Question

Use the sign \[ > , < \]or$ = $in the box to make the following statement true:
$( - 11) + ( - 7)..........( - 11) - ( - 7)$

Answer 1

Hint: We’ll discuss the arithmetic and its property related to addition, subtraction, and multiplication that will be used in our solution.

Using those properties we’ll simplify the expressions given in the left-hand and the right-hand side to compare both the expression and will get the required answer.

Complete step by step solution: Given data: $( - 11) + ( - 7)..........( - 11) - ( - 7)$

Arithmetic is a branch of mathematics that deals with the numbers and its operations like addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

And some of the properties of arithmetic operations are the multiplication of two same-sign numbers is positive and numbers having a different sign is negative.

Summation or subtraction of two numbers is also dependent on the sign of the two numbers, if the sign of both the numbers is the same then the summation has to take place with the sign that the two numbers have, and if the two numbers have different signs then the subtraction has to be done with the sign of the greater number taken without the sign.

Now solving the given terms

Left-hand side $ = ( - 11) + ( - 7)$

$ = - 11 - 7$

$ = - 18$

Right-hand side $ = ( - 11) - ( - 7)$

$ = - 11 + 7$

$ = - 4$

The greater the negative value the lesser,

i.e. $ - 18 < - 4$

Therefore the required answer is$( - 11) + ( - 7) < ( - 11) - ( - 7)$

Note: In this question, some of the students say that the exact same two numbers are added and subtracted so obviously the sum will be greater mark it as greater which is incorrect so remember the properties mentioned and simplify according to that to get the correct required solution.