Question

question
complete the standard multiplication algorithm for 96 × 0.79, including any \carried,\ or regrouped
digits, if necessary.
you can use tab/shift tab or the arrow keys to move from one box to another.

9 6
× 0 . 7 9

Explanation:

Step1: Multiply by 9 (units place of 0.79)

First, multiply 96 by 9. \( 96 \times 9 = 864 \). So the first partial product (under the line, rightmost two boxes) is 864? Wait, no, let's do the standard algorithm. Wait, the standard multiplication algorithm for decimals: we can treat 0.79 as 79 hundredths, so multiply 96 by 79 first, then adjust the decimal. But let's do the step-by-step as per the algorithm.

First, multiply 96 by 9 (the 9 in 0.79, which is the hundredths place? Wait, no, 0.79 is 7 tenths and 9 hundredths. Wait, the algorithm:

```
96
x0.79
------
First, multiply 96 by 9: 96*9 = 864. Write this down, shifted right by 0 (since 9 is in the hundredths place? Wait, no, standard algorithm for decimal multiplication: we can ignore the decimal first, multiply 96 by 79, then count the decimal places. But the given grid has:

□
96
x0.79
------
□□

Wait, maybe the first box is the carried digit when multiplying? Wait, let's do 96 * 9 first. 6*9=54, so we write 4 in the units place of the partial product, and carry over 5. Then 9*9=81, plus 5=86. So the first partial product (from multiplying by 9) is 864? Wait, no, 96*9:

96
x 9
----
54 (6*9)
810 (9*9, shifted left)
Wait, no, 96*9 is 864. So when writing the partial product, we have:

96
x 9
----
864

But in the given problem, the multiplier is 0.79, so first multiply by 9 (the 9 in 0.79, which is the second digit after the decimal, so the partial product is shifted by 2? Wait, maybe the problem is structured as:

□ (carry)
96
x0.79
------
□□ (first partial product, 96*9)

Wait, let's compute 96*9:

6*9 = 54. So we write 4 in the units place of the partial product, and carry over 5 (the 5 from 54). So the carry is 5? Wait, no, 6*9=54, so the units digit is 4, carryover is 5. Then 9*9=81, plus 5=86. So the partial product is 864. So the first partial product (from 96*9) is 864. But the boxes are two digits? Wait, maybe the first box is the carry when multiplying 6*9. Wait, 6*9=54, so carryover is 5. So the first box (above 96) is 5? Then the partial product (the two boxes) is 64? Wait, no, 6*9=54, so we write 4, carry 5. Then 9*9=81 +5=86. So the partial product is 864. But the boxes are two digits? Maybe the problem is simplified. Wait, maybe the first step is multiplying 96 by 9:

Step 1: Multiply 6 (units of 96) by 9 (units of 0.79? No, 0.79 is 0.7 + 0.09). Wait, maybe the problem is a typo, but let's proceed.

Wait, the standard multiplication algorithm for two-digit by two-digit (ignoring decimal):

96
x 79
------
First, 96*9=864 (partial product 1)
Then, 96*70=6720 (partial product 2, shifted left by 1)
Then add them: 864 + 6720 = 7584
Then, since 0.79 has two decimal places, 96*0.79 = 75.84

But in the given problem, the grid is:

□
96
x0.79
------
□□

Wait, maybe the first box is the carry when multiplying 6*9. 6*9=54, so carryover is 5. So the first box (above 96) is 5. Then the partial product (the two boxes) is 64? Wait, no, 6*9=54, so we write 4, carry 5. Then 9*9=81 +5=86. So the partial product is 864. But the boxes are two digits? Maybe the problem is showing the first partial product's last two digits and the carry. Wait, maybe the first box is the carry (5) when multiplying 6*9, and the two boxes are 64 (from 54, but with carry 5, so 4 and carry 5). Wait, this is confusing. Alternatively, maybe the problem is to compute 96*9 first, which is 864, so the two boxes are 64 (last two digits) and the carry is 8? No, 96*9=864, so the last two digits are 64, and the first digit is 8. Wait, maybe the first box is 8 (the carry or the first digit of the partial product), and the two boxes are 64.

Wait, let's re-express:

When multiplying 96 by 9:

96
x 9
----
864

So the partial product is 864. So if the grid has:

□ (the 8 from 864)
96
x0.79
------
□□ (64 from 864)

So the first box is 8, and the two boxes are 64.

Let me check:

6*9=54 → write 4, carry 5.

9*9=81 +5=86 → write 86. Wait, no, 96*9 is 864. So the digits are 8 (hundreds), 6 (tens), 4 (units). So if the grid is:

□ (hundreds place of partial product)
96
x0.79
------
□□ (tens and units place of partial product)

Then the first box is 8, and the two boxes are 64.

Yes, that makes sense. So:

First, multiply 96 by 9:

- 6*9 = 54 → write 4, carry 5.
- 9*9 = 81 + 5 = 86 → write 86 (so the partial product is 864, which is 8 (hundreds), 6 (tens), 4 (units)).

So the first box (above 96) is 8 (the hundreds digit of the partial product), and the two boxes below are 64 (tens and units digits).

Step2: Verify

So the first partial product (from multiplying by 9) is 864, so the first box (carry or leading digit) is 8, and the two boxes are 64.

Answer:

The first box (above 96) is 8, and the two boxes below are 64. So:

8
96
x0.79
------
64

(Note: This is the first partial product from multiplying 96 by 9. The next step would be multiplying by 7 and shifting, but the problem seems to focus on the first partial product.)