Basic Math Decoded
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This example has been taken directly from the solution given by Basic Math Decoded to the formulated problem.
58.378 × 0.396
Place one number above the other aligned to the right. Draw a line under the bottom number. Temporarily disregard the decimal points and multiply the numbers like you would multiply integer numbers.
58.378
× 0.396
Multiply the number 58378 by the digit 6 and place the answer below the line aligned to the right.
Multiply the digits 6 and 8 (6 × 8 = 48).
This number is larger than 9, so place the 4 above the column on the left to be added in the next step and place the 8 below the line.
4
58.378
× 0.396
8
Multiply the digits 6 and 7 (6 × 7 = 42). Add the 4 to the answer which equals 46.
This number is larger than 9, so place the 4 above the column on the left to be added in the next step and place the 6 below the line and to the left of the other digits.
44
58.378
× 0.396
68
Multiply the digits 6 and 3 (6 × 3 = 18). Add the 4 to the answer which equals 22.
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 2 below the line and to the left of the other digits.
2 44
58.378
× 0.396
268
Multiply the digits 6 and 8 (6 × 8 = 48). Add the 2 to the answer which equals 50.
This number is larger than 9, so place the 5 above the column on the left to be added in the next step and place the 0 below the line and to the left of the other digits.
52 44
58.378
× 0.396
0268
Multiply the digits 6 and 5 (6 × 5 = 30). Add the 5 to the answer which equals 35.
This number is larger than 9, but there are no more columns, so place the answer below the line and to the left of the other digits.
52 44
58.378
× 0.396
350268
Multiply the number 58378 by the digit 9 and place the answer in a new row below the last one, moving one place to the left.
Multiply the digits 9 and 8 (9 × 8 = 72).
This number is larger than 9, so place the 7 above the column on the left to be added in the next step and place the 2 below the line in the corresponding row.
7
58.378
× 0.396
350268
2
Multiply the digits 9 and 7 (9 × 7 = 63). Add the 7 to the answer which equals 70.
This number is larger than 9, so place the 7 above the column on the left to be added in the next step and place the 0 below the line in the corresponding row, and to the left of the other digits.
77
58.378
× 0.396
350268
02
Multiply the digits 9 and 3 (9 × 3 = 27). Add the 7 to the answer which equals 34.
This number is larger than 9, so place the 3 above the column on the left to be added in the next step and place the 4 below the line in the corresponding row, and to the left of the other digits.
3 77
58.378
× 0.396
350268
402
Multiply the digits 9 and 8 (9 × 8 = 72). Add the 3 to the answer which equals 75.
This number is larger than 9, so place the 7 above the column on the left to be added in the next step and place the 5 below the line in the corresponding row, and to the left of the other digits.
73 77
58.378
× 0.396
350268
5402
Multiply the digits 9 and 5 (9 × 5 = 45). Add the 7 to the answer which equals 52.
This number is larger than 9, but there are no more columns, so place the answer below the line in the corresponding row, and to the left of the other digits.
73 77
58.378
× 0.396
350268
525402
Multiply the number 58378 by the digit 3 and place the answer in a new row below the last one, moving one place to the left.
Multiply the digits 3 and 8 (3 × 8 = 24).
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 4 below the line in the corresponding row.
2
58.378
× 0.396
350268
525402
4
Multiply the digits 3 and 7 (3 × 7 = 21). Add the 2 to the answer which equals 23.
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 3 below the line in the corresponding row, and to the left of the other digits.
22
58.378
× 0.396
350268
525402
34
Multiply the digits 3 and 3 (3 × 3 = 9). Add the 2 to the answer which equals 11.
This number is larger than 9, so place the 1 above the column on the left to be added in the next step and place the 1 below the line in the corresponding row, and to the left of the other digits.
1 22
58.378
× 0.396
350268
525402
134
Multiply the digits 3 and 8 (3 × 8 = 24). Add the 1 to the answer which equals 25.
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 5 below the line in the corresponding row, and to the left of the other digits.
21 22
58.378
× 0.396
350268
525402
5134
Multiply the digits 3 and 5 (3 × 5 = 15). Add the 2 to the answer which equals 17.
This number is larger than 9, but there are no more columns, so place the answer below the line in the corresponding row, and to the left of the other digits.
21 22
58.378
× 0.396
350268
525402
175134
Final answer
Add all the rows together and write the answer.
58.378
× 0.396
350268
525402
175134
23117688
We must now count up the decimal places of both numbers and move the decimal place to its proper location. We have 3 decimal place(s) in the first number and 3 in the second one, so we move the decimal point 6 place(s) to the left to give the final answer.
23.117688