Answer:
we conclude that:
5/7 - 3/7: B 2/7
1/6+3/6: C 2/3
1/2+1/4: E 3/4
1/5+1/2: D 7/10
1/6-1/8: A 1/24
Step-by-step explanation:
1)
Given the expression
[tex]\frac{5}{7}-\frac{3}{7}[/tex]
Apply the fraction rule: [tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex]
[tex]\frac{5}{7}-\frac{3}{7}=\frac{5-3}{7}[/tex]
Add the numbers: [tex]5-3=2[/tex]
[tex]=\frac{2}{7}[/tex]
2)
Given the expression
[tex]\frac{1}{6}+\frac{3}{6}[/tex]
Apply the fraction rule: [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]\frac{1}{6}+\frac{3}{6}=\frac{1+3}{6}[/tex]
Add the numbers: [tex]1+3=4[/tex]
[tex]=\frac{4}{6}[/tex]
Cancel 4/6: 2/3
[tex]=\frac{2}{3}[/tex]
3)
Given the expression
[tex]\frac{1}{2}+\frac{1}{4}[/tex]
Lease common multiplier of 2, 4: 4
Adjust fractions based on LCM
[tex]\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}[/tex]
Apply the fraction rule: [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]\frac{2}{4}+\frac{1}{4}=\frac{2+1}{4}[/tex]
Add the numbers: [tex]2+1=3[/tex]
[tex]=\frac{3}{4}[/tex]
4)
[tex]\frac{1}{5}+\frac{1}{2}[/tex]
Lease common multiplier of 5, 2: 10
Adjust fractions based on LCM
[tex]\frac{1}{5}+\frac{1}{2}=\frac{2}{10}+\frac{5}{10}[/tex]
Apply the fraction rule: [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]\frac{2}{10}+\frac{5}{10}=\frac{2+5}{10}[/tex]
Add the numbers: 2+5 = 7
[tex]=\frac{7}{10}[/tex]
5)
Given the expression
[tex]\frac{1}{6}-\frac{1}{8}[/tex]
Lease common multiplier of 6, 8: 24
Adjust fractions based on LCM
[tex]\frac{1}{6}-\frac{1}{8}=\frac{4}{24}-\frac{3}{24}[/tex]
Apply the fraction rule: [tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex]
[tex]\frac{4}{24}-\frac{3}{24}=\frac{4-3}{24}[/tex]
[tex]=\frac{1}{24}[/tex]
Therefore, we conclude that:
5/7 - 3/7: B 2/7
1/6+3/6: C 2/3
1/2+1/4: E 3/4
1/5+1/2: D 7/10
1/6-1/8: A 1/24
