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$34782$ $\times$ $549$

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Geometric sequences

Full solution

Q.

34782

\times

549

Set up multiplication problem: Set up the multiplication problem in the standard format. $\newline$ Write the larger number, $34782$ , on top and the smaller number, $549$ , below it, aligning the digits by place value.
Multiply by rightmost digit: Multiply the top number by the rightmost digit of the bottom number ( $9$ ). $\newline$ $9 \times 2 = 18$ , write down $8$ and carry over $1$ . $\newline$ $9 \times 8 = 72$ , add the carried over $1$ to get $73$ , write down $3$ and carry over $7$ . $\newline$ $9 \times 7 = 63$ , add the carried over $7$ to get $9 \times 2 = 18$ $1$ , write down $9 \times 2 = 18$ $2$ and carry over $7$ . $\newline$ $9 \times 2 = 18$ $4$ , add the carried over $7$ to get $9 \times 2 = 18$ $6$ , write down $3$ and carry over $9 \times 2 = 18$ $8$ . $\newline$ $9 \times 2 = 18$ $9$ , add the carried over $9 \times 2 = 18$ $8$ to get $8$ $1$ , write down $8$ $1$ . $\newline$ The partial product is $8$ $3$ .
Multiply by middle digit: Multiply the top number by the middle digit of the bottom number ( $4$ ), remembering to add a zero (place holder) at the end of this partial product. $\newline$ $4 \times 2 = 8$ , write down $8$ and add a zero (place holder) to get $80$ . $\newline$ $4 \times 8 = 32$ , write down $2$ and carry over $3$ . $\newline$ $4 \times 7 = 28$ , add the carried over $3$ to get $31$ , write down $4 \times 2 = 8$ $0$ and carry over $3$ . $\newline$ $4 \times 2 = 8$ $2$ , add the carried over $3$ to get $4 \times 2 = 8$ $4$ , write down $4 \times 2 = 8$ $5$ and carry over $4 \times 2 = 8$ $0$ . $\newline$ $4 \times 2 = 8$ $7$ , add the carried over $4 \times 2 = 8$ $0$ to get $4 \times 2 = 8$ $9$ , write down $4 \times 2 = 8$ $9$ . $\newline$ The partial product is $8$ $1$ .
Multiply by leftmost digit: Multiply the top number by the leftmost digit of the bottom number ( $5$ ), remembering to add two zeros (place holders) at the end of this partial product. $\newline$ $5 \times 2 = 10$ , write down $0$ and carry over $1$ . $\newline$ $5 \times 8 = 40$ , add the carried over $1$ to get $41$ , write down $1$ and carry over $4$ . $\newline$ $5 \times 7 = 35$ , add the carried over $4$ to get $5 \times 2 = 10$ $1$ , write down $5 \times 2 = 10$ $2$ and carry over $5 \times 2 = 10$ $3$ . $\newline$ $5 \times 2 = 10$ $4$ , add the carried over $5 \times 2 = 10$ $3$ to get $5 \times 2 = 10$ $6$ , write down $5 \times 2 = 10$ $3$ and carry over $5 \times 2 = 10$ $8$ . $\newline$ $5 \times 2 = 10$ $9$ , add the carried over $5 \times 2 = 10$ $8$ to get $0$ $1$ , write down $0$ $1$ . $\newline$ The partial product is $0$ $3$ .
Add partial products: Add all the partial products together. $\newline$ Align all the partial products by their place value and add them. $\newline$ $313098$ $\newline$ + $1391200$ $\newline$ + $17391000$ $\newline$ --------- $\newline$ The sum will give us the final product.
Perform final addition: Perform the addition of the partial products. $\newline$ $313098$ $\newline$ + $1391200$ $\newline$ + $17391000$ $\newline$ --------- $\newline$ $19109398$ $\newline$ Write down the final sum.

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