Problem 272
Question
In the following exercises, divide. Round money monetary answers to the nearest cent. $$ -1.15 \div(-0.05) $$
Step-by-Step Solution
Verified Answer
23
1Step 1: Identify the division components
The division problem is -1.15 divided by -0.05. The dividend is -1.15 and the divisor is -0.05.
2Step 2: Divide the absolute values
Ignore the negative signs for now and divide the absolute values: 1.15 divided by 0.05.
3Step 3: Perform the division
Perform the calculation: 1.15 divided by 0.05 = 23.
4Step 4: Determine the sign of the result
Since both the dividend and the divisor are negative, the result of dividing two negative numbers is positive. Thus, the answer is 23.
Key Concepts
Understanding DivisionWorking With Absolute ValuesDealing With Negative Numbers
Understanding Division
Division is one of the four basic arithmetic operations we use in mathematics. When we divide, we are essentially splitting a number into equal parts. For example, if you have 12 apples and divide them among 4 people, each person gets 3 apples. Here, 12 is the dividend (the number being divided), 4 is the divisor (the number you divide by), and 3 is the quotient (the result of the division).
In terms of mathematical notation, we write this as: \ \(12 ÷ 4 = 3\).
In the given exercise, our problem is to divide \ \(-1.15 \div (-0.05)\). To solve this, we need to follow specific steps, which include understanding the role of the dividend and divisor, performing the division, and determining the sign of the result.
Remember, practicing division is crucial as it helps in various real-life scenarios like splitting bills, distributing items, and even in higher mathematics.
In terms of mathematical notation, we write this as: \ \(12 ÷ 4 = 3\).
In the given exercise, our problem is to divide \ \(-1.15 \div (-0.05)\). To solve this, we need to follow specific steps, which include understanding the role of the dividend and divisor, performing the division, and determining the sign of the result.
Remember, practicing division is crucial as it helps in various real-life scenarios like splitting bills, distributing items, and even in higher mathematics.
Working With Absolute Values
Absolute values are a way to measure the distance of a number from zero on the number line, regardless of direction. The absolute value of a number is always non-negative. For example, the absolute value of both 3 and -3 is 3. This is because both are 3 units away from zero.
We denote absolute values with vertical bars around the number: \ \( |3| = 3\) and \( |-3| = 3 \).
In our division problem, we have \ \(-1.15\) and \ \(-0.05\). Their absolute values are \( |-1.15| = 1.15 \) and \( |-0.05| = 0.05 \). Ignoring the negative signs and dividing these absolute values makes the calculation simpler. Dividing \ \(1.15 \div 0.05\) gives us 23.
Always remember: when dealing with negative numbers, calculate using absolute values first. Then, determine the sign of your answer based on the original numbers.
We denote absolute values with vertical bars around the number: \ \( |3| = 3\) and \( |-3| = 3 \).
In our division problem, we have \ \(-1.15\) and \ \(-0.05\). Their absolute values are \( |-1.15| = 1.15 \) and \( |-0.05| = 0.05 \). Ignoring the negative signs and dividing these absolute values makes the calculation simpler. Dividing \ \(1.15 \div 0.05\) gives us 23.
Always remember: when dealing with negative numbers, calculate using absolute values first. Then, determine the sign of your answer based on the original numbers.
Dealing With Negative Numbers
Negative numbers represent values less than zero and are denoted with a minus sign (-). They are commonly used in various scenarios like temperatures below freezing, debts, or elevations below sea level.
One key rule is that multiplying or dividing two negative numbers results in a positive number. This might seem counterintuitive at first, but it's a fundamental property of arithmetic.
In our division exercise, both the dividend (-1.15) and the divisor (-0.05) are negative. Dividing their absolute values gives us 23. Since we are dividing two negative numbers, the result is positive.
Recap on rules:
One key rule is that multiplying or dividing two negative numbers results in a positive number. This might seem counterintuitive at first, but it's a fundamental property of arithmetic.
In our division exercise, both the dividend (-1.15) and the divisor (-0.05) are negative. Dividing their absolute values gives us 23. Since we are dividing two negative numbers, the result is positive.
Recap on rules:
- Positive ÷ Positive = Positive
- Negative ÷ Positive = Negative
- Positive ÷ Negative = Negative
- Negative ÷ Negative = Positive
Other exercises in this chapter
Problem 270
In the following exercises, divide. Round money monetary answers to the nearest cent. $$ \$ 109.24 \div 36 $$
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