Answer :
Answer:
Step-by-step explanation:
Sure, let's simplify the given expression and mention the property used.
The expression given is:
6
11
+
6
11
+
6
11
11
6
+
11
6
+
11
6
We need to show that:
6
11
+
6
11
+
6
11
=
18
11
11
6
+
11
6
+
11
6
=
11
18
Let's simplify the left-hand side:
Recognize that adding fractions with the same denominator involves adding the numerators and keeping the denominator the same.
So,
6
11
+
6
11
+
6
11
11
6
+
11
6
+
11
6
can be simplified as:
6
+
6
+
6
11
11
6+6+6
This simplifies further to:
18
11
11
18
Thus,
6
11
+
6
11
+
6
11
=
18
11
11
6
+
11
6
+
11
6
=
11
18
Property Used:
The property used here is the associative property of addition for fractions. This property states that the way in which numbers are grouped in an addition operation does not change their sum. In simpler terms,
+
+
=
(
+
)
+
=
+
(
+
)
a+b+c=(a+b)+c=a+(b+c).
Additionally, the commutative property of addition for fractions is also implied, which states that the order in which numbers are added does not change their sum. In this case, it’s the same number being added multiple times.
Therefore, we have shown that:
6
11
+
6
11
+
6
11
=
18
11
11
6
+
11
6
+
11
6
=
11
18
using the associative and commutative properties of addition.