Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
To determine what number must be added to [tex]\(\frac{7}{13}\)[/tex] to obtain [tex]\(\frac{-5}{6}\)[/tex], we'll follow these steps:
1. Let [tex]\( x \)[/tex] be the number we need to find. We can write the equation as:
[tex]\[ \frac{7}{13} + x = \frac{-5}{6} \][/tex]
2. Isolate [tex]\( x \)[/tex] by subtracting [tex]\(\frac{7}{13} \)[/tex] from both sides of the equation:
[tex]\[ x = \frac{-5}{6} - \frac{7}{13} \][/tex]
3. To subtract the fractions, we need a common denominator. The denominators here are 6 and 13. The least common multiple (LCM) of 6 and 13 is 78.
4. Convert both fractions to have a common denominator of 78:
[tex]\[ \frac{7}{13} = \frac{7 \times 6}{13 \times 6} = \frac{42}{78} \][/tex]
[tex]\[ \frac{-5}{6} = \frac{-5 \times 13}{6 \times 13} = \frac{-65}{78} \][/tex]
5. Now we can subtract these two fractions:
[tex]\[ x = \frac{-65}{78} - \frac{42}{78} \][/tex]
6. Combine the numerators over the common denominator:
[tex]\[ x = \frac{-65 - 42}{78} = \frac{-107}{78} \][/tex]
7. Simplifying the fraction, we get:
[tex]\[ x = -\frac{107}{78} \][/tex]
8. Converting [tex]\(-\frac{107}{78}\)[/tex] to a decimal, we get approximately:
[tex]\[ x \approx -1.3717948717948718 \][/tex]
So, the number [tex]\( x \)[/tex] that must be added to [tex]\(\frac{7}{13}\)[/tex] to get [tex]\(\frac{-5}{6}\)[/tex] is [tex]\(-\frac{107}{78}\)[/tex], or approximately [tex]\(-1.3717948717948718\)[/tex].
1. Let [tex]\( x \)[/tex] be the number we need to find. We can write the equation as:
[tex]\[ \frac{7}{13} + x = \frac{-5}{6} \][/tex]
2. Isolate [tex]\( x \)[/tex] by subtracting [tex]\(\frac{7}{13} \)[/tex] from both sides of the equation:
[tex]\[ x = \frac{-5}{6} - \frac{7}{13} \][/tex]
3. To subtract the fractions, we need a common denominator. The denominators here are 6 and 13. The least common multiple (LCM) of 6 and 13 is 78.
4. Convert both fractions to have a common denominator of 78:
[tex]\[ \frac{7}{13} = \frac{7 \times 6}{13 \times 6} = \frac{42}{78} \][/tex]
[tex]\[ \frac{-5}{6} = \frac{-5 \times 13}{6 \times 13} = \frac{-65}{78} \][/tex]
5. Now we can subtract these two fractions:
[tex]\[ x = \frac{-65}{78} - \frac{42}{78} \][/tex]
6. Combine the numerators over the common denominator:
[tex]\[ x = \frac{-65 - 42}{78} = \frac{-107}{78} \][/tex]
7. Simplifying the fraction, we get:
[tex]\[ x = -\frac{107}{78} \][/tex]
8. Converting [tex]\(-\frac{107}{78}\)[/tex] to a decimal, we get approximately:
[tex]\[ x \approx -1.3717948717948718 \][/tex]
So, the number [tex]\( x \)[/tex] that must be added to [tex]\(\frac{7}{13}\)[/tex] to get [tex]\(\frac{-5}{6}\)[/tex] is [tex]\(-\frac{107}{78}\)[/tex], or approximately [tex]\(-1.3717948717948718\)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.