Respuesta :
Question 1:
We have to find the LCD of [tex]\frac{3}{5}[/tex] and [tex]\frac{1}{6}[/tex]
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 = [tex]5 \times 1[/tex]
6 = [tex]2 \times 3[/tex]
LCM of 5 and 6 = [tex]2 \times 3 \times 5[/tex]
= 30
Therefore, the LCD of these numbers is 30.
Question 2:
We have to find the difference between [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{14}[/tex].
Difference = [tex]\frac{3}{7}- \frac{1}{14}[/tex]
LCM of 7 and 14 is 14
Therefore, difference = [tex]\frac{6-1}{14}[/tex]
= [tex]\frac{5}{14}[/tex]
Question 3:
Amount of brown sugar used by Sandy = [tex]\frac{1}{3}[/tex]
Amount of sugar increased by Sandy = [tex]\frac{2}{9}[/tex]
Total amount of Sugar used by Sandy = [tex]\frac{1}{3}+\frac{2}{9}[/tex]
LCM of 3 and 9 is 9.
Total amount of Sugar used = [tex]\frac{3+2}{9}[/tex]
= [tex]\frac{5}{9}[/tex] cup
Question 4:
Let the number which should be added to [tex]\frac{2}{15}[/tex] to make the sum greater than [tex]\frac{1}{2}[/tex] be 'x'
So, [tex]\frac{2}{15}+x >\frac{1}{2}[/tex]
[tex]x > \frac{1}{2}-\frac{2}{15}[/tex]
LCM of 2 and 15 is 30.
[tex]x>\frac{15-4}{30}[/tex]
[tex]x>\frac{11}{30}[/tex]
So, the number is [tex]\frac{11}{30}[/tex]
Question 5:
We have to identify the set of mixed numbers has a difference less than 1.
Set 1: [tex]1 \frac{2}{9}[/tex] and [tex]1 \frac{1}{9}[/tex]
Difference = [tex]1 \frac{2}{9}-1 \frac{1}{9}[/tex]
= [tex]\frac{11}{9}- \frac{10}{9}[/tex]
= [tex]\frac{1}{9}[/tex]
This set has difference less than 1.
Set 2:
[tex]3 \frac{4}{7}[/tex] and [tex]2 \frac{1}{7}[/tex]
Difference = [tex]3 \frac{4}{7}-2 \frac{1}{7}[/tex]
= [tex]\frac{25}{7}- \frac{15}{7}[/tex]
= [tex]\frac{10}{7}[/tex]
This set does'not have difference less than 1.
Set 3:
[tex]2 \frac{4}{5}[/tex] and [tex]1 \frac{1}{3}[/tex]
Difference = [tex]2 \frac{4}{5}-1 \frac{1}{3}[/tex]
= [tex]\frac{14}{5}- \frac{4}{3}[/tex]
= [tex]\frac{42-20}{15}[/tex]
= [tex]\frac{22}{15}[/tex]
This set does'not have difference less than 1.
Set 4:
[tex]2 \frac{7}{9}[/tex] and [tex]1 \frac{1}{3}[/tex]
Difference = [tex]2 \frac{7}{9}-1 \frac{1}{3}[/tex]
= [tex]\frac{25}{9}- \frac{4}{3}[/tex]
= [tex]\frac{13}{9}[/tex]
This set does'not have difference less than 1.
