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What are the partial products of [tex]$36 \times 42$[/tex]? Choose all that apply.

A. 60
B. 1,200
C. 140
D. 150
E. 240
F. 1,512

Answer :

We start by breaking down each number based on its place value. We write

[tex]$$
36 = 30 + 6 \quad \text{and} \quad 42 = 40 + 2.
$$[/tex]

Next, we multiply each term from the first number by each term of the second number:

1. Multiply the tens of 36 and the tens of 42:

[tex]$$
30 \times 40 = 1200.
$$[/tex]

2. Multiply the tens of 36 by the ones of 42:

[tex]$$
30 \times 2 = 60.
$$[/tex]

3. Multiply the ones of 36 by the tens of 42:

[tex]$$
6 \times 40 = 240.
$$[/tex]

4. Multiply the ones of 36 by the ones of 42:

[tex]$$
6 \times 2 = 12.
$$[/tex]

Therefore, the partial products obtained in the multiplication are

[tex]$$
1200,\quad 60,\quad 240,\quad \text{and} \quad 12.
$$[/tex]

Among the provided options:
- Option A: [tex]$60$[/tex]
- Option B: [tex]$1200$[/tex]
- Option C: [tex]$140$[/tex]
- Option D: [tex]$150$[/tex]
- Option E: [tex]$240$[/tex]
- Option F: [tex]$1512$[/tex]

We see that the partial products [tex]$60$[/tex], [tex]$1200$[/tex], and [tex]$240$[/tex] match the options. The product [tex]$12$[/tex] is not among the choices.

Thus, the correct partial products are:

[tex]$$
60,\quad 1200,\quad \text{and} \quad 240.
$$[/tex]

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