Question

multiply:
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$$\begin{align*} &\\ \\ \\ \\ \\ \\ 9.07 \\\\ &\\times\\ 8.32 \\\\ \\cline{1-1} \\end{align*}$$

Explanation:

Step1: Multiply 9.07 by 2 (the hundredths place of 8.32)

$9.07\times2 = 18.14$

Step2: Multiply 9.07 by 30 (the tenths place of 8.32, note it's 3 in tenths so 3×10 = 30)

$9.07\times30 = 272.1$

Step3: Multiply 9.07 by 800 (the ones place of 8.32 is 8, so 8×100 = 800)

$9.07\times800 = 7256$

Step4: Add the results together: 18.14 + 272.1 + 7256

First, add 18.14 and 272.1: $18.14 + 272.1 = 290.24$
Then add 290.24 and 7256: $290.24 + 7256 = 7546.24$ Wait, no, actually, when multiplying decimals, we should count the total number of decimal places. 9.07 has 2 decimal places, 8.32 has 2 decimal places, so the product should have 2 + 2 = 4 decimal places. Let's do it properly by multiplying as integers and then placing the decimal.

Treat 9.07 as 907 and 8.32 as 832 (multiplying both by 100 to eliminate decimals). Then $907\times832$.

Calculate $907\times832$:

First, $907\times2 = 1814$

$907\times30 = 27210$

$907\times800 = 725600$

Now add them: 1814 + 27210 + 725600 = 1814 + 27210 = 29024; 29024 + 725600 = 754624.

Now, since we multiplied both numbers by 100 (9.07×100 = 907, 8.32×100 = 832), the total multiplication factor is 100×100 = 10000. So we divide 754624 by 10000: $754624\div10000 = 75.4624$.

Answer:

75.4624