Question

1. julius and walt are finding the product of 25 and 16. part a julius’ answer is incorrect. what did julius do wrong? julius \

$$\begin{tabular}{r} 25 \\\\ $\\times$ 16 \\\\ \\hline 150 \\\\ + 250 \\\\ \\hline 500 \\end{tabular}$$

\

$$\begin{tabular}{r} 25 \\\\ $\\times$ 16 \\\\ \\hline 200 \\\\ 50 \\\\ 120 \\\\ + 300 \\\\ \\hline 670 \\end{tabular}$$

Explanation:

Step1: Recall Multiplication Steps

When multiplying \(25\times16\) using the standard algorithm, we break \(16\) into \(6 + 10\). First, multiply \(25\times6 = 150\) (this is correct for the ones place). Then, we multiply \(25\times10=250\), but since we are multiplying by the tens place, we should write \(250\) as \(2500\) (or shift one position to the left, so it's \(250\) with a space or a zero in the ones place, meaning it's \(250\times10 = 2500\) when adding).

Step2: Analyze Julius' Work

Julius added \(150 + 250\) directly, but he forgot that the \(250\) from \(25\times10\) should be considered as \(250\) in the tens place (i.e., \(2500\) when adding to the ones place product). So he incorrectly added \(250\) instead of \(2500\) (or treating the \(10\) in \(16\) as a single digit instead of a tens place, leading to a wrong addition step).

Answer:

Julius forgot to account for the place value when multiplying by the tens digit (1 in 16, which represents 10). He should have shifted the product of \(25\times10\) (which is 250) one place to the left (making it 2500 in terms of addition with the product of the ones place) but instead added 250 directly to 150, leading to an incorrect sum.