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Answer :
To subtract the fractions, follow these steps:
1. Find a common denominator. The least common multiple of [tex]$15$[/tex] and [tex]$9$[/tex] is [tex]$45$[/tex].
2. Convert each fraction to an equivalent fraction with denominator [tex]$45$[/tex]:
- For [tex]$\frac{13}{15}$[/tex], multiply numerator and 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]$\frac{4}{9}$[/tex], multiply numerator and denominator by [tex]$5$[/tex] (since [tex]$9 \times 5 = 45$[/tex]):
[tex]$$\frac{4}{9} = \frac{4 \times 5}{9 \times 5} = \frac{20}{45}.$$[/tex]
3. Subtract the fractions:
[tex]$$\frac{39}{45} - \frac{20}{45} = \frac{39 - 20}{45} = \frac{19}{45}.$$[/tex]
4. Since the greatest common divisor of [tex]$19$[/tex] and [tex]$45$[/tex] is [tex]$1$[/tex], the fraction [tex]$\frac{19}{45}$[/tex] is already in its simplest form.
Thus, the final answer is:
[tex]$$\frac{19}{45}.$$[/tex]
1. Find a common denominator. The least common multiple of [tex]$15$[/tex] and [tex]$9$[/tex] is [tex]$45$[/tex].
2. Convert each fraction to an equivalent fraction with denominator [tex]$45$[/tex]:
- For [tex]$\frac{13}{15}$[/tex], multiply numerator and 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]$\frac{4}{9}$[/tex], multiply numerator and denominator by [tex]$5$[/tex] (since [tex]$9 \times 5 = 45$[/tex]):
[tex]$$\frac{4}{9} = \frac{4 \times 5}{9 \times 5} = \frac{20}{45}.$$[/tex]
3. Subtract the fractions:
[tex]$$\frac{39}{45} - \frac{20}{45} = \frac{39 - 20}{45} = \frac{19}{45}.$$[/tex]
4. Since the greatest common divisor of [tex]$19$[/tex] and [tex]$45$[/tex] is [tex]$1$[/tex], the fraction [tex]$\frac{19}{45}$[/tex] is already in its simplest form.
Thus, the final answer is:
[tex]$$\frac{19}{45}.$$[/tex]
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