Problem 17 - Calculate With Confidence

Question

Solve the following. Carry division to the hundredths place where necessary. $$3.75 \div 2.5=$$

Step-by-Step Solution

Answer

The result is 1.5.

Step 1: Remove Decimal by Multiplying

Both the dividend (3.75) and the divisor (2.5) have decimals. Multiply both by 10 to eliminate the decimals. This changes the division to 37.5 divided by 25.

Step 2: Set Up Long Division

Set up the division of 37.5 by 25. Begin with setting 37.5 inside the division bracket and 25 outside.

Step 3: Divide Whole Numbers

Determine how many times 25 goes into 37. 25 fits once into 37, so write 1 above the division bracket.

Step 4: Subtract and Bring Down

Subtract 25 from 37 to get 12. Bring down the next digit, which is 5, making 125.

Step 5: Divide Again

Determine how many times 25 goes into 125. 25 fits exactly 5 times into 125, so write 5 above the division bracket next to the 1. Now, the division is complete.

Step 6: Compile Final Result

The result of the division is 1.5, as indicated by digits 1 and 5 placed above the division bracket.

Key Concepts

Understanding Decimal Division

Decimal division involves dividing numbers that are not whole, and it can initially seem tricky. However, the key is to simplify the process by transforming it into a problem involving whole numbers. This is done by eliminating the decimal points for easier calculation.
In our example, we started with dividing 3.75 by 2.5. To eliminate the decimals, we multiply both numbers by 10. This changes the problem from dividing by decimals to dividing 37.5 by 25.
This step ensures that you don't have to deal with decimal points in the divisors, which simplifies the calculation considerably. Understanding this transformation is crucial because it allows the division to be executed like a regular whole number division, making the arithmetic more straightforward.

Exploring the Long Division Method

The long division method is a systematic approach that helps break down the division process into manageable steps. Here's how you do it with our example:
First, set up the division by placing 37.5 under the long division bracket and 25 outside it. This setup ensures that each step is measurable and results can be easily traced.
Begin the division by asking how many times 25 can fit into 37. This gives you the first digit of the quotient. In this case, it's 1. You then write this number on top, above the bracket.
The next step is subtracting 25 from 37, resulting in 12. Bring down the next digit after 3.7, which is 5, to the result, forming 125. Now divide 125 by 25, which fits exactly 5 times. Write 5 above the bracket, completing the number 1.5 as the quotient.

Crafting Step-by-Step Solutions

Step-by-step solutions are all about breaking complex problems into digestible parts. Let’s revisit our decimal division problem using this approach.

• **Step 1**: Convert the division into whole numbers by multiplying both figures (3.75 and 2.5) by 10, making it 37.5 ÷ 25.
• **Step 2**: Position 37.5 inside and 25 outside the long division bracket.
• **Step 3**: Calculate how many times 25 goes into 37, which is 1, and place it above the bracket.
• **Step 4**: Subtract 25 from 37 to get 12 and bring down the next number, forming 125.
• **Step 5**: Divide 125 by 25 to get 5, completing the quotient as 1.5 when written next to the 1.

Executing through these steps simplifies the division process, teaching students a logical sequence they can reliably follow for similar problems.