Half of half and one third of three quarters are equal ? do you agree? how will you show this?
The Correct Answer and Explanation is:
To determine if half of half and one third of three quarters are equal, calculate each expression separately:
Half of half:
Start with 1/2.
Half of 1/2 is:12×12=14\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}21×21=41
One third of three quarters:
Start with 3/4.
One third of 3/4 is:13×34=312=14\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}31×43=123=41
The result for both expressions is 1/4.
Therefore, the two are equal.
Explanation (300 words):
In comparing two mathematical expressions, it is important to break each one into smaller parts and follow the rules of fractions. The phrase half of half means taking a half portion from a quantity that is already halved. Mathematically, this is represented by multiplying 1/2 by 1/2. When two fractions are multiplied, the numerators and denominators are multiplied directly. In this case, 1 multiplied by 1 gives 1, and 2 multiplied by 2 gives 4, resulting in 1/4.
The second expression, one third of three quarters, involves taking a third portion from a quantity that is already three-fourths of a whole. This is represented as 1/3 multiplied by 3/4. The multiplication of these two fractions gives 3 in the numerator and 12 in the denominator, which simplifies to 1/4 after dividing both terms by 3.
After computing both expressions separately, each results in the same fraction: 1/4. This confirms that half of half and one third of three quarters are indeed equal. The comparison shows that different-looking expressions in mathematics can sometimes lead to the same result, especially when fractional operations are involved.
Understanding these operations helps in developing deeper mathematical reasoning and highlights the importance of breaking problems into manageable steps. This method ensures accuracy and clarity in mathematical thinking.
