Answer :
To solve the expression \(\left(-\frac{6}{5}+\frac{1}{3}\right) \cdot\left(\frac{3}{26}\right)\), let's break it down into detailed steps:
1. Combine the fractions inside the parentheses:
[tex]\[ \left(-\frac{6}{5} + \frac{1}{3}\right) \][/tex]
To add these fractions, we need a common denominator. For \(-\frac{6}{5}\) and \(\frac{1}{3}\), the least common multiple of 5 and 3 is 15.
- Convert \(-\frac{6}{5}\) to a fraction with a denominator of 15:
[tex]\[ -\frac{6}{5} = -\frac{6 \times 3}{5 \times 3} = -\frac{18}{15} \][/tex]
- Convert \(\frac{1}{3}\) to a fraction with a denominator of 15:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
Now that both fractions have the same denominator, we can add them:
[tex]\[ -\frac{18}{15} + \frac{5}{15} = \frac{-18 + 5}{15} = \frac{-13}{15} \][/tex]
So, the sum inside the parentheses is:
[tex]\[ -\frac{13}{15} \][/tex]
2. Multiply the result with the third fraction:
[tex]\[ \left(-\frac{13}{15}\right) \cdot \left(\frac{3}{26}\right) \][/tex]
Multiply the numerators and the denominators:
[tex]\[ \frac{-13 \times 3}{15 \times 26} = \frac{-39}{390} \][/tex]
Simplify the fraction by finding the greatest common divisor (GCD) of 39 and 390, which is 39. Divide both the numerator and the denominator by 39:
[tex]\[ \frac{-39 \div 39}{390 \div 39} = \frac{-1}{10} \][/tex]
Therefore, the result of the expression \(\left(-\frac{6}{5}+\frac{1}{3}\right) \cdot\left(\frac{3}{26}\right)\) is:
[tex]\[ -\frac{1}{10} \][/tex]
In decimal form, this is:
[tex]\[ -0.1 \][/tex]
So, the detailed solution yields:
1. The sum inside the parentheses is approximately \(-0.8666666666666667\).
2. The final result of the entire expression is [tex]\(-0.1\)[/tex].
1. Combine the fractions inside the parentheses:
[tex]\[ \left(-\frac{6}{5} + \frac{1}{3}\right) \][/tex]
To add these fractions, we need a common denominator. For \(-\frac{6}{5}\) and \(\frac{1}{3}\), the least common multiple of 5 and 3 is 15.
- Convert \(-\frac{6}{5}\) to a fraction with a denominator of 15:
[tex]\[ -\frac{6}{5} = -\frac{6 \times 3}{5 \times 3} = -\frac{18}{15} \][/tex]
- Convert \(\frac{1}{3}\) to a fraction with a denominator of 15:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
Now that both fractions have the same denominator, we can add them:
[tex]\[ -\frac{18}{15} + \frac{5}{15} = \frac{-18 + 5}{15} = \frac{-13}{15} \][/tex]
So, the sum inside the parentheses is:
[tex]\[ -\frac{13}{15} \][/tex]
2. Multiply the result with the third fraction:
[tex]\[ \left(-\frac{13}{15}\right) \cdot \left(\frac{3}{26}\right) \][/tex]
Multiply the numerators and the denominators:
[tex]\[ \frac{-13 \times 3}{15 \times 26} = \frac{-39}{390} \][/tex]
Simplify the fraction by finding the greatest common divisor (GCD) of 39 and 390, which is 39. Divide both the numerator and the denominator by 39:
[tex]\[ \frac{-39 \div 39}{390 \div 39} = \frac{-1}{10} \][/tex]
Therefore, the result of the expression \(\left(-\frac{6}{5}+\frac{1}{3}\right) \cdot\left(\frac{3}{26}\right)\) is:
[tex]\[ -\frac{1}{10} \][/tex]
In decimal form, this is:
[tex]\[ -0.1 \][/tex]
So, the detailed solution yields:
1. The sum inside the parentheses is approximately \(-0.8666666666666667\).
2. The final result of the entire expression is [tex]\(-0.1\)[/tex].
