Question

Find each quantity. \(\frac{1}{2}\) of 1

Short answer

\frac{1}{2} of 1 is \frac{1}{2}.

Step-by-step solution

Understand the Task

The task is to find what \(\frac{1}{2}\) of 1 is. In other words, we need to multiply \(\frac{1}{2}\) by 1.

Set Up the Multiplication

Write the expression for the multiplication: \(\frac{1}{2} \times 1\).

Perform the Multiplication

Multiply \(\frac{1}{2}\) by 1. This is done by multiplying the numerators and the denominators: \[ \frac{1 \times 1}{2 \times 1} = \frac{1}{2} \]

Simplify the Answer

The fraction \(\frac{1}{2}\) is already in its simplest form. Therefore, the final answer is \(\frac{1}{2}\).

Key concepts

Fraction Multiplication

Multiplying fractions might seem tricky at first, but it’s really straightforward. To multiply two fractions, simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

For example, when multiplying \( \frac{1}{2} \) by 1, the numerators are 1 and 1, and the denominators are 2 and 1. Here's how it looks in formula form:

\[ \frac{1}{2} \times 1 = \frac{1 \times 1}{2 \times 1} = \frac{1}{2} \]

• First, multiply the numerators: 1 \(\times\) 1 = 1
• Then, multiply the denominators: 2 \(\times\) 1 = 2
• Combine them into a fraction: \(\frac{1}{2}\)
That's it! The result is \( \frac{1}{2} \).

Simplifying Fractions

Simplifying fractions means making the fraction as simple as possible. A fraction is in its simplest form when the numerator (the top number) and the denominator (the bottom number) have no common factors other than 1. Simplifying makes calculations easier and solutions more understandable.

For example, let’s simplify \[ \frac{6}{8} \]:

• First, find the greatest common divisor (GCD) of the numerator and the denominator, which is the largest number that divides both evenly. The GCD of 6 and 8 is 2.
• Then, divide both the numerator and the denominator by this number: \[ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]
  You’ve simplified \[ \frac{6}{8} \] to \[ \frac{3}{4} \]. Always check if you can simplify the fraction further.

Numerator and Denominator

Understanding numerators and denominators is vital. In any fraction, the numerator is the top number, and it represents the part of the whole you have. The denominator is the bottom number, and it shows how many equal parts the whole is divided into.

Consider the fraction \[ \frac{3}{4} \]:

• The numerator is 3, meaning we have 3 parts.
• The denominator is 4, meaning the whole is divided into 4 equal parts.
So \[ \frac{3}{4} \] represents three out of four parts. When multiplying fractions like \[ \frac{1}{2} \times 1 \], keep in mind the roles of numerators and denominators to make the multiplication process easy to understand.

In summary, the numerator tells you the 'what' you have, and the denominator tells you the 'how many parts' it is divided into.