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 $\frac{3}{5}$ and $\frac{1}{6}$

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 = $5 \times 1$

6 = $2 \times 3$

LCM of 5 and 6 = $2 \times 3 \times 5$

= 30

Therefore, the LCD of these numbers is 30.

Question 2:

We have to find the difference between  $\frac{3}{7}$  and  $\frac{1}{14}$.

Difference = $\frac{3}{7}- \frac{1}{14}$

LCM of 7 and 14 is 14

Therefore, difference = $\frac{6-1}{14}$

= $\frac{5}{14}$

Question 3:

Amount of brown sugar used by Sandy = $\frac{1}{3}$

Amount of sugar increased by Sandy = $\frac{2}{9}$

Total amount of Sugar used by Sandy = $\frac{1}{3}+\frac{2}{9}$

LCM of 3 and 9 is 9.

Total amount of Sugar used = $\frac{3+2}{9}$

= $\frac{5}{9}$ cup

Question 4:

Let the number which should be added to $\frac{2}{15}$ to make the sum greater than $\frac{1}{2}$ be 'x'

So, $\frac{2}{15}+x >\frac{1}{2}$

$x > \frac{1}{2}-\frac{2}{15}$

LCM of 2 and 15 is 30.

$x>\frac{15-4}{30}$

$x>\frac{11}{30}$

So, the number is $\frac{11}{30}$

Question 5:

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

Set 1: $1 \frac{2}{9}$ and $1 \frac{1}{9}$

Difference = $1 \frac{2}{9}-1 \frac{1}{9}$

= $\frac{11}{9}- \frac{10}{9}$

= $\frac{1}{9}$

This set has difference less than 1.

Set 2:

$3 \frac{4}{7}$ and $2 \frac{1}{7}$

Difference = $3 \frac{4}{7}-2 \frac{1}{7}$

= $\frac{25}{7}- \frac{15}{7}$

= $\frac{10}{7}$

This set does'not have difference less than 1.

Set 3:

$2 \frac{4}{5}$ and $1 \frac{1}{3}$

Difference = $2 \frac{4}{5}-1 \frac{1}{3}$

= $\frac{14}{5}- \frac{4}{3}$

= $\frac{42-20}{15}$

= $\frac{22}{15}$

This set does'not have difference less than 1.

Set 4:

$2 \frac{7}{9}$ and $1 \frac{1}{3}$

Difference = $2 \frac{7}{9}-1 \frac{1}{3}$

= $\frac{25}{9}- \frac{4}{3}$

= $\frac{13}{9}$

This set does'not have difference less than 1.