Problem 47 - Prealgebra

Question

Find the following quotients. (Divide.) $$2.8 \div 0.7$$

Step-by-Step Solution

Answer

The quotient of 2.8 divided by 0.7 is 4.

Step 1: Set Up the Division

The problem given is \( 2.8 \div 0.7 \). We will divide 2.8 by 0.7 to find the quotient.

Step 2: Eliminate the Decimal in the Divisor

To make division easier, eliminate the decimal from the divisor (0.7) by multiplying both the dividend (2.8) and the divisor (0.7) by 10. This transforms the problem into \( 28 \div 7 \).

Step 3: Perform the Division

Now, perform the division: \( 28 \div 7 = 4 \). This means that 28 divided by 7 equals 4.

Key Concepts

Understanding Quotients

A quotient is the result obtained when one number is divided by another. In simple terms, it's the answer to a division problem. For example, in the exercise given, the division of 2.8 by 0.7 results in a quotient of 4. This means when 2.8 is divided by 0.7, we get 4 as the result.

Quotients can be whole numbers or decimals, depending on how the two numbers divide. If the dividend (the number being divided) is evenly divisible by the divisor (the number by which the dividend is divided), the quotient is a whole number. Otherwise, it could be a decimal or a fraction. Understanding how to find and interpret quotients is a fundamental skill in mathematics, particularly in operations involving division.

Decimal Division Made Simple

Decimal division might sound tricky at first because of the involvement of decimal points. However, the process becomes much easier if you understand a few key concepts. In our division exercise, the problem is simplified by eliminating the decimal points.

To achieve this, both the dividend and the divisor have to be multiplied by the same power of ten, which effectively moves the decimal point to the right, turning them into whole numbers. For instance, multiplying 2.8 and 0.7 each by 10 changes the problem to 28 divided by 7. This simplifies the division since dividing by whole numbers is generally more straightforward for many.

By converting decimals into whole numbers, you maintain the integrity of the division's quotient, as it is mathematically equivalent to the original division problem.

Mastering Step by Step Solutions

Learning to solve problems with a step-by-step approach is vital in mathematics. This methodical process helps students to break down complex problems into manageable pieces. In the given solution, we approached the division by first setting up the problem clearly, multiplying to eliminate the decimal, and then carrying out the division.

Such solutions involve several logical steps:

• Reading and understanding the problem correctly.
• Manipulating the numbers to simplify the problem, such as eliminating decimals.
• Performing the actual operation, in this case, division.
• Revisiting the answer to ensure its correctness within the context of the original problem.

Practicing with step-by-step solutions not only enhances your division skills but also builds your confidence in tackling more challenging problems in various mathematical areas.