Problem 55 Multiply or divide as indicated.... [FREE SOLUTION]

Chapter 2: Problem 55

Multiply or divide as indicated. See Examples 1 through 14. $$ -18 \div 3 $$

Short Answer

Expert verified

The result of $-18 \div 3$ is -6.

Step by step solution

Understanding Division

The expression $-18 \div 3$ involves division. To divide means to split a number into equal parts. In this case, we will determine how many times 3 fits into -18.

Perform the Division

Calculate how many times 3 fits into -18. Since division with a negative number is involved, the result will take the sign of the dividend. So, we compute: $-18 \div 3 = -6$.

Verify the Sign Rule

In division, if you divide a negative number by a positive number, the result is negative. Our division $-18 \div 3 = -6$ follows this rule as -18 is negative and 3 is positive, leading to the negative result -6.

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Key Concepts

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

Division

Division is one of the four basic arithmetic operations, where we separate a number into equal parts. Suppose you have 18 apples and you want to divide them among 3 friends. You would give 6 apples to each friend because 18 divided by 3 equals 6. Similarly, in the expression $-18 \div 3$, we are looking to spread -18 into groups of 3. This operation might be less about apples and more about understanding how frequently 3 fits into -18. To perform division, consider the following:

The number being divided is called the dividend.
The number you are dividing by is called the divisor.
The result is known as the quotient.

In our exercise, -18 is the dividend, 3 is the divisor, and the goal is to find the quotient.

Negative Numbers

Negative numbers represent values less than zero, typically used to indicate an opposite direction or decrease. In mathematical terms, they follow the same arithmetic rules as positive numbers but include a negative sign, often denoted with a minus symbol (-).Visualize a number line to understand negative numbers easily:

To the left of zero, values are negative.
To the right, they are positive.

This line helps in comprehending operations involving negatives. For example, -18 means 18 units but in an opposite direction from positive 18. Thus, division with negatives, such as $-18 \div 3$, requires considering these opposite directions.

Sign Rule in Division

Understanding the sign rule in division is crucial to avoid mistakes. The sign of the result in division largely depends on the signs of the dividend and the divisor:

If both numbers are positive, the quotient is positive.
If both numbers are negative, the quotient is also positive because two negatives make a positive.
If one number is negative and the other positive, the quotient is negative.

In the exercise $-18 \div 3$, the dividend is negative while the divisor is positive. Following our rule, since one number is negative, the quotient becomes negative. Therefore, $-18 \div 3 = -6$. Remembering these sign rules simplifies arithmetic operations involving division and negative numbers.

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91影视

Multiply or divide as indicated. See Examples 1 through 14. $$ -18 \div 3 $$

Short Answer

Step by step solution

Understanding Division

Perform the Division

Verify the Sign Rule

Key Concepts

Division

Negative Numbers

Sign Rule in Division

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