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Answer :
Sure! Let's analyze each proportion to determine whether it is true or false.
1. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- First, simplify [tex]\(\frac{18}{48}\)[/tex]:
- [tex]\(18\)[/tex] and [tex]\(48\)[/tex] have a common factor of [tex]\(6\)[/tex].
- Dividing both, we get: [tex]\(\frac{18 \div 6}{48 \div 6} = \frac{3}{8}\)[/tex].
- Next, simplify [tex]\(\frac{30}{50}\)[/tex]:
- [tex]\(30\)[/tex] and [tex]\(50\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing both, we get: [tex]\(\frac{30 \div 10}{50 \div 10} = \frac{3}{5}\)[/tex].
- Since [tex]\(\frac{3}{8} \neq \frac{3}{5}\)[/tex], this proportion is false.
2. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplify [tex]\(\frac{25}{45}\)[/tex]:
- [tex]\(25\)[/tex] and [tex]\(45\)[/tex] have a common factor of [tex]\(5\)[/tex].
- Dividing both, we get: [tex]\(\frac{25 \div 5}{45 \div 5} = \frac{5}{9}\)[/tex].
- Simplify [tex]\(\frac{50}{90}\)[/tex]:
- [tex]\(50\)[/tex] and [tex]\(90\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing both, we get: [tex]\(\frac{50 \div 10}{90 \div 10} = \frac{5}{9}\)[/tex].
- Since [tex]\(\frac{5}{9} = \frac{5}{9}\)[/tex], this proportion is true.
3. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Both [tex]\(20\)[/tex] and [tex]\(50\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing, we get: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{40}{100}\)[/tex]:
- Both [tex]\(40\)[/tex] and [tex]\(100\)[/tex] have a common factor of [tex]\(20\)[/tex].
- Dividing, we get: [tex]\(\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\)[/tex].
- Since [tex]\(\frac{2}{5} = \frac{2}{5}\)[/tex], this proportion is true.
4. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplify [tex]\(\frac{12}{15}\)[/tex]:
- Both [tex]\(12\)[/tex] and [tex]\(15\)[/tex] have a common factor of [tex]\(3\)[/tex].
- Dividing, we get: [tex]\(\frac{12 \div 3}{15 \div 3} = \frac{4}{5}\)[/tex].
- Simplify [tex]\(\frac{20}{25}\)[/tex]:
- Both [tex]\(20\)[/tex] and [tex]\(25\)[/tex] have a common factor of [tex]\(5\)[/tex].
- Dividing, we get: [tex]\(\frac{20 \div 5}{25 \div 5} = \frac{4}{5}\)[/tex].
- Since [tex]\(\frac{4}{5} = \frac{4}{5}\)[/tex], this proportion is true.
After evaluating the proportions, we find that the first proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false.
1. Proportion: [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
- First, simplify [tex]\(\frac{18}{48}\)[/tex]:
- [tex]\(18\)[/tex] and [tex]\(48\)[/tex] have a common factor of [tex]\(6\)[/tex].
- Dividing both, we get: [tex]\(\frac{18 \div 6}{48 \div 6} = \frac{3}{8}\)[/tex].
- Next, simplify [tex]\(\frac{30}{50}\)[/tex]:
- [tex]\(30\)[/tex] and [tex]\(50\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing both, we get: [tex]\(\frac{30 \div 10}{50 \div 10} = \frac{3}{5}\)[/tex].
- Since [tex]\(\frac{3}{8} \neq \frac{3}{5}\)[/tex], this proportion is false.
2. Proportion: [tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
- Simplify [tex]\(\frac{25}{45}\)[/tex]:
- [tex]\(25\)[/tex] and [tex]\(45\)[/tex] have a common factor of [tex]\(5\)[/tex].
- Dividing both, we get: [tex]\(\frac{25 \div 5}{45 \div 5} = \frac{5}{9}\)[/tex].
- Simplify [tex]\(\frac{50}{90}\)[/tex]:
- [tex]\(50\)[/tex] and [tex]\(90\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing both, we get: [tex]\(\frac{50 \div 10}{90 \div 10} = \frac{5}{9}\)[/tex].
- Since [tex]\(\frac{5}{9} = \frac{5}{9}\)[/tex], this proportion is true.
3. Proportion: [tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
- Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Both [tex]\(20\)[/tex] and [tex]\(50\)[/tex] have a common factor of [tex]\(10\)[/tex].
- Dividing, we get: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{40}{100}\)[/tex]:
- Both [tex]\(40\)[/tex] and [tex]\(100\)[/tex] have a common factor of [tex]\(20\)[/tex].
- Dividing, we get: [tex]\(\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\)[/tex].
- Since [tex]\(\frac{2}{5} = \frac{2}{5}\)[/tex], this proportion is true.
4. Proportion: [tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
- Simplify [tex]\(\frac{12}{15}\)[/tex]:
- Both [tex]\(12\)[/tex] and [tex]\(15\)[/tex] have a common factor of [tex]\(3\)[/tex].
- Dividing, we get: [tex]\(\frac{12 \div 3}{15 \div 3} = \frac{4}{5}\)[/tex].
- Simplify [tex]\(\frac{20}{25}\)[/tex]:
- Both [tex]\(20\)[/tex] and [tex]\(25\)[/tex] have a common factor of [tex]\(5\)[/tex].
- Dividing, we get: [tex]\(\frac{20 \div 5}{25 \div 5} = \frac{4}{5}\)[/tex].
- Since [tex]\(\frac{4}{5} = \frac{4}{5}\)[/tex], this proportion is true.
After evaluating the proportions, we find that the first proportion, [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex], is false.
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