What Is 2 1/4 Divided By 2? Simple Explanation!
Table of Contents :
To understand the division of fractions, particularly the expression 2 1/4 divided by 2, we need to follow a few steps that will make the process clear and simple. Let's delve into the details with explanations, examples, and practical tips that will help you grasp this concept effortlessly.
Understanding Mixed Numbers
Before we dive into the division, it’s essential to clarify what a mixed number is. A mixed number combines a whole number and a fraction, for instance, 2 1/4.
- Whole Number: This is the part before the fraction. In this case, it's 2.
- Fraction: This is the part after the whole number. Here, it’s 1/4.
Converting a Mixed Number to an Improper Fraction
To perform division with mixed numbers, it's best to convert them into improper fractions. An improper fraction is when the numerator (the top part of the fraction) is greater than the denominator (the bottom part).
Step 1: Convert 2 1/4 to an improper fraction.
-
Multiply the whole number (2) by the denominator (4):
(2 \times 4 = 8) -
Add this result to the numerator (1):
(8 + 1 = 9) -
Therefore, (2 1/4) can be represented as:
[ \frac{9}{4} ]
Setting Up the Division Problem
Now that we have converted 2 1/4 into an improper fraction, we can express the division problem as:
[
\frac{9}{4} \div 2
]
Converting the Whole Number to a Fraction
The next step is to convert the whole number 2 into a fraction so that we can perform the division more easily:
[
2 = \frac{2}{1}
]
Dividing Fractions
When dividing fractions, you multiply by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping it upside down.
Step 2: Multiply by the reciprocal.
So, we can rewrite our expression:
[
\frac{9}{4} \div \frac{2}{1} = \frac{9}{4} \times \frac{1}{2}
]
Performing the Multiplication
Now, we multiply the numerators and the denominators:
[
\text{Numerator: } 9 \times 1 = 9
\text{Denominator: } 4 \times 2 = 8
]
This gives us:
[
\frac{9}{8}
]
Converting Back to a Mixed Number
Since we have an improper fraction, we can convert it back into a mixed number if needed.
Step 3: Convert (\frac{9}{8}) to a mixed number.
-
Divide the numerator (9) by the denominator (8):
(9 ÷ 8 = 1) with a remainder of 1. -
This tells us there is one whole and the remainder can be expressed as a fraction:
[ 1 \frac{1}{8} ]
Conclusion
Putting it all together, 2 1/4 divided by 2 equals (\frac{9}{8}) or 1 (\frac{1}{8}) in mixed number format.
Summary of Steps
To recap, here’s a summary of the steps taken to solve (2 1/4 \div 2):
-
Convert the mixed number to an improper fraction:
[2 1/4 = \frac{9}{4}] -
Set up the division as a multiplication problem by taking the reciprocal:
[\frac{9}{4} \div 2 = \frac{9}{4} \times \frac{1}{2}] -
Perform the multiplication:
[\frac{9 \times 1}{4 \times 2} = \frac{9}{8}] -
Convert back to a mixed number, if necessary:
[\frac{9}{8} = 1 \frac{1}{8}]
Now you have a clear understanding of how to divide mixed numbers, and specifically how to handle (2 1/4) divided by (2). This process can be applied to other mixed numbers and is an essential skill in basic arithmetic. Happy calculating! 🧮✨