Simplify the following ratios: a. \( 57: 342 \) b. \( 81: 3 \) d. \( 48: 36: 240 \) e. \( 250 \mathrm{~g}: 5 \mathrm{~kg} \) f. \( 800 \mathrm{~mm}: 24 \mathrm{~m} \)

Here are the simplified ratios: a. 57:342  Divide both terms by 57. Since 57 ÷ 57 = 1 and 342 ÷ 57 = 6, the simplified ratio is 1:6. b. 81:3  Divide both terms by 3. Since 81 ÷ 3 = 27 and 3 ÷ 3 = 1, the simplified ratio is 27:1. d. 48:36:240  Find the greatest common divisor (GCD) of 48, 36, and 240, which is 12. Dividing each term by 12 gives:   48 ÷ 12 = 4, 36 ÷ 12 = 3, and 240 ÷ 12 = 20.  The simplified ratio is 4:3:20. e. 250 g : 5 kg  First convert 5 kg to grams: 5 kg = 5000 g. Now the ratio is 250 g:5000 g.  Divide by 250: 250 ÷ 250 = 1 and 5000 ÷ 250 = 20, so the simplified ratio is 1:20. f. 800 mm : 24 m  Convert 24 m to millimeters: 24 m = 24 × 1000 mm = 24000 mm. Now the ratio is 800 mm:24000 mm.  Dividing by 800 gives: 800 ÷ 800 = 1 and 24000 ÷ 800 = 30, so the simplified ratio is 1:30.