Question

How do you multiply \[48\times .78\]?

Answer 1

Hint: In order to find the solution to the given question, that is to multiply \[48\times .78\] apply Long multiplication means you are doing the multiplication of positive or negative whole numbers or decimal numbers as the multiplicand\[\left( 48 \right)\] and multiplier \[\left( .78 \right)\] to calculate the product using long multiplication. The solution shows the work for the Standard Algorithm or the traditional method involves multiplying numbers and lining up results according to place value.

Complete step-by-step answer:
According to the question, given expression in the question is as follows:
\[48\times .78\]
To multiply the above expression, using the long multiplication method means doing multiplication by hand. These are the steps to do long multiplication by hand:
Step-1: Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand. And ignore the decimal places and complete the multiplication as if operating on two integers.
\[\begin{align}
  & \text{ }48 \\
 & \underline{\times \text{ }78} \\
\end{align}\]
Step-2: Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number and write the answer below the equal’s line. If that answer is greater than nine, write the ones place as the answer and carry the tens digit. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equal’s line. If you need to carry again, do so.
\[\begin{align}
  & \text{ }48 \\
 & \underline{\times \text{ }78} \\
 & \text{ }384 \\
\end{align}\]
Step-3: When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number. Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
\[\begin{align}
  & \text{ }48 \\
 & \underline{\times \text{ }78} \\
 & \text{ }384 \\
 & \underline{\text{ }336\text{ }} \\
\end{align}\]
Step-4: When you finish multiplying, draw another answer line below your last row of answer numbers. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
\[\begin{align}
  & \text{ }48 \\
 & \underline{\times \text{ }78} \\
 & \text{ }384 \\
 & \underline{+\text{ }336\text{ }} \\
 & \text{ }3744 \\
\end{align}\]
Now, the product with \[2\] total decimal places, we get \[37.44\].
Therefore, \[48\times .78=37.44\].

Note: Students make mistakes while multiplying the last digit in the top number and they write the complete answer below the equal’s line which is completely wrong as It’s important to check if that answer is greater than nine, write the ones place as the answer and carry the tens digit. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equal’s line.