9514 1404 393
Answer:
-4.438
Step-by-step explanation:
Subtraction, or addition of numbers with different signs, proceeds like this. The smaller number is subtracted from the larger, and the sign of the larger number is applied to the result. Here, "larger" and "smaller" refer to the magnitudes of the numbers, not their left-right position on the number line.
Various methods are taught for doing the subtraction. The result is shown in the first attachment.
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If you work from right to left, the first step will be to "borrow" from the column to the left, essentially rewriting the digits of (8.)(0)(0)(0) to (7.)(9)(9)(10). Then the digits of the differences are ...
(7 -3)(9 -5)(9-6)(10-2) = (4.)(4)(3)(8)
When the sign of -8 is applied to the result, it is -4.438.
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Alternate approach
If you work from left to right, you essentially compute ...
(((8 -3) -0.5) -0.06) -0.002
You do the first subtraction in the usual way:
(8.)-(3.) = (5.)
Subtracting the digit in the next place to the right makes use of the arithmetic fact -5 = -10 +5. Then considering the pair of digits in the ones and tenths places, you have essentially ...
50 -5 = 50 -10 +5 = 45 . . . . . the partial difference 8.0 -3.5 is now 4.5
Considering the pair of digits in the tenths and hundredths places, the next subtraction is ...
50 -6 = 50 -10 +4 = 44 . . . . . . the partial difference 8.00 -3.56 is now 4.44
Considering the pair of digits in the hundredths and thousandths