Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To solve the problem [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex], we will follow these steps to understand and find the ratio between the two fractions:
### Step-by-Step Solution:
1. Understand the Colon Notation (:):
- The colon (:) in mathematics typically represents a ratio. So, [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] is asking for the ratio of [tex]\(\frac{2}{7}\)[/tex] to [tex]\(\frac{5}{7}\)[/tex].
2. Convert the Ratio to Division:
- A ratio [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] can be interpreted as [tex]\(\frac{\frac{2}{7}}{\frac{5}{7}}\)[/tex].
3. Simplify the Division of Fractions:
- When dividing fractions, we multiply by the reciprocal of the divisor.
- [tex]\(\frac{\frac{2}{7}}{\frac{5}{7}} = \frac{2}{7} \times \frac{7}{5}\)[/tex].
4. Multiply the Fractions:
- Multiply the numerators together and the denominators together:
[tex]\[ \frac{2}{7} \times \frac{7}{5} = \frac{2 \times 7}{7 \times 5} = \frac{14}{35}. \][/tex]
5. Simplify the Resulting Fraction:
- Simplify [tex]\(\frac{14}{35}\)[/tex] by finding the greatest common divisor of 14 and 35. The GCD is 7.
- Divide both the numerator and the denominator by 7.
[tex]\[ \frac{14 \div 7}{35 \div 7} = \frac{2}{5}. \][/tex]
Therefore, the ratio [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
For exact values:
- The decimal representation of [tex]\(\frac{2}{7}\)[/tex] is approximately 0.2857142857142857.
- The decimal representation of [tex]\(\frac{5}{7}\)[/tex] is approximately 0.7142857142857143.
- When you divide 0.2857142857142857 by 0.7142857142857143, the result is approximately 0.4.
Thus, the ratio of [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] is indeed [tex]\(\frac{2}{5}\)[/tex], which in decimal form is 0.4.
### Step-by-Step Solution:
1. Understand the Colon Notation (:):
- The colon (:) in mathematics typically represents a ratio. So, [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] is asking for the ratio of [tex]\(\frac{2}{7}\)[/tex] to [tex]\(\frac{5}{7}\)[/tex].
2. Convert the Ratio to Division:
- A ratio [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] can be interpreted as [tex]\(\frac{\frac{2}{7}}{\frac{5}{7}}\)[/tex].
3. Simplify the Division of Fractions:
- When dividing fractions, we multiply by the reciprocal of the divisor.
- [tex]\(\frac{\frac{2}{7}}{\frac{5}{7}} = \frac{2}{7} \times \frac{7}{5}\)[/tex].
4. Multiply the Fractions:
- Multiply the numerators together and the denominators together:
[tex]\[ \frac{2}{7} \times \frac{7}{5} = \frac{2 \times 7}{7 \times 5} = \frac{14}{35}. \][/tex]
5. Simplify the Resulting Fraction:
- Simplify [tex]\(\frac{14}{35}\)[/tex] by finding the greatest common divisor of 14 and 35. The GCD is 7.
- Divide both the numerator and the denominator by 7.
[tex]\[ \frac{14 \div 7}{35 \div 7} = \frac{2}{5}. \][/tex]
Therefore, the ratio [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
For exact values:
- The decimal representation of [tex]\(\frac{2}{7}\)[/tex] is approximately 0.2857142857142857.
- The decimal representation of [tex]\(\frac{5}{7}\)[/tex] is approximately 0.7142857142857143.
- When you divide 0.2857142857142857 by 0.7142857142857143, the result is approximately 0.4.
Thus, the ratio of [tex]\(\frac{2}{7} : \frac{5}{7}\)[/tex] is indeed [tex]\(\frac{2}{5}\)[/tex], which in decimal form is 0.4.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.