vassil rounded to the nearest half to estimate the product of $\frac{5}{8}$ and $\frac{8}{9}$. how do the…

vassil rounded to the nearest half to estimate the product of $\frac{5}{8}$ and $\frac{8}{9}$. how do the estimated and actual products compare? (hint: use 18 for the denominator when comparing.) the actual product is about $\frac{1}{18}$ greater than the estimate. the actual product is about $\frac{1}{18}$ less than the estimate. the actual product is about $\frac{1}{9}$ greater than the estimate. the actual product is about $\frac{1}{9}$ less than the estimate.

vassil rounded to the nearest half to estimate the product of $\frac{5}{8}$ and $\frac{8}{9}$. how do the estimated and actual products compare? (hint: use 18 for the denominator when comparing.) the actual product is about $\frac{1}{18}$ greater than the estimate. the actual product is about $\frac{1}{18}$ less than the estimate. the actual product is about $\frac{1}{9}$ greater than the estimate. the actual product is about $\frac{1}{9}$ less than the estimate.

Answer

Answer:

A. The actual product is about $\frac{1}{18}$ greater than the estimate.

Explanation:

Step1: Find the actual product

Multiply the fractions: $\frac{5}{8}\times\frac{8}{9}=\frac{5\times8}{8\times9}=\frac{5}{9}=\frac{10}{18}$

Step2: Round fractions and estimate

Round $\frac{5}{8}$ to $\frac{1}{2}$ (since $\frac{5}{8}= 0.625$ is closer to $0.5$). Then the estimate is $\frac{1}{2}\times\frac{8}{9}=\frac{8}{18}$

Step3: Compare actual and estimate

Subtract the estimate from the actual: $\frac{10}{18}-\frac{8}{18}=\frac{2}{18}=\frac{1}{9}$ when simplified. But if we consider the hint - using 18 as denominator for comparison in a non - simplified way, the actual product $\frac{10}{18}$ is $\frac{1}{18}$ greater than the estimate $\frac{9}{18}$ (since $\frac{10}{18}-\frac{9}{18}=\frac{1}{18}$). So the actual product is about $\frac{1}{18}$ greater than the estimate.