Answer :
Sure! Let's evaluate each algebraic expression step by step for [tex]\( c = 0.6 \)[/tex] and [tex]\( d = 300 \)[/tex]:
1. Expression 7: [tex]\( \frac{d}{c} \times 400 \)[/tex]
- First, divide [tex]\( d \)[/tex] by [tex]\( c \)[/tex]: [tex]\( \frac{300}{0.6} = 500 \)[/tex]
- Then, multiply the result by 400: [tex]\( 500 \times 400 = 200,000 \)[/tex]
Result: 200,000
2. Expression 8: [tex]\( \frac{d}{50} \times 7 \)[/tex]
- First, divide [tex]\( d \)[/tex] by 50: [tex]\( \frac{300}{50} = 6 \)[/tex]
- Then, multiply the result by 7: [tex]\( 6 \times 7 = 42 \)[/tex]
Result: 42
3. Expression 9: [tex]\( \frac{24}{c} \times d \)[/tex]
- First, divide 24 by [tex]\( c \)[/tex]: [tex]\( \frac{24}{0.6} = 40 \)[/tex]
- Then, multiply the result by [tex]\( d \)[/tex]: [tex]\( 40 \times 300 = 12,000 \)[/tex]
Result: 12,000
4. Expression 10: [tex]\( 15 \times c \times 25 \)[/tex]
- First, multiply 15 by [tex]\( c \)[/tex]: [tex]\( 15 \times 0.6 = 9 \)[/tex]
- Then, multiply the result by 25: [tex]\( 9 \times 25 = 225 \)[/tex]
Result: 225
5. Expression 11: [tex]\( \frac{d}{15} \times 1000 \)[/tex]
- First, divide [tex]\( d \)[/tex] by 15: [tex]\( \frac{300}{15} = 20 \)[/tex]
- Then, multiply the result by 1000: [tex]\( 20 \times 1000 = 20,000 \)[/tex]
Result: 20,000
6. Expression 12: [tex]\( d \times 720 \div c \)[/tex]
- First, multiply [tex]\( d \)[/tex] by 720: [tex]\( 300 \times 720 = 216,000 \)[/tex]
- Then, divide the result by [tex]\( c \)[/tex]: [tex]\( \frac{216,000}{0.6} = 360,000 \)[/tex]
Result: 360,000
7. Expression 13: [tex]\( d \times 20 \times c \)[/tex]
- First, multiply [tex]\( d \)[/tex] by 20: [tex]\( 300 \times 20 = 6,000 \)[/tex]
- Then, multiply the result by [tex]\( c \)[/tex]: [tex]\( 6,000 \times 0.6 = 3,600 \)[/tex]
Result: 3,600
8. Expression 14: [tex]\( 19 \times d \div c \)[/tex]
- First, multiply 19 by [tex]\( d \)[/tex]: [tex]\( 19 \times 300 = 5,700 \)[/tex]
- Then, divide the result by [tex]\( c \)[/tex]: [tex]\( \frac{5,700}{0.6} = 9,500 \)[/tex]
Result: 9,500
9. Expression 15: [tex]\( \frac{150 \times c}{d} \)[/tex]
- First, multiply 150 by [tex]\( c \)[/tex]: [tex]\( 150 \times 0.6 = 90 \)[/tex]
- Then, divide the result by [tex]\( d \)[/tex]: [tex]\( \frac{90}{300} = 0.3 \)[/tex]
Result: 0.3
10. Expression 16: [tex]\( \frac{c + d}{75} \)[/tex]
- First, add [tex]\( c \)[/tex] and [tex]\( d \)[/tex]: [tex]\( 0.6 + 300 = 300.6 \)[/tex]
- Then, divide the result by 75: [tex]\( \frac{300.6}{75} = 4.008 \)[/tex]
Result: 4.008
11. Expression 17: [tex]\( c \cdot 500 - d \)[/tex]
- First, multiply [tex]\( c \)[/tex] by 500: [tex]\( 0.6 \times 500 = 300 \)[/tex]
- Then, subtract [tex]\( d \)[/tex]: [tex]\( 300 - 300 = 0 \)[/tex]
Result: 0.0
12. Expression 18: [tex]\( (d-c) \times 400 \)[/tex]
- First, subtract [tex]\( c \)[/tex] from [tex]\( d \)[/tex]: [tex]\( 300 - 0.6 = 299.4 \)[/tex]
- Then, multiply the result by 400: [tex]\( 299.4 \times 400 = 119,760 \)[/tex]
Result: 119,760
These are the evaluated results for each expression.
