What is 1/3 divided by 2 in fraction form
The correct Answer and Explanation is:
To solve ( \frac{1}{3} \div 2 ) in fraction form, follow these steps:
Step 1: Rewrite the division problem as multiplication by the reciprocal
When dividing by a number, you can multiply by its reciprocal. The reciprocal of 2 is ( \frac{1}{2} ). Therefore, the division problem ( \frac{1}{3} \div 2 ) can be rewritten as:
[
\frac{1}{3} \times \frac{1}{2}
]
Step 2: Multiply the fractions
To multiply two fractions, multiply the numerators together and the denominators together. For ( \frac{1}{3} \times \frac{1}{2} ), multiply:
- The numerators: ( 1 \times 1 = 1 )
- The denominators: ( 3 \times 2 = 6 )
So, the product is:
[
\frac{1}{6}
]
Thus, ( \frac{1}{3} \div 2 = \frac{1}{6} ).
Explanation (300 words)
Dividing fractions can sometimes seem confusing, but it follows a straightforward process. The key is to understand that dividing by a whole number is the same as multiplying by the reciprocal of that number. In this case, you are dividing ( \frac{1}{3} ) by 2. Instead of performing direct division, you flip 2 to its reciprocal, ( \frac{1}{2} ), and change the division operation into multiplication. This is a rule in mathematics: “Dividing by a number is the same as multiplying by its reciprocal.”
When you multiply fractions, you follow a simple process: multiply the numerators and the denominators. The numerators of ( \frac{1}{3} \times \frac{1}{2} ) are 1 and 1, and their product is 1. The denominators are 3 and 2, and their product is 6. As a result, the fraction ( \frac{1}{3} \div 2 ) simplifies to ( \frac{1}{6} ).
This process is an essential concept in fractions and rational numbers because it helps simplify complex fraction problems, especially when dividing. Understanding how to divide fractions using reciprocals allows for more efficient calculations and deeper insight into the relationships between numbers. This technique will also be useful when working with mixed numbers, improper fractions, and algebraic expressions involving fractions.