What is half of 7/8?
The Correct Answer and Explanation is :
To find half of ( \frac{7}{8} ), you can use the formula for dividing fractions, which involves multiplying by the reciprocal. The reciprocal of a fraction is created by swapping its numerator and denominator.
Here’s the calculation step-by-step:
- Identify the Fraction: The fraction we want to halve is ( \frac{7}{8} ).
- Multiply by 1/2: To find half, you can multiply the fraction by ( \frac{1}{2} ):
[
\frac{7}{8} \times \frac{1}{2}
] - Multiply the Numerators: Multiply the numerators (the top parts of the fractions):
[
7 \times 1 = 7
] - Multiply the Denominators: Multiply the denominators (the bottom parts of the fractions):
[
8 \times 2 = 16
] - Combine the Results: Now you have the new fraction:
[
\frac{7}{16}
]
So, half of ( \frac{7}{8} ) is ( \frac{7}{16} ).
Explanation
Understanding how to manipulate fractions is essential in mathematics. When working with fractions, it’s important to remember that they represent parts of a whole. The numerator indicates how many parts we have, while the denominator indicates how many equal parts the whole is divided into.
Dividing by two is a common operation, which essentially means finding what one half of a given quantity is. When we multiply a fraction by ( \frac{1}{2} ), we are effectively saying, “What is half of this fraction?”
In this case, by multiplying ( \frac{7}{8} ) by ( \frac{1}{2} ), we are splitting the ( \frac{7}{8} ) into two equal parts. The result, ( \frac{7}{16} ), indicates that if you were to divide a whole into 16 equal parts, 7 of those parts would represent half of ( \frac{7}{8} ).
This method of fraction manipulation can be applied to various problems in both basic arithmetic and more advanced mathematical concepts, making it a fundamental skill to master.