1. Expression 7: [tex]\( \frac{d}{c} \times 400 \)[/tex]
- First, divide [tex]\( d \)[/tex] by [tex]\( c \)[/tex]: [tex]\( \frac{300}{0.6} = 500 \)[/tex]
- Then, multiply the result by 400: [tex]\( 500 \times 400 = 200,000 \)[/tex]
Result: 200,000
2. Expression 8: [tex]\( \frac{d}{50} \times 7 \)[/tex]
- First, divide [tex]\( d \)[/tex] by 50: [tex]\( \frac{300}{50} = 6 \)[/tex]
- Then, multiply the result by 7: [tex]\( 6 \times 7 = 42 \)[/tex]
Result: 42
3. Expression 9: [tex]\( \frac{24}{c} \times d \)[/tex]
- First, divide 24 by [tex]\( c \)[/tex]: [tex]\( \frac{24}{0.6} = 40 \)[/tex]
- Then, multiply the result by [tex]\( d \)[/tex]: [tex]\( 40 \times 300 = 12,000 \)[/tex]
Result: 12,000
4. Expression 10: [tex]\( 15 \times c \times 25 \)[/tex]
- First, multiply 15 by [tex]\( c \)[/tex]: [tex]\( 15 \times 0.6 = 9 \)[/tex]
- Then, multiply the result by 25: [tex]\( 9 \times 25 = 225 \)[/tex]
Result: 225
5. Expression 11: [tex]\( \frac{d}{15} \times 1000 \)[/tex]
- First, divide [tex]\( d \)[/tex] by 15: [tex]\( \frac{300}{15} = 20 \)[/tex]
- Then, multiply the result by 1000: [tex]\( 20 \times 1000 = 20,000 \)[/tex]
Result: 20,000
6. Expression 12: [tex]\( d \times 720 \div c \)[/tex]
- First, multiply [tex]\( d \)[/tex] by 720: [tex]\( 300 \times 720 = 216,000 \)[/tex]
- Then, divide the result by [tex]\( c \)[/tex]: [tex]\( \frac{216,000}{0.6} = 360,000 \)[/tex]
Result: 360,000
7. Expression 13: [tex]\( d \times 20 \times c \)[/tex]
- First, multiply [tex]\( d \)[/tex] by 20: [tex]\( 300 \times 20 = 6,000 \)[/tex]
- Then, multiply the result by [tex]\( c \)[/tex]: [tex]\( 6,000 \times 0.6 = 3,600 \)[/tex]
Result: 3,600
8. Expression 14: [tex]\( 19 \times d \div c \)[/tex]
- First, multiply 19 by [tex]\( d \)[/tex]: [tex]\( 19 \times 300 = 5,700 \)[/tex]
- Then, divide the result by [tex]\( c \)[/tex]: [tex]\( \frac{5,700}{0.6} = 9,500 \)[/tex]
Result: 9,500
9. Expression 15: [tex]\( \frac{150 \times c}{d} \)[/tex]
- First, multiply 150 by [tex]\( c \)[/tex]: [tex]\( 150 \times 0.6 = 90 \)[/tex]
- Then, divide the result by [tex]\( d \)[/tex]: [tex]\( \frac{90}{300} = 0.3 \)[/tex]
Result: 0.3
10. Expression 16: [tex]\( \frac{c + d}{75} \)[/tex]
- First, add [tex]\( c \)[/tex] and [tex]\( d \)[/tex]: [tex]\( 0.6 + 300 = 300.6 \)[/tex]
- Then, divide the result by 75: [tex]\( \frac{300.6}{75} = 4.008 \)[/tex]
Result: 4.008
11. Expression 17: [tex]\( c \cdot 500 - d \)[/tex]
- First, multiply [tex]\( c \)[/tex] by 500: [tex]\( 0.6 \times 500 = 300 \)[/tex]
- Then, subtract [tex]\( d \)[/tex]: [tex]\( 300 - 300 = 0 \)[/tex]
Result: 0.0
12. Expression 18: [tex]\( (d-c) \times 400 \)[/tex]
- First, subtract [tex]\( c \)[/tex] from [tex]\( d \)[/tex]: [tex]\( 300 - 0.6 = 299.4 \)[/tex]
- Then, multiply the result by 400: [tex]\( 299.4 \times 400 = 119,760 \)[/tex]
Result: 119,760
These are the evaluated results for each expression.
