Mastering the Art of Dividing Decimals by Decimals: A Step-by-Step Guide

I. Introduction

Dividing decimals by decimals can be a difficult concept for students to master. However, it is an important skill to learn as it is frequently used in real-life situations such as calculating prices at the grocery store or determining rates of change. In this article, we will explore the step-by-step process for dividing decimals by decimals, common mistakes to avoid, practical real-life examples, tips and tricks for easier division, the importance of rounding, common misconceptions, and fun practice exercises to improve skills.

II. Step-by-Step Guide to Dividing Decimals by Decimals

The process of dividing decimals by decimals is similar to dividing whole numbers, but with the added step of moving the decimal point. To divide decimals by decimals:

1. Write the division problem as a fraction
2. Multiply the numerator and denominator by a power of 10 to make the divisor a whole number
3. Multiply both the numerator and denominator by the same power of 10 again to keep the value the same
4. Divide the resulting numerator by the resulting denominator
5. Place the decimal point in the quotient directly above the decimal point in the dividend

For example, let’s divide 2.5 by 0.5:

1. Write the problem as a fraction: 2.5/0.5
2. Multiply both the numerator and denominator by 10: 25/5
3. Multiply both the numerator and denominator by 10 again: 250/50
4. Divide the numerator by the denominator: 5
5. Place the decimal point in the quotient: 5.0

To check your answer, multiply the quotient by the divisor. In this example, 5.0 x 0.5 = 2.5, which is the original dividend, so the answer is correct.

Some tips to make the division process easier are:

• Clear any extra zeros before and after the numbers in the problem
• Align the decimal points in the division problem when setting it up
• Keep track of the number of decimal places in the divisor and quotient

III. Top Common Mistakes to Avoid When Dividing Decimals by Decimals

One common mistake students make when dividing decimals by decimals is forgetting to move the decimal point when setting up the problem. This can lead to an incorrect answer. Another mistake is mixing up the divisor and dividend, which can also result in an incorrect answer.

To avoid these common mistakes, students should:

• Double check the placement of the decimal point
• Label the dividend and divisor correctly
• Use scratch paper to keep track of the decimal point when moving it

Let’s look at an example problem of dividing 14.3 by 0.4:

1. Write the problem as a fraction: 14.3/0.4
2. Multiply both the numerator and denominator by 10 to make the divisor a whole number: 143/4
3. Multiply both the numerator and denominator by 10 again: 1430/40
4. Divide the numerator by the denominator: 35.75
5. Place the decimal point in the quotient: 35.75

If the decimal point in the quotient were placed one place to the left, the answer would be 357.5, which is incorrect.

IV. Practical Real-Life Examples of Dividing Decimals by Decimals

Decimals are frequently used in real-life situations such as determining the price per unit of an item or calculating the miles per gallon of a vehicle. Let’s look at some practical real-life examples involving division of decimals by decimals:

Example 1:

A 25-pound turkey costs $37.50. What is the cost per pound?

To solve this problem, divide the cost by the weight:

1. Write the problem as a fraction: $37.50/25 lbs
2. Divide the numerator by the denominator: $1.50/lb

The cost per pound of the turkey is $1.50.

Example 2:

A car travels 240 miles on 8 gallons of gasoline. What is the miles per gallon?

To solve this problem, divide the distance by the amount of fuel:

1. Write the problem as a fraction: 240 miles/8 gallons
2. Divide the numerator by the denominator: 30 miles/gallon

The car travels 30 miles on one gallon of gasoline.

V. Tips and Tricks for Faster and Easier Division of Decimals by Decimals

There are a few tips and tricks that can make dividing decimals by decimals faster and easier. One such trick is to move the decimal point in the divisor to the right until it becomes a whole number. Then, move the decimal point in the dividend the same number of places to the right. Divide and move the decimal point in the quotient the same number of places to the left.

Let’s look at an example problem of dividing 0.06 by 0.2:

1. Move the decimal point in the divisor one place to the right to make it a whole number: 0.2 becomes 2
2. Move the decimal point in the dividend one place to the right: 0.06 becomes 0.6
3. Divide 0.6 by 2: 0.3
4. Move the decimal point in the quotient one place to the left: 0.03

The answer is 0.03.

VI. The Importance of Rounding When Dividing Decimals by Decimals

Rounding is important when dividing decimals by decimals as it can help simplify the problem and provide a more accurate estimate. When rounding, it is important to keep track of the number of decimal places in the divisor and dividend.

Let’s look at an example problem of dividing 8.563 by 3.72:

1. Round 3.72 to 4
2. Divide 8.563 by 4: 2.14
3. Round 2.14 to the nearest hundredth: 2.14

The answer is approximately 2.14.

VII. Common Misconceptions About Dividing Decimals by Decimals

One common misconception about dividing decimals by decimals is that it is always necessary to move the decimal point. While it is necessary in most cases, there are some problems where it is not needed.

Another misconception is that the quotient will always have the same number of decimal places as the dividend. In reality, the number of decimal places in the quotient will vary based on the values of the dividend and divisor.

VIII. Fun Practice Exercises for Mastering Division of Decimals by Decimals

Practicing division of decimals by decimals can be both fun and engaging. Some exercises to try include:

• Divide the distance of a road trip by the number of gallons of gasoline used
• Calculate the cost per ounce of a food item
• Find the time it takes to fill a swimming pool based on gallons per minute

When checking the answers, make sure to multiply the quotient by the divisor to make sure the result is correct.

IX. Conclusion

Dividing decimals by decimals can be a daunting task, but with the step-by-step process outlined in this article, common mistakes to avoid, practical real-life examples, tips and tricks, and fun practice exercises, anyone can master this skill.