Question

Simplify the number $-7-\left( -8 \right)$ \[\]
A. $15$ \[\]
B. $-15$ \[\]
C. $1$ \[\]
D. $0$ \[\]

Answer 1

Hint: We follow the BODMAS (bracket, order, division, multiplication, addition, subtraction as the sequence of arithmetic operations) and first operate on the bracket. We use the knowledge that the negative of a negative number is the positive number that is $-\left( -a \right)=a$. We add up the integers in the next step to get the result. \[\]

Complete step-by-step solution:
We know from the BODMAS rule that when we are given a numerical expression with multiple arithmetic operations like addition, subtraction multiplication, etc. The word BODMAS is an acronym with bracket, order (otherwise known as power or exponent), division, multiplication, addition, subtraction. BODMAS rule states the order (sequence) of operations in numerical expression is a bracket, order, division, multiplication, addition, subtraction. \[\]
We know that a negative integer is an integer less than zero. All negative numbers are prefixed by a minus ${}^{'}{{-}^{'}}$ sign. The negative number represents measurements below the standard or reference point. If earth level is a reference then the height of a small soil pyramid is positive and the depth of the hole is negative. The removal is also represented with negative. \[\]
We also know that if we multiply a negative number with a negative number is a positive number. Specifically, if $a$ is any positive number then we have,
\[-\left( -a \right)=-1\times \left( -a \right)=a\]
It means if we remove (the negative sign outside bracket) the hole (negative sign inside bracket) we will get a small sand pyramid (positive) above the earth. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, $-\left( -a \right)=a$because the opposite of an opposite is the original value. \[\]
We are given in the question the following numerical expression to simplify
\[ -7-\left( -8 \right)\]
We see that there are two operations one is the bracket and the other is subtraction involved with two negative integers$-7,-8$. We follow the BODMAS rule and operate on brackets, which has the negative integer $-8$ inside 8. We use the law of arithmetic of negative numbers in this case multiplication and have
\[=-7+8 \]
We add the above integers and have the sum as
\[=1\]
So the correct option is C.\[\]

Note: We must not confuse the multiplication of two negative numbers from multiplication one positive and one negative number where the product is always negative, which means for some positive numbers $a,b$ we have$-a\times b=a\times \left( -b \right)=-ab$. The negative number $-a$ is also called the additive inverse of $a$ and the operation $-\left( -a \right)$ is called involution operation.