Taking a=-⅔,b= ⅕ and c=-⅗ verify the distributive property over addition and subtraction
Answers
Answer:
Given:
\dfrac{2}{3} \times \dfrac{7}{5} - \dfrac{3}{4} \times \dfrac{7}{5} + \dfrac{5}{6}
3
2
×
5
7
−
4
3
×
5
7
+
6
5
\begin{gathered}\\\end{gathered}
To Find:
Apply distributive property to evaluate the equation
\begin{gathered}\\\end{gathered}
Explanation
Distributive Property states that :
ab + ac = a(b + c)
\begin{gathered}\\\end{gathered}
Solution
\begin{gathered}\\\end{gathered}
\dfrac{2}{3} \times \dfrac{7}{5} - \dfrac{3}{4} \times \dfrac{7}{5} + \dfrac{5}{6}
3
2
×
5
7
−
4
3
×
5
7
+
6
5
\begin{gathered}\\\end{gathered}
Taking out common factor 7/5:
= \dfrac{7}{5}\bigg (\dfrac{2}{3} \bigg) -\dfrac{7}{5} \bigg( \dfrac{3}{4} \bigg) + \dfrac{5}{6}=
5
7
(
3
2
)−
5
7
(
4
3
)+
6
5
\begin{gathered}\\\end{gathered}
Applying the distributive property:
= \dfrac{7}{5}\bigg (\dfrac{2}{3} - \dfrac{3}{4}\bigg) + \dfrac{5}{6}=
5
7
(
3
2
−
4
3
)+
6
5
\begin{gathered}\\\end{gathered}
Simplify the terms in the bracket:
= \dfrac{7}{5}\bigg (-\dfrac{1}{12} \bigg) + \dfrac{5}{6}=
5
7
(−
12
1
)+
6
5
\begin{gathered}\\\end{gathered}
Do the multiplication before addition:
= -\dfrac{7}{60} + \dfrac{5}{6}=−
60
7
+
6
5
\begin{gathered}\\\end{gathered}
Subtract the fractions:
= -\dfrac{7}{60} + \dfrac{50}{60}=−
60
7
+
60
50
= \dfrac{43}{60}=
60
43
\begin{gathered}\\\end{gathered}
Answer: 43/60
Answer:
43/60 this is the answer