Question

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standard algorithm.
products. visualize the area model to help you..
b.
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$$\begin{array}{r}\\ 49 \\\\ \\times 33 \\\\ \\hline 147 \\\\ 1470 quad\\underline{quad\\quad\\quad\\quad} \\times \\underline{quad\\quad\\quad\\quad} \\\\ \\hline 1617 \\\\ \\underline{quad\\quad\\quad\\quad} \\times \\underline{quad\\quad\\quad\\quad} \\\\ \\hline \\end{array}$$

Explanation:

Step1: Analyze the multiplication 49×33

We use the standard algorithm for multiplication, which involves breaking down the numbers. 33 can be written as 30 + 3. So we first multiply 49 by 3 (the ones place of 33) and then by 30 (the tens place of 33).

Step2: Identify the partial products

• The first partial product 147 comes from \( 49\times3 \) (because we multiply by the 3 in the ones place of 33).
• The second partial product 1470 comes from \( 49\times30 \) (because we multiply by the 3 in the tens place of 33, which is 30).

Step3: Sum the partial products

To get the final product, we add the two partial products: \( 147 + 1470 = 1617 \).

Answer:

For the partial product 1470, it is \( 49\times30 \).
For the partial product 147, it is \( 49\times3 \).
The final product is \( 1617 \).

(In the blanks:
1470 is \( \boldsymbol{49} \times \boldsymbol{30} \)
147 is \( \boldsymbol{49} \times \boldsymbol{3} \)
Final answer: \( \boldsymbol{1617} \))