Question

(1 2/3 - 3/5) / 3 * 1/2 + 1/3

Answer 1

Answer:

23/45

Step-by-step explanation:

Answer 2

Answer:

23/45

Step-by-step explanation:

1) Convert $1\frac{2}{3}$  to improper fraction. Use this rule: $a \frac{b}{c}=\frac{ac+b}{c}$

$\frac{\frac{1\times 3+2}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}$

2) Simplify $1\times 3$ to  $3$.

$\frac{\frac{3+2}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}$

3) Simplify  $3+2$  to  $5$.

$\frac{\frac{5}{3}-\frac{3}{5}}{3}\times \frac{1}{2}+\frac{1}{3}$

4)  Find the Least Common Denominator (LCD) of $\frac{5}{3},\frac{3}{5}$. 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:$3\times 5=15$,. This is the LCM.

LCM = 15

5) Make the denominators the same as the LCD.

$\frac{5\times 5}{3\times 5}-\frac{3\times 3}{5\times 3}$

6) Simplify. Denominators are now the same.

$\frac{25}{15}-\frac{9}{15}$

7) Join the denominators.

$\frac{25-9}{15}$

8) Simplify$\frac{5}{3}-\frac{3}{5}$  to $\frac{16}{15}$

$\frac{\frac{16}{15}}{3}\times \frac{1}{2}+\frac{1}{3}$

9) Simplify  $\frac{\frac{16}{15}}{3}$ to    $\frac{16}{15\times 3}$.

$\frac{16}{15\times 3}\times \frac{1}{2}+\frac{1}{3}$

10) Simplify $15\times 3$ to  $45.$

$\frac{16}{45}\times \frac{1}{2}+\frac{1}{3}$

11)  Use this rule: $\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.$

$\frac{16\times 1}{45\times 2}+\frac{1}{3}$

12) Simplify $16\times 1$ to  16.

$\frac{16}{45\times 2}+\frac{1}{3}$

13) Simplify  $45\times 2$  to  90.

$\frac{16}{90}+\frac{1}{3}$

14) Simplify $\frac{16}{90}$ to $\frac{8}{45}$.

$\frac{8}{45}+\frac{1}{3}$

15) Find the Least Common Denominator (LCD) of $\frac{8}{45},\frac{1}{3}$ . 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$: 3\times 3\times 5=45$. This is the LCM.

LCM = 45

Result: $LCD=45$

16)  Make the denominators the same as the LCD.

$\frac{8}{45}+\frac{1\times 15}{3\times 15}$

17) Simplify. Denominators are now the same.

$\frac{8}{45}+\frac{15}{45}$

18)  Join the denominators.

$\frac{8+15}{45}$

19) Simplify.

$\frac{23}{45}$

Decimal Form: 0.511111