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Chapter 5: Problem 125

Simplify: \((-10)(-7) \div(1-8)\)

Short Answer

Expert verified
The simplified form of \((-10)(-7) \div (1-8)\) is \(-10\).

Step by step solution

01

Simplify Brackets

The brackets in this equation indicate the part which should be performed first according to BIDMAS/BODMAS rule. Therefore, we first simplify \((-10)(-7)\) and \(1-8\). So the expression becomes \(70 \div -7\).
02

Division

Next, perform the division operation. \(70 \div -7\) equals \(-10\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

BODMAS Rule
The BODMAS rule, also known as BIDMAS, is a crucial principle in mathematics used to determine the order of operations in calculations. BODMAS stands for Brackets, Orders (powers and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). Following this sequence ensures that mathematical expressions are calculated accurately.
In the given exercise \((-10)(-7) \div (1-8)\), the BODMAS rule guides us to simplify the expression inside the brackets first, which includes both multiplication \((-10)(-7)\) and subtraction \((1-8)\). Only after these operations are completed do we proceed to division. Remembering and applying BODMAS helps avoid errors and makes complex problems more manageable.
Mathematical Operations
Mathematical operations are the basic actions we perform in math, such as addition, subtraction, multiplication, and division. Each operation plays a distinct role and has its rules governing how it interacts with numbers.
For the exercise \((-10)(-7) \div (1-8)\), we start with multiplication \((-10) \times (-7)\) leading to a positive product 70, since multiplying two negative numbers results in a positive number.

Next is division: \(70 \div -7\). Division requires distributing a number into equal parts, and in this scenario, it involves a positive number divided by a negative number, resulting in a negative quotient, specifically -10. Understanding these basic operations helps in simplifying equations effectively.
Negative Numbers
Negative numbers are numbers less than zero, shown with a minus sign (-). They represent values below zero, such as losses, depths, or temperatures below freezing. Understanding how to work with negative numbers is crucial for solving many mathematical problems.
In our exercise \((-10)(-7) \div (1-8)\), negative numbers are present in the multiplication and the division. Multiplying two negatives \((-10) \times (-7)\) yields a positive result (because two negatives cancel each other out), while dividing a positive by a negative \(70 \div -7\) results in a negative outcome.

This illustrates the rules of arithmetic involving signs, which are vital for understanding and calculating expressions accurately.

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Most popular questions from this chapter

You just signed a contract for a new job. The salary for the first year is \(\$ 30,000\) and there is to be a percent increase in your salary each year. The algebraic expression $$\frac{30,000 x^{n}-30,000}{x-1}$$ describes your total salary over n years, where \(x\) is the sum of 1 and the yearly percent increase, expressed as a decimal. a. Use the expression given above and write a quotient of polynomials that describes your total salary over four years. b. Simplify the expression in part (a) by performing the division. c. Suppose you are to receive an increase of \(8 \%\) per year. Thus, \(x\) is the sum of 1 and \(0.08,\) or \(1.08 .\) Substitute 1.08 for \(x\) in the expression in part (a) as well as in the simplified form of the expression in part (b). Evaluate each expression. What is your total salary over the fouryear period?

What polynomial, when divided by \(3 x^{2},\) yields the trinomial \(-6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(y-1)\left(y^{2}+y+1\right)=y^{3}-1$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Each statement applies to the division problem $$\frac{x^{3}+1}{x+1}$$ Rewriting \(x^{3}+1\) as \(x^{3}+0 x^{2}+0 x+1\) can change the value of the variable expression for certain values of \(x .\)

perform the indicated operations. $$\begin{aligned} &\left[\left(4 y^{2}-3 y+8\right)-\left(5 y^{2}+7 y-4\right)\right]-\left[\left(8 y^{2}+5 y-7\right)+\left(-10 y^{2}+4 y+3\right)\right] \end{aligned}$$
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