Question

Find the missing values: \[571+\left( ......+394 \right)=\left( .....+429 \right)+394\]
(a) 571, 394
(b) 429, 571
(c) 571, 429
(d) 429, 329

Answer 1

Hint: In this question, from the properties of real numbers according to the associative property of addition we have that \[a+\left( b+c \right)=\left( a+b \right)+c\]. Now, on comparing the given expression with the associative property of addition we get the respective values of a, b, c and so the missing numbers which gives the result.

Complete step by step answer:
REAL NUMBER:
Any number, which is either rational or irrational is called real number and it is denoted by the symbol R.
Now, from the properties of the real numbers on addition we have
Commutative property of addition which is given by
\[a+b=b+a\]
Associative property of addition which is given by
\[a+\left( b+c \right)=\left( a+b \right)+c\]
Now, from the given expression in the question we have that
\[\Rightarrow 571+\left( ......+394 \right)=\left( .....+429 \right)+394\]
Now, from the associative property of addition from the properties of real numbers we have
\[\Rightarrow a+\left( b+c \right)=\left( a+b \right)+c\]
Let us now compare the given expression in the question with this associative property of addition.
Now, on comparison we get the respective values of a, b, c as
\[\Rightarrow a=571,b=429,c=394\]
Now, let us consider the left part of the given expression
\[\Rightarrow 571+\left( ......+394 \right)\]
Now, on considering this with left part of associative property of addition we get,
\[\Rightarrow a+\left( b+c \right)\]
The missing part is b whose value is 429
Now, on considering the right part of the given expression we have
\[\Rightarrow \left( .....+429 \right)+394\]
Now, on considering this with right part of associative property of addition we get,
\[\Rightarrow \left( a+b \right)+c\]
The missing part is a whose value is 571
Hence, the correct option is (b).

Note:
Instead of using the associative property of addition from properties of real numbers we can also solve it by considering the sum to be equal on both sides then cancel the common term and then the missing part of left will be the known value on the right and vice versa.
It is important to note that while comparing the given expression with the associative property of addition we need to equate the corresponding values accordingly because if we consider the same value twice then we neglect any other value which will be incorrect.