: 3: 20 \). e. For \( 250 \mathrm{~g}: 5 \mathrm{~kg} \), we need to convert kilograms to grams (5 kg = 5000 g). The GCD of \( 250 \) and \( 5000 \) is \( 250 \). Dividing both by 250 gives us \( 1: 20 \). f. For \( 800 \mathrm{~mm}: 24 \mathrm{~m} \), we convert meters to millimeters (24 m = 24000 mm). The GCD of \( 800 \) and \( 24000 \) is \( 800 \). Dividing both by 800 gives us \( 1: 30 \).
