How to Solve 18 Divided by 1.5: Simplifying Division with STEM

Understanding division and its applications in everyday scenarios is a fundamental part of STEM (Science, Technology, Engineering, and Mathematics) education. This guide will walk through a step-by-step process to solve a specific division problem: 18 divided by 1.5, explaining common strategies and methods used by educators and practitioners.

Understanding Division

Division can be seen as determining how many times one number, known as the divisor, fits into another number, known as the dividend. In our problem, we have 18 as the dividend and 1.5 as the divisor. The goal is to figure out how many times 1.5 can be subtracted from 18 completely.

Converting to Whole Numbers

A common strategy to simplify division involves converting the divisor, which contains a decimal, into a whole number. This is achieved by multiplying both the dividend and the divisor by the same number so that the decimal in the divisor disappears. In this case, we can convert 1.5 to 15 (a whole number) by multiplying both the numbers by 10.

Step 1: Multiplication for Conversion

Dividend: 18 × 10 180 Divisor: 1.5 × 10 15

Step 2: Performing the Division

Now that both numbers are whole numbers, it's simpler to perform the division: 180 ÷ 15.

180 ÷ 15 12

This means 1.5 fits into 18 exactly 12 times. Therefore, the final answer is 12.

Alternative Methods

There are multiple ways to approach this problem. Let's explore an alternative explanation that uses algebraic and conceptual methods.

Words and Algebraic Approach

Another way to solve the problem involves conceptualizing division by fractions. One-point-five (1.5) is the same as three divided by two (3/2). Therefore, dividing 18 by 1.5 can be seen as finding 18 divided by 3 and then multiplying by 2, or more straightforwardly, multiplying 18 by the reciprocal of 1.5, which is 2/3.

Step-by-Step Algebraic Solution

18 ÷ 1.5 18 ÷ (3/2) 18 × (2/3) (18 × 2) ÷ 3 36 ÷ 3 12

This step-by-step solution elucidates the process of converting the division into a multiplication by the reciprocal of the divisor.

Using a Divider

For a visual and concrete approach, you can set up the division problem using the long division method. Write 18 above the dividing line and 1.5 below it. To remove the decimal, multiply both the numbers by 10, making the division 180 ÷ 15.

This method is particularly useful for understanding the process behind long division and can be a valuable tool in STEM education.

Conclusion

Whether through multiplication for conversion, conceptual division by fractions, or long division, the answer remains 12. This problem showcases the flexibility and multiple methods available for solving division problems, emphasizing the importance of understanding various techniques in STEM education.

Keywords

division, STEM education, decimal conversion