Question

Find the LCD of 3/5 and 1/6.

a. 5B. 6C. 11D. 302. what is the difference between 3/7 and 1/14.
a. 1\2B. 4/14C. 5/14D. 9/143. if Sandy's cookie recipe calls for 1/3 cup of brown sugar and she increases it by 2/9 of a cup, how much brown sugar does she use?
a. 7/9 cupB. 5/9 cup
c. 4/9 cupD. 1/9 cup4. what value could be added to 2/15 to make the sum greater than 1/2?
a. 1/15B. 8/30C. 5/15D. 8/15 5. which set of mixed numbers has a difference less than 1?
a. 1 2/9, 1 1/9B. 3 4/7, 2 1/7C. 2 4/5, 1 1/3D. 2 7/9, 1 1/3

Answer 1

Question 1:

We have to find the LCD of
`(3)/(5)` and
`(1)/(6)`

LCD is the least common denominator is the lowest common multiple of the denominators of a set of fractions.

Here the denominators are 5 and 6.

So, we will find the LCM of 5 and 6

5 =
`5 * 1`

6 =
`2 * 3`

LCM of 5 and 6 =
`2 * 3 * 5`

= 30

Therefore, the LCD of these numbers is 30.

Question 2:

We have to find the difference between
`(3)/(7)` and
`(1)/(14)`.

Difference =
`(3)/(7)- (1)/(14)`

LCM of 7 and 14 is 14

Therefore, difference =
`(6-1)/(14)`

=
`(5)/(14)`

Question 3:

Amount of brown sugar used by Sandy =
`(1)/(3)`

Amount of sugar increased by Sandy =
`(2)/(9)`

Total amount of Sugar used by Sandy =
`(1)/(3)+(2)/(9)`

LCM of 3 and 9 is 9.

Total amount of Sugar used =
`(3+2)/(9)`

=
`(5)/(9)` cup

Question 4:

Let the number which should be added to
`(2)/(15)` to make the sum greater than
`(1)/(2)` be 'x'

So,
`(2)/(15)+x >(1)/(2)`

`x > (1)/(2)-(2)/(15)`

LCM of 2 and 15 is 30.

`x>(15-4)/(30)`

`x>(11)/(30)`

So, the number is
`(11)/(30)`

Question 5:

We have to identify the set of mixed numbers has a difference less than 1.

Set 1:
`1 (2)/(9)` and
`1 (1)/(9)`

Difference =
`1 (2)/(9)-1 (1)/(9)`

=
`(11)/(9)- (10)/(9)`

=
`(1)/(9)`

This set has difference less than 1.

Set 2:

`3 (4)/(7)` and
`2 (1)/(7)`

Difference =
`3 (4)/(7)-2 (1)/(7)`

=
`(25)/(7)- (15)/(7)`

=
`(10)/(7)`

This set does'not have difference less than 1.

Set 3:

`2 (4)/(5)` and
`1 (1)/(3)`

Difference =
`2 (4)/(5)-1 (1)/(3)`

=
`(14)/(5)- (4)/(3)`

=
`(42-20)/(15)`

=
`(22)/(15)`

This set does'not have difference less than 1.

Set 4:

`2 (7)/(9)` and
`1 (1)/(3)`

Difference =
`2 (7)/(9)-1 (1)/(3)`

=
`(25)/(9)- (4)/(3)`

=
`(13)/(9)`

This set does'not have difference less than 1.