(4) \( 20000: ?=1000: 1 \) (5) \( ?: 400=4: 100 \) (7) \( 7: 0,2=7: 6 \), (8) \( 8 \mathrm{~cm}: 1 \mathrm{~m}=?: 250 \) (9) 20 seconds \( : 2 \) minutes \( =1: \) ? (10) \( 30 \mathrm{~g}: ? \mathrm{mg}=40: 1 \) (11) ? hours, 10 seconds \( =720: 1 \) Divide the number 720 into the following ratios: (1) \( 5: 4 \) (2) \( 1: 9 \) (3) \( 2: 1: 3 \) Divide each of the following numbers in a ratio of \( 5: 3 \) : (1) 80 (2) 176 (3) 100 Divide the following numbers in a ratio \( 1: 5: 5 \) : (1) (2) 33 (3) 253 The ratio- of boys to eirls at a party is \( 4: 3 \). If there are 20 boys, how many

Sure, let's solve each of the ratio and proportion problems step by step. --- ### **Problem (4)** \[ 20000 : \, ? \, = \, 1000 : 1 \] **Solution:** Set up the proportion: \[ \frac{20000}{x} = \frac{1000}{1} \] Cross-multiply: \[ 20000 \times 1 = 1000 \times x \\ 20000 = 1000x \\ x = \frac{20000}{1000} = 20 \] **Answer:** **20** --- ### **Problem (5)** \[ \, ? \, : \, 400 \, = \, 4 : 100 \] **Solution:** Set up the proportion: \[ \frac{x}{400} = \frac{4}{100} \] Cross-multiply: \[ 100x = 4 \times 400 \\ 100x = 1600 \\ x = \frac{1600}{100} = 16 \] **Answer:** **16** --- ### **Problem (7)** \[ 7 : 0.2 \, = \, 7 : 6 \] **Solution:** This appears to be an incomplete or incorrectly stated problem. If the intention is to find an equivalent ratio or to solve for a missing value, additional information is needed. Please provide more details or clarify the problem statement. --- ### **Problem (8)** \[ 8 \, \text{cm} : 1 \, \text{m} = \, ? : 250 \] **Solution:** First, convert meters to centimeters: \[ 1 \, \text{m} = 100 \, \text{cm} \] Set up the proportion: \[ \frac{8}{100} = \frac{x}{250} \] Solve for \( x \): \[ x = \frac{8 \times 250}{100} = \frac{2000}{100} = 20 \] **Answer:** **20** --- ### **Problem (9)** \[ 20 \, \text{seconds} : 2 \, \text{minutes} = 1 : \, ? \] **Solution:** Convert minutes to seconds: \[ 2 \, \text{minutes} = 120 \, \text{seconds} \] Set up the proportion: \[ \frac{20}{120} = \frac{1}{x} \] Solve for \( x \): \[ x = \frac{120 \times 1}{20} = 6 \] **Answer:** **6** --- ### **Problem (10)** \[ 30 \, \text{g} : \, ? \, \text{mg} = 40 : 1 \] **Solution:** Convert grams to milligrams: \[ 30 \, \text{g} = 30000 \, \text{mg} \] Set up the proportion: \[ \frac{30000}{x} = \frac{40}{1} \] Solve for \( x \): \[ x = \frac{30000}{40} = 750 \] **Answer:** **750 mg** --- ### **Problem (11)** \[ \, ? \, \text{hours} : 10 \, \text{seconds} = 720 : 1 \] **Solution:** First, convert hours and seconds to the same unit. Let's convert hours to seconds: \[ x \, \text{hours} = x \times 3600 \, \text{seconds} \] Set up the proportion: \[ \frac{x \times 3600}{10} = \frac{720}{1} \] Solve for \( x \): \[ x \times 3600 = 720 \times 10 \\ x \times 3600 = 7200 \\ x = \frac{7200}{3600} = 2 \] **Answer:** **2 hours** --- ### **Dividing the Number 720 into Given Ratios** #### **(1) Ratio \( 5 : 4 \)** - **Total parts:** \( 5 + 4 = 9 \) - **Each part:** \( \frac{720}{9} = 80 \) - **Division:** - First part: \( 5 \times 80 = 400 \) - Second part: \( 4 \times 80 = 320 \) **Answer:** **400 : 320** #### **(2) Ratio \( 1 : 9 \)** - **Total parts:** \( 1 + 9 = 10 \) - **Each part:** \( \frac{720}{10} = 72 \) - **Division:** - First part: \( 1 \times 72 = 72 \) - Second part: \( 9 \times 72 = 648 \) **Answer:** **72 : 648** #### **(3) Ratio \( 2 : 1 : 3 \)** - **Total parts:** \( 2 + 1 + 3 = 6 \) - **Each part:** \( \frac{720}{6} = 120 \) - **Division:** - First part: \( 2 \times 120 = 240 \) - Second part: \( 1 \times 120 = 120 \) - Third part: \( 3 \times 120 = 360 \) **Answer:** **240 : 120 : 360** --- ### **Dividing Numbers in the Ratio \( 5 : 3 \)** #### **(1) Number 80** - **Total parts:** \( 5 + 3 = 8 \) - **Each part:** \( \frac{80}{8} = 10 \) - **Division:** - First part: \( 5 \times 10 = 50 \) - Second part: \( 3 \times 10 = 30 \) **Answer:** **50 : 30** #### **(2) Number 176** - **Total parts:** \( 5 + 3 = 8 \) - **Each part:** \( \frac{176}{8} = 22 \) - **Division:** - First part: \( 5 \times 22 = 110 \) - Second part: \( 3 \times 22 = 66 \) **Answer:** **110 : 66** #### **(3) Number 100** - **Total parts:** \( 5 + 3 = 8 \) - **Each part:** \( \frac{100}{8} = 12.5 \) - **Division:** - First part: \( 5 \times 12.5 = 62.5 \) - Second part: \( 3 \times 12.5 = 37.5 \) **Answer:** **62.5 : 37.5** --- ### **Dividing Numbers in the Ratio \( 1 : 5 : 5 \)** #### **(2) Number 33** - **Total parts:** \( 1 + 5 + 5 = 11 \) - **Each part:** \( \frac{33}{11} = 3 \) - **Division:** - First part: \( 1 \times 3 = 3 \) - Second part: \( 5 \times 3 = 15 \) - Third part: \( 5 \times 3 = 15 \) **Answer:** **3 : 15 : 15** #### **(3) Number 253** - **Total parts:** \( 1 + 5 + 5 = 11 \) - **Each part:** \( \frac{253}{11} = 23 \) - **Division:** - First part: \( 1 \times 23 = 23 \) - Second part: \( 5 \times 23 = 115 \) - Third part: \( 5 \times 23 = 115 \) **Answer:** **23 : 115 : 115** --- ### **Final Problem** **The ratio of boys to girls at a party is \( 4 : 3 \). If there are 20 boys, how many girls are there?** **Solution:** Given the ratio \( 4 : 3 \) (boys : girls), and there are 20 boys. - **Each part for boys:** \( \frac{20 \text{ boys}}{4} = 5 \) - **Girls:** \( 3 \times 5 = 15 \) **Answer:** **15 girls** --- If you have any further questions or need additional explanations, feel free to ask!