Question

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

Answer 1

23/45

Explanation:

1) Convert
`1(2)/(3)` to improper fraction. Use this rule:
`a (b)/(c)=(ac+b)/(c)`

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

2) Simplify
`1* 3` to
`3`.

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

3) Simplify
`3+2` to
`5`.

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

4) Find the Least Common Denominator (LCD) of
`(5)/(3),(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* 5=15`,. This is the LCM.

LCM = 15

5) Make the denominators the same as the LCD.

`(5* 5)/(3* 5)-(3* 3)/(5* 3)`

6) Simplify. Denominators are now the same.

`(25)/(15)-(9)/(15)`

7) Join the denominators.

`(25-9)/(15)`

8) Simplify
`(5)/(3)-(3)/(5)` to
`(16)/(15)`

`((16)/(15))/(3)* (1)/(2)+(1)/(3)`

9) Simplify
`((16)/(15))/(3)` to
`(16)/(15* 3)`.

`(16)/(15* 3)* (1)/(2)+(1)/(3)`

10) Simplify
`15* 3` to
`45.`

`(16)/(45)* (1)/(2)+(1)/(3)`

11) Use this rule:
`(a)/(b) * (c)/(d)=(ac)/(bd).`

`(16* 1)/(45* 2)+(1)/(3)`

12) Simplify
`16* 1` to 16.

`(16)/(45* 2)+(1)/(3)`

13) Simplify
`45* 2` to 90.

`(16)/(90)+(1)/(3)`

14) Simplify
`(16)/(90)` to
`(8)/(45)`.

`(8)/(45)+(1)/(3)`

15) Find the Least Common Denominator (LCD) of
`(8)/(45),(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* 3* 5=45`. This is the LCM.

LCM = 45

Result:
`LCD=45`

16) Make the denominators the same as the LCD.

`(8)/(45)+(1* 15)/(3* 15)`

17) Simplify. Denominators are now the same.

`(8)/(45)+(15)/(45)`

18) Join the denominators.

`(8+15)/(45)`

19) Simplify.

`(23)/(45)`

Decimal Form: 0.511111

Answer 2

23/45

Explanation: