To find the value of [tex]\((213) \times 7\)[/tex] and [tex]\((917) \times 6\)[/tex], we will perform the following multiplications step-by-step.
First, let us handle the multiplication of [tex]\(213 \times 7\)[/tex]:
1. Multiply the digit in the ones place:
[tex]\[
3 \times 7 = 21
\][/tex]
Write down 1 in the ones place and carry over 2.
2. Multiply the digit in the tens place and add the carry:
[tex]\[
1 \times 7 = 7, \quad 7 + 2 = 9
\][/tex]
Write down 9 in the tens place.
3. Multiply the digit in the hundreds place:
[tex]\[
2 \times 7 = 14
\][/tex]
Write down 14 followed by the digits we already have.
Thus, [tex]\(213 \times 7 = 1491\)[/tex].
Next, let us calculate [tex]\(917 \times 6\)[/tex]:
1. Multiply the digit in the ones place:
[tex]\[
7 \times 6 = 42
\][/tex]
Write down 2 in the ones place and carry over 4.
2. Multiply the digit in the tens place and add the carry:
[tex]\[
1 \times 6 = 6, \quad 6 + 4 = 10
\][/tex]
Write down 0 in the tens place and carry over 1.
3. Multiply the digit in the hundreds place:
[tex]\[
9 \times 6 = 54, \quad 54 + 1 = 55
\][/tex]
Write down 55 followed by the digits we already have.
Thus, [tex]\(917 \times 6 = 5502\)[/tex].
The values obtained from the calculations are:
[tex]\[
213 \times 7 = 1491
\][/tex]
[tex]\[
917 \times 6 = 5502
\][/tex]
So, the values are [tex]\(1491\)[/tex] and [tex]\(5502\)[/tex], respectively.
