Using appropriate properties solve the following: 2/5×-3/7-1/14-3/7×3/5
Answers
Answer:
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Answer:
\frac{2}{5}\times \frac{-3}{7} -\frac{1}{14}-\frac{3}{7}\times\frac{3}{5}=-\frac{1}{2}
5
2
×
7
−3
−
14
1
−
7
3
×
5
3
=−
2
1
Step-by-step explanation:
Given : Expression \frac{2}{5}\times \frac{-3}{7} -\frac{1}{14}-\frac{3}{7}\times\frac{3}{5}
5
2
×
7
−3
−
14
1
−
7
3
×
5
3
To find : The expression using appropriate properties ?
Solution :
\frac{2}{5}\times \frac{-3}{7} -\frac{1}{14}-\frac{3}{7}\times\frac{3}{5}
5
2
×
7
−3
−
14
1
−
7
3
×
5
3
Applying commutative property, a+b=b+aa+b=b+a
=\frac{2}{5}\times \frac{-3}{7}-\frac{3}{7}\times\frac{3}{5} -\frac{1}{14}=
5
2
×
7
−3
−
7
3
×
5
3
−
14
1
Applying distributive property, ab+ac=a(b+c)ab+ac=a(b+c)
=\frac{-3}{7}(\frac{2}{5}+\frac{3}{5})-\frac{1}{14}=
7
−3
(
5
2
+
5
3
)−
14
1
=\frac{-3}{7}(\frac{5}{5})-\frac{1}{14}=
7
−3
(
5
5
)−
14
1
=-\frac{3}{7}-\frac{1}{14}=−
7
3
−
14
1
Taking LCD and solve,
=\frac{-6-1}{14}=
14
−6−1
=\frac{-7}{14}=
14
−7
=\frac{-1}{2}=
2
−1
Therefore, \frac{2}{5}\times \frac{-3}{7} -\frac{1}{14}-\frac{3}{7}\times\frac{3}{5}=-\frac{1}{2}
5
2
×
7
−3
−
14
1
−
7
3
×
5
3
=−
2
1