1/2 X 2/3 multiply fraction
The Correct Answer and Explanation is :
To multiply the fractions ( \frac{1}{2} ) and ( \frac{2}{3} ), you follow a straightforward process. The general rule for multiplying fractions is to multiply the numerators together and the denominators together.
Step 1: Multiply the Numerators
The numerator of the first fraction is 1, and the numerator of the second fraction is 2:
[
1 \times 2 = 2
]
Step 2: Multiply the Denominators
The denominator of the first fraction is 2, and the denominator of the second fraction is 3:
[
2 \times 3 = 6
]
Step 3: Form the New Fraction
Now that we have our new numerator and denominator, we can form the resulting fraction:
[
\frac{2}{6}
]
Step 4: Simplify the Fraction
The final step is to simplify the fraction if possible. Both the numerator and the denominator can be divided by their greatest common divisor, which in this case is 2:
[
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
]
Thus, the product of ( \frac{1}{2} ) and ( \frac{2}{3} ) is ( \frac{1}{3} ).
Explanation
When multiplying fractions, it’s essential to understand that you are finding a part of a part. For instance, ( \frac{1}{2} ) represents half of something, and ( \frac{2}{3} ) represents two-thirds of that half. Visualizing it can help: if you have a pizza divided into 3 slices, taking two of those slices gives you two-thirds of the pizza. Now, if you only take half of that, you end up with one-third of the entire pizza.
Multiplication of fractions is useful in many real-life scenarios, such as cooking, where recipes may require scaling ingredients down or up. It is also a fundamental skill in mathematics that lays the groundwork for more complex operations involving fractions and rational numbers. Understanding how to multiply fractions will enhance your ability to work with ratios, proportions, and percentages.