Step 1: Understand the Division Concept
Reasoning: Division is essentially the process of determining how many times one number fits into another. When we divide a number, we are splitting it into equal parts. In this case, we want to find out how many times 2 fits into 0.5.
Step 2: Rewrite the Numbers in Fraction Form
Mathematical Expression:
0.5 ÷ 2
Reasoning: Converting decimal numbers to fractions can make the division easier to visualize. The decimal 0.5 can be written as the fraction:
0.5 = 11⁄2
Thus, our division problem becomes:
11⁄2 ÷ 2
Step 3: Use the Property of Division by a Fraction
Mathematical Expression:
11⁄2 ÷ 2 = 11⁄2 × 11⁄2
Reasoning: This step relies on the principle that dividing by a number is the same as multiplying by its reciprocal, making calculations simpler.
Step 4: Multiply the Fractions
Mathematical Expression:
1 × 1 ⁄ 2 × 2 = 11⁄4
Reasoning: To multiply fractions, you multiply the numerators together and the denominators together. This gives you a new fraction that represents the division.
Step 5: Convert Back to Decimal (if necessary)
Result:
11⁄4 can be converted back to decimal form. Since 1 ÷ 4 equals 0.25, we have:
0.5 ÷ 2 = 0.25
Reasoning: Understanding how to convert between fractions and decimals is crucial, especially in practical applications.
Multiple approaches (showing work) in PDF format:
Additional Context
Visual Representation: You can visualize dividing 0.5 by 2 by thinking of it as taking a half (0.5) and splitting it into two equal parts. Each part would then be 0.25.
Real-Life Application: This kind of division is common in various scenarios, such as measuring ingredients in cooking or calculating portions.
Ending notes:
This is not all on the subject of division. You can learn much more by downloading our free resources, for example this PDF in our “downloads” section has much more information on division of decimals. As always, we ensured that it includes simple examples and a step-by-step progression, allowing you to gradually absorb the complex information.