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Chapter 2: Problem 23

Find the quotient. $$-35 \div(-70)$$

Short Answer

Expert verified
The quotient of -35 divided by -70 is 0.5.

Step by step solution

01

Identify the values

Identify the values for the division operation. Here, the dividend is -35 and the divisor is -70.
02

Perform the division

Perform the division operation. Remember, the division of two negative numbers is a positive number. The two negative signs effectively cancel out, so divide 35 by 70 normally.
03

Simplify if necessary

Simplify the result if necessary. In this case, the outcome is already in its simplest form, as no further simplification is possible.

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Key Concepts

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

Negative Numbers
Negative numbers have a unique place in mathematics. They can be confusing at first, but understanding them is crucial. A negative number is any number less than zero, marked by a minus sign (\(-\)). For example, \(-35\) and \(-70\) are negative numbers.
Negative numbers play a significant role in various mathematical operations, especially in division. When two negative numbers are divided, the result is positive. You can think of the negatives canceling each other out. For instance, the division of \(-35\) and \(-70\) yields a positive result. Just count the negatives: \(-- = +\).
Keep in mind these useful tips:
  • An odd number of negative signs results in a negative product or quotient.
  • An even number of negative signs results in a positive outcome.
  • This rule helps simplify complex equations by focusing on the sign patterns first.
Division Operation
Division is a fundamental concept in mathematics. It involves splitting a number into equal parts. The number you are dividing is the dividend, while the number by which you divide is the divisor. In the exercise example, \(-35\) is the dividend and \(-70\) is the divisor.
When dividing with negative numbers, it鈥檚 important to focus on the signs, as they affect the outcome. Negative divided by negative results in a positive quotient.
  • To perform division, calculate as if dealing with positive numbers.
  • Then apply the sign rule: two negatives make a positive.
This method simplifies complex problems by reducing them to basic division facts, reminding you to always address the signs both before and after computations.
Simplification in Division
Simplification in division refers to reducing fractions or outcomes to their simplest form. It's the final step to ensure the result is as straightforward as possible. When there is nothing more to reduce, you know the fraction is in its simplest form.
In the division of \(-35\) by \(-70\), simplification shows that the quotient is in its simplest form right from the start. The factors between numerators and denominators are common, but cannot reduce \(1/2\) any further because it is already simplified.
  • Check divisibility to find common factors.
  • Reduce the fraction if there are common factors other than 1.
  • A fraction is simplest when you can no longer divide the numerator and the denominator by the same number other than 1.
Simplification makes calculations manageable and results clear, avoiding unnecessary complexity.

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Most popular questions from this chapter

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ If the jeans cost \(\$ 35,\) can you buy both the T-shirt and the jeans?

EVALUATING EXPRESSIONS Evaluate the expression. $$ 12.4-9.7-(-6.1) $$

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 7 x-3 x(x+1) $$

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ (6-3 w)\left(-w^{2}\right) $$

Use the distributive property and mental math to simplify the expression. $$ 6 x^{2}-4 x^{2} $$
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