Respuesta :
Answer:
23/45
Step-by-step explanation:
1) Convert [tex]1\frac{2}{3}[/tex] to improper fraction. Use this rule: [tex]a \frac{b}{c}=\frac{ac+b}{c}[/tex]
[tex]\frac{\frac{1\times 3+2}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}[/tex]
2) Simplify [tex]1\times 3[/tex] to [tex]3[/tex].
[tex]\frac{\frac{3+2}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}[/tex]
3) Simplify [tex]3+2[/tex] to [tex]5[/tex].
[tex]\frac{\frac{5}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}[/tex]
4) Find the Least Common Denominator (LCD) of [tex]\frac{5}{3},\frac{3}{5}[/tex]. In other words, find the Least Common Multiple (LCM) of 3,5.
Method 1: By Listing Multiples
1 - List the multiples of each number.
Multiples of 3 : 3, 6, 9, 12, 15, ...
Multiples of 5 : 5, 10, 15, ...
2 - Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 15
Method 2: By Prime Factors
1- List the prime factors of each number.
Prime Factors of 3 : 3
Prime Factors of 5 : 5
2 - Find the union of these primes.
3, 5
3- Multiply these numbers:[tex]3\times 5=15[/tex],. This is the LCM.
LCM = 15
5) Make the denominators the same as the LCD.
[tex]\frac{5\times 5}{3\times 5}-\frac{3\times 3}{5\times 3}[/tex]
6) Simplify. Denominators are now the same.
[tex]\frac{25}{15}-\frac{9}{15}[/tex]
7) Join the denominators.
[tex]\frac{25-9}{15}[/tex]
8) Simplify[tex]\frac{5}{3}-\frac{3}{5}[/tex] to [tex]\frac{16}{15}[/tex]
[tex]\frac{\frac{16}{15}}{3}\times \frac{1}{2}+\frac{1}{3}[/tex]
9) Simplify [tex]\frac{\frac{16}{15}}{3}[/tex] to [tex]\frac{16}{15\times 3}[/tex].
[tex]\frac{16}{15\times 3}\times \frac{1}{2}+\frac{1}{3}[/tex]
10) Simplify [tex]15\times 3[/tex] to [tex]45.[/tex]
[tex]\frac{16}{45}\times \frac{1}{2}+\frac{1}{3}[/tex]
11) Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.[/tex]
[tex]\frac{16\times 1}{45\times 2}+\frac{1}{3}[/tex]
12) Simplify [tex]16\times 1[/tex] to 16.
[tex]\frac{16}{45\times 2}+\frac{1}{3}[/tex]
13) Simplify [tex]45\times 2[/tex] to 90.
[tex]\frac{16}{90}+\frac{1}{3}[/tex]
14) Simplify [tex]\frac{16}{90}[/tex] to [tex]\frac{8}{45}[/tex].
[tex]\frac{8}{45}+\frac{1}{3}[/tex]
15) Find the Least Common Denominator (LCD) of [tex]\frac{8}{45},\frac{1}{3}[/tex] . In other words, find the Least Common Multiple (LCM) of 45, 3.
Method 1: By Listing Multiples
1 - List the multiples of each number.
Multiples of 45 : 45, ...
Multiples of 3 : 3, 6, 9, ... , 39, 42, 45, ...
2 - Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 45
Method 2: By Prime Factors
1 - List the prime factors of each number.
Prime Factors of 45 : 3, 3, 5
Prime Factors of 3 : 3
2 - Find the union of these primes.
3, 3, 5
Multiply these numbers[tex]: 3\times 3\times 5=45[/tex]. This is the LCM.
LCM = 45
Result: [tex]LCD=45[/tex]
16) Make the denominators the same as the LCD.
[tex]\frac{8}{45}+\frac{1\times 15}{3\times 15}[/tex]
17) Simplify. Denominators are now the same.
[tex]\frac{8}{45}+\frac{15}{45}[/tex]
18) Join the denominators.
[tex]\frac{8+15}{45}[/tex]
19) Simplify.
[tex]\frac{23}{45}[/tex]
Decimal Form: 0.511111
