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Answer :
To subtract and simplify the expression
[tex]$$
\frac{13}{15} - \frac{5}{9},
$$[/tex]
follow these steps:
1. Find a Common Denominator
The denominators are [tex]$15$[/tex] and [tex]$9$[/tex]. Their least common denominator (LCD) is [tex]$45$[/tex].
2. Rewrite Each Fraction with the Common Denominator
For [tex]$\frac{13}{15}$[/tex]: Multiply the numerator and the denominator by [tex]$3$[/tex] (since [tex]$15 \times 3 = 45$[/tex]):
[tex]$$
\frac{13}{15} = \frac{13 \times 3}{15 \times 3} = \frac{39}{45}.
$$[/tex]
For [tex]$\frac{5}{9}$[/tex]: Multiply the numerator and the denominator by [tex]$5$[/tex] (since [tex]$9 \times 5 = 45$[/tex]):
[tex]$$
\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}.
$$[/tex]
3. Subtract the Numerators
Now that both fractions have the same denominator, subtract the numerators:
[tex]$$
\frac{39}{45} - \frac{25}{45} = \frac{39 - 25}{45} = \frac{14}{45}.
$$[/tex]
4. Simplify the Result
The fraction [tex]$\frac{14}{45}$[/tex] is already in simplest form because [tex]$14$[/tex] and [tex]$45$[/tex] have no common factors other than [tex]$1$[/tex].
Thus, the final answer is:
[tex]$$
\frac{14}{45}.
$$[/tex]
[tex]$$
\frac{13}{15} - \frac{5}{9},
$$[/tex]
follow these steps:
1. Find a Common Denominator
The denominators are [tex]$15$[/tex] and [tex]$9$[/tex]. Their least common denominator (LCD) is [tex]$45$[/tex].
2. Rewrite Each Fraction with the Common Denominator
For [tex]$\frac{13}{15}$[/tex]: Multiply the numerator and the denominator by [tex]$3$[/tex] (since [tex]$15 \times 3 = 45$[/tex]):
[tex]$$
\frac{13}{15} = \frac{13 \times 3}{15 \times 3} = \frac{39}{45}.
$$[/tex]
For [tex]$\frac{5}{9}$[/tex]: Multiply the numerator and the denominator by [tex]$5$[/tex] (since [tex]$9 \times 5 = 45$[/tex]):
[tex]$$
\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}.
$$[/tex]
3. Subtract the Numerators
Now that both fractions have the same denominator, subtract the numerators:
[tex]$$
\frac{39}{45} - \frac{25}{45} = \frac{39 - 25}{45} = \frac{14}{45}.
$$[/tex]
4. Simplify the Result
The fraction [tex]$\frac{14}{45}$[/tex] is already in simplest form because [tex]$14$[/tex] and [tex]$45$[/tex] have no common factors other than [tex]$1$[/tex].
Thus, the final answer is:
[tex]$$
\frac{14}{45}.
$$[/tex]
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