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Chapter 5: Problem 13

Divide. Check the answer by using multiplication. $$1 . 0 8 \div { 6 } \quad \text { Check: } \\__ \times 6=1.08$$

Short Answer

Expert verified
0.18, check: 0.18 x 6 = 1.08

Step by step solution

01

Set up the division

Set up the division problem by writing it in fractional form: \[ \frac{1.08}{6} \]
02

Perform the division

Divide 1.08 by 6:1.08 divided by 6 equals 0.18. So, \[ 1.08 \times 6 = 0.18 \]
03

Check the answer by multiplication

Multiply the quotient (0.18) by the divisor (6):\[0.18 \times 6 = 1.08 \]Since the product is 1.08, the division is correct.

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Key Concepts

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

division
Division is a fundamental arithmetic operation that involves splitting a number into equal parts. In the exercise, we needed to divide 1.08 by 6. To set up the division problem, we can write it as a fraction: \( \frac{1.08}{6} \). This tells us how much one part will be when 1.08 is divided into 6 equal parts.
When performing division:
  • You need a dividend (the number being divided, which is 1.08)
  • You also need a divisor (the number you're dividing by, which is 6)
Dividing these, we find that \( 1.08 \div 6 = 0.18 \). Breaking it down into smaller steps can help:
For example, breaking down 1.08 into smaller components makes it easier to understand.
multiplication
Multiplication is essentially repeated addition. When we multiply, we are combining groups of equal sizes. In the context of our problem, we checked the answer by reversing the division process using multiplication.
To verify: Multiply the quotient \( (0.18) \) by the divisor \( (6) \). The calculation \( 0.18 \times 6 \) should give us the original dividend. This acts as a verification step to ensure our division was performed correctly.
The result, \( 0.18 \times 6 = 1.08 \), confirms the accuracy of our division.
fractions
Fractions represent parts of a whole and are another way to express division. In our exercise, we started with a fraction: \( \frac{1.08}{6} \). This means 1.08 divided by 6. Converting division problems to fraction form can help visualize the problem and simplify calculations.
Understanding fractions involves knowing two main parts: the numerator (the top number) and the denominator (the bottom number). Here, 1.08 is the numerator and 6 is the denominator.
Working with fractions:
  • Make sure the numerator and denominator are in the correct places.

  • Simplify fractions if possible.

  • Convert fractions to decimals when necessary for easier calculation.
decimal arithmetic
Decimal arithmetic is essential for working with numbers not whole, especially in practical applications like currency. In this exercise, we dealt with the decimal 1.08. Each step must keep decimal precision.
Key tips for decimal arithmetic:
  • Align decimal points vertically for addition and subtraction.

  • For multiplication, count total decimal places from both numbers combined and adjust the product accordingly.

  • In division, make the divisor a whole number by shifting the decimal, concurrently shifting the dividend's decimal.
Practicing these steps ensures accuracy, especially when confirming answers like we did by multiplying 0.18 by 6 to get 1.08.

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Most popular questions from this chapter

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$27.88 \div 2.46 \text { thousandths }$$

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ Between which two consecutive months did the IBM stock decrease the most? What was the amount of decrease?

What is the least number with three places to the right of the decimal that can be created with the digits 2, 9, and 7? Assume that the digits cannot be repeated.

What is the greatest number with three places to the right of the decimal that can be created from the digits 2, 9, and 7? Assume that the digits cannot be repeated.

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ By how much did the FedEx stock decrease between January and May?
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