Question

Complete the addition square by finding the missing numbers. Find $\left( A-B \right)-\left( C-D \right)$

+	10,923	8,473
18,732	A	B
9,018	C	D

(a) 0
(b) 450
(c) 1000
(d) 300

Answer 1

Hint: To solve this important to all the missing elements accurately. This is done by the addition operator. By substituting in the equation $\left( A-B \right)-\left( C-D \right)$ we can achieve the final solution. The value of A is found by finding the element of the second row and first column with the element of the first row and second column. Similarly, all the elements can be found.

Complete step-by-step answer:
Let us begin with finding the missing elements in the table.
The operator to be used in the table is given in the first row and first column.
The operator used in all the operations to find the missing elements is the addition (+).
Let us begin by finding the value of A.
The element lies in the second row and second column. To get the value we need to add the element of the second row and first column with the element of the first row and second column.
Therefore, keeping all the points we get,
$A=18,732+10,923=29,655..................(i)$
Let go ahead with element B.
The element lies in the second row and third column. To get the value we need to add the element of the second row and first column with the element of the first row and third column.
Therefore, keeping all the points we get,
$B=18,732+8,473=27,205..................(ii)$
Let go ahead with element C.
The element lies in the third row and second column. To get the value we need to add the element of the third row and first column with the element of the first row and second column.
Therefore, keeping all the points we get,
$C=9,018+10,923=19,941..................(iii)$
Let go ahead with element D.
The element lies in the third row and third column. To get the value we need to add the element of the third row and first column with the element of the first row and third column.
Therefore, keeping all the points we get,
$D=9,018+8,473=17,491..................(iv)$
The required equation to be found is $\left( A-B \right)-\left( C-D \right)$
From (i),(ii),(iii),(iv), substituting the value of A,B,C,D we get
$\left( A-B \right)-\left( C-D \right)=\left( 29,655-27,205 \right)-\left( 19,941-17,491 \right)=2,450-2,450=0$
Therefore, after simplification, the value of the equation is zero.
Hence option (a) is correct.

Note: We need to be careful while finding the individual elements. It is easily confused between rows and columns. Also, the horizontal terms are rows and the vertical ones are columns. There needs to be extra attention while interpreting the operator. It is shown in the first row and first column. In this problem the operator used is of addition.