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Answer :
We want to subtract the fractions
[tex]$$\frac{13}{15} - \frac{1}{5}.$$[/tex]
Step 1. Rewrite with a common denominator
To subtract fractions, they must have the same denominator. The first fraction has denominator 15. To convert the second fraction [tex]$\frac{1}{5}$[/tex] to a denominator of 15, multiply both its numerator and denominator by 3:
[tex]$$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}.$$[/tex]
Step 2. Subtract the fractions
Now subtract the fractions:
[tex]$$\frac{13}{15} - \frac{3}{15} = \frac{13-3}{15} = \frac{10}{15}.$$[/tex]
Step 3. Simplify the resulting fraction
To simplify [tex]$\frac{10}{15}$[/tex], find the greatest common divisor (GCD) of 10 and 15, which is 5. Divide both the numerator and the denominator by 5:
[tex]$$\frac{10}{15} = \frac{10\div 5}{15\div 5} = \frac{2}{3}.$$[/tex]
Thus, the final answer is
[tex]$$\frac{2}{3}.$$[/tex]
[tex]$$\frac{13}{15} - \frac{1}{5}.$$[/tex]
Step 1. Rewrite with a common denominator
To subtract fractions, they must have the same denominator. The first fraction has denominator 15. To convert the second fraction [tex]$\frac{1}{5}$[/tex] to a denominator of 15, multiply both its numerator and denominator by 3:
[tex]$$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}.$$[/tex]
Step 2. Subtract the fractions
Now subtract the fractions:
[tex]$$\frac{13}{15} - \frac{3}{15} = \frac{13-3}{15} = \frac{10}{15}.$$[/tex]
Step 3. Simplify the resulting fraction
To simplify [tex]$\frac{10}{15}$[/tex], find the greatest common divisor (GCD) of 10 and 15, which is 5. Divide both the numerator and the denominator by 5:
[tex]$$\frac{10}{15} = \frac{10\div 5}{15\div 5} = \frac{2}{3}.$$[/tex]
Thus, the final answer is
[tex]$$\frac{2}{3}.$$[/tex]
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