Question

parent results not recorded. continue practising or switch user. which is the most accurate way to estimate 73% of 34? \\(\frac{1}{3} \times 32\\) \\(\frac{3}{4} \times 37\\) \\(\frac{1}{3} \times 37\\) \\(\frac{3}{4} \times 32\\)

Explanation:

Step1: Analyze 73% approximation

73% is close to 75% (which is $\frac{3}{4}$ since $75\%=\frac{75}{100}=\frac{3}{4}$).

Step2: Analyze 34 approximation

34 is close to 32 or 37. 34 is closer to 32? Wait, 34 and 32: difference is 2; 34 and 37: difference is 3. So 34 is closer to 32? Wait, no, wait 73% of 34: let's see the options. The options have 32 or 37. Let's check the fractions. $\frac{3}{4}$ is 75%, which is close to 73%. And 34 is closer to 32? Wait, no, 34 and 32: 34 - 32 = 2; 37 - 34 = 3. So 34 is closer to 32? Wait, but let's check the options. The fourth option is $\frac{3}{4}×32$. Let's verify:

First, calculate 73% of 34: $0.73×34 = 24.82$.

Now calculate each option:

1. $\frac{1}{3}×32 ≈ 10.67$ (way off)
2. $\frac{3}{4}×37 = 27.75$ (37 is 3 more than 34, 27.75 - 24.82 = 2.93)
3. $\frac{1}{3}×37 ≈ 12.33$ (way off)
4. $\frac{3}{4}×32 = 24$ (32 is 2 less than 34, 24.82 - 24 = 0.82, which is closer than 2.93)

So $\frac{3}{4}×32$ is the most accurate as 73% is close to 75% ($\frac{3}{4}$) and 34 is close to 32 (closer than 37 in terms of the product's accuracy here).

Answer:

$\frac{3}{4}×32$ (the fourth option, $\boldsymbol{\frac{3}{4}×32}$)