6) common denominator = 54
7) common denominator = 80
8) common denominator = 108
9) least common denominator = 10
10) least common denominator = 24
11) common denominator = 21
Step-by-step explanation:
6) common denominator of 1/6 , 1/9
example: A/B where A is de numerator and B is the denominator.
common denominators are numbers that have te same composition
1/6 , 1/9 ⇒ if we want to add this fractions we need to find the common denominator.
therefore: (1/6)*(9/9) , (1/9)*(6/6) ⇒ ((1*9)/(6*9)) . ((1*6)/(9*6)) ⇒ 9/54 , 6/54
the common denominator is 54
7) 3/8 , 3/10
(3*10)/(8*10) , (3*8)/(10*8) ⇒ 30/80 , 24/80
common denominator of this two fractions is 80
Note: We can see that the common denominator can be find just by multiplying the denominators. in 7) 6*9=54 and in 8) 10*8=80. This is because in this cases we are asked just for the common denominator
9) 1/9 , 5/12 ⇒ common denominator = 9*12 = 108
10) Least common denominator of 2/5 , 1/10
in this case is the smmallest number that the denominator have in common:
first, from 2/5: denominator=5
multiples of 5: ⇒5, 10, 15,
then from 1/10: denominator=10
multiples of 10 ⇒ 10, 20, 30,
The least common denominator is the smalles number this two denominators have in common. We can see that this number is 10.
There are other ways because you should also think of it as the minimun common denominator. 5 =5*1 and  10 = 2*5 (minimun expresions)
the least minimun denominator willbe the one that includes all de numbers included in their minimum expresion without making it doble (just the amount of times to make the denominator number in each fraction).
therefore we would know that the least common denominator in this fractions is: 1*2*5 = 2*5 = 10
But just have fun and make it simple
10. least common denominator for: 5/6 , 3/8
first: 5/6 ⇒ denominator: 6, so ⇒ 6, 12, 18, 24, 30, 36
then: 3/8 ⇒ denominator: 8, so ⇒ 8, 16, 24. 32, 40
least common denominator for this fractions is ⇒24
or also:
5/6 ⇒ denominator is 6 ⇒ 6=2*3
3/8 ⇒ denominator is 8 ⇒ 8=2*2*2
least common denominator for this fractions is ⇒ 2*2*2*3 =24
11. common denominator of: 1/3 , 2/7
because in this case 3 and 7 are in their minimum expresion ⇔ 3=1*3 & 7=1*7
we can jus find the common denominator by multiplying both denominators:
7*3=21
Hope it helps.
