At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Certainly! To add the fractions [tex]\(\frac{1}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex], we need to follow these steps:
1. Find a common denominator: The denominators of the given fractions are 7 and 14. The least common denominator (LCD) is the least common multiple (LCM) of these two numbers. The least common multiple of 7 and 14 is 14.
2. Convert the fractions to have the same denominator:
- For the fraction [tex]\(\frac{1}{7}\)[/tex], we need to convert it to a fraction with a denominator of 14.
- To do this, we multiply both the numerator and the denominator by [tex]\(2\)[/tex] (since [tex]\(14 \div 7 = 2\)[/tex]):
[tex]\[ \frac{1 \times 2}{7 \times 2} = \frac{2}{14} \][/tex]
- For the fraction [tex]\(\frac{3}{14}\)[/tex], it already has the denominator of 14, so we don't need to change it.
[tex]\[ \frac{3}{14} \][/tex]
3. Add the fractions:
- Now that both fractions have the same denominator, we can add their numerators directly:
[tex]\[ \frac{2}{14} + \frac{3}{14} = \frac{2 + 3}{14} = \frac{5}{14} \][/tex]
4. Reduce the fraction (if possible):
- To check if the fraction can be reduced, we find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 5 and 14 is 1, as 5 is a prime number and does not share any common factors with 14 other than 1. Thus, [tex]\(\frac{5}{14}\)[/tex] is already in its simplest form.
In summary:
[tex]\[ \begin{array}{r} \frac{1}{7}=\frac{2}{14} \\ +\frac{3}{14} \\ \hline \frac{5}{14} \end{array} \][/tex]
1. Find a common denominator: The denominators of the given fractions are 7 and 14. The least common denominator (LCD) is the least common multiple (LCM) of these two numbers. The least common multiple of 7 and 14 is 14.
2. Convert the fractions to have the same denominator:
- For the fraction [tex]\(\frac{1}{7}\)[/tex], we need to convert it to a fraction with a denominator of 14.
- To do this, we multiply both the numerator and the denominator by [tex]\(2\)[/tex] (since [tex]\(14 \div 7 = 2\)[/tex]):
[tex]\[ \frac{1 \times 2}{7 \times 2} = \frac{2}{14} \][/tex]
- For the fraction [tex]\(\frac{3}{14}\)[/tex], it already has the denominator of 14, so we don't need to change it.
[tex]\[ \frac{3}{14} \][/tex]
3. Add the fractions:
- Now that both fractions have the same denominator, we can add their numerators directly:
[tex]\[ \frac{2}{14} + \frac{3}{14} = \frac{2 + 3}{14} = \frac{5}{14} \][/tex]
4. Reduce the fraction (if possible):
- To check if the fraction can be reduced, we find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 5 and 14 is 1, as 5 is a prime number and does not share any common factors with 14 other than 1. Thus, [tex]\(\frac{5}{14}\)[/tex] is already in its simplest form.
In summary:
[tex]\[ \begin{array}{r} \frac{1}{7}=\frac{2}{14} \\ +\frac{3}{14} \\ \hline \frac{5}{14} \end{array} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.