Question

parent results not recorded. continue practising or switch unit: which is the most accurate way to estimate 23% of 50? \\(\frac{1}{4} \times 53\\) \\(\frac{1}{4} \times 48\\) \\(\frac{2}{3} \times 53\\) \\(\frac{2}{3} \times 48\\)

Explanation:

Step1: Analyze 23% approximation

23% is close to 25% (which is $\frac{1}{4}$). 50 is close to 48 or 53? 50 is closer to 48? Wait, 23% of 50: first, 25% is $\frac{1}{4}$, and 50 is around 48? Wait, no, 50 is the original. Wait, the options are $\frac{1}{4}×53$, $\frac{1}{4}×48$, $\frac{2}{3}×53$, $\frac{2}{3}×48$. Let's calculate 23% of 50: $0.23×50 = 11.5$. Now check each option:

• $\frac{1}{4}×53 = 13.25$
• $\frac{1}{4}×48 = 12$
• $\frac{2}{3}×53 ≈ 35.33$
• $\frac{2}{3}×48 = 32$

Now, 23% is close to 25% ($\frac{1}{4}$), and 50 is close to 48? Wait, 53 is also close. Wait, 23% of 50: 23% is $\frac{23}{100}$, and $\frac{1}{4}$ is 25%, which is close. Now, 50: 48 is 2 less, 53 is 3 more. Let's see the product: $\frac{1}{4}×48 = 12$, $\frac{1}{4}×53 = 13.25$. The actual value is 11.5. Wait, 12 is closer to 11.5 than 13.25. Wait, but 50: 48 is 2 less, 53 is 3 more. Wait, maybe I made a mistake. Wait, 23% of 50: 50×0.23 = 11.5. Now, $\frac{1}{4}×48 = 12$, which is 0.5 more. $\frac{1}{4}×53 = 13.25$, which is 1.75 more. So 12 is closer. But wait, is 48 a better approximation for 50? 50 - 48 = 2, 53 - 50 = 3. So 48 is closer to 50 than 53? Wait, 48 is 2 less, 53 is 3 more. So 48 is closer. And 23% is closer to 25% ($\frac{1}{4}$) than to $\frac{2}{3}$ (66.67%). So the best is $\frac{1}{4}×48$. Wait, but let's check again. Wait, the question is "estimate 23% of 50". So 23% is ~25% (1/4), and 50 is ~48? Wait, 50 is 50, but 48 is an option. Wait, maybe the numbers in the options are 53 and 48 instead of 50? Maybe a typo, but the options are given. So among the options, $\frac{1}{4}×48$ gives 12, which is closest to 11.5. $\frac{1}{4}×53$ gives 13.25, which is further. So the most accurate is $\frac{1}{4}×48$.

Step2: Verify each option

• Option 1: $\frac{1}{4}×53 = 13.25$, difference from 11.5: $13.25 - 11.5 = 1.75$
• Option 2: $\frac{1}{4}×48 = 12$, difference: $12 - 11.5 = 0.5$
• Option 3: $\frac{2}{3}×53 ≈ 35.33$, difference: $35.33 - 11.5 = 23.83$
• Option 4: $\frac{2}{3}×48 = 32$, difference: $32 - 11.5 = 20.5$

The smallest difference is 0.5, so $\frac{1}{4}×48$ is the most accurate.

Answer:

$\boldsymbol{\frac{1}{4} \times 48}$ (the second option, $\frac{1}{4} \times 48$)