Question

Simplify 7/12 + 5/18 =

Answer 1

31/36

Explanation:

1) Find the Least Common Denominator (LCD) of
`(7)/(12)`,
`(5)/(18)`. In other words, find the Least Common Multiple (LCM) of 12, 18.

Method 1: By Listing Multiples

1) List the multiples of each number

Multiples of 12: 12, 24, 36, ...

Multiples of 18: 18, 36, ...

2) Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 36

Method 2: By Prime Factors

1) List the prime factors of each number.

Prime Factors of 12: 2, 2, 3

Prime Factors of 18: 2, 3, 3

2) Find the union of these primes.

2, 2, 3, 3

3) Multiply these number: 2 x 2 x 3 x 3 = 36. This is the LCM.

LCM = 36

STEP 2: Make the denominators the same as the LCD.

`(7*3)/(12*3) +(5*2)/(18*2)`

3) Simplify. Denominators are now the same.

`(21)/(36) +(10)/(36)`

4) Join the denominators.

`(21+10)/(36)`

5) Simplify.

`(31)/(36)`

Thank you,

Eddie.

Answer 2

Answer:31/36

Explanation:

we should find greatest common divisor(GCD) ,

GCD(12,18)=36

7/12=7*3/36=21/36

5/18=5*2/36=10/36

21/36+10/36=31/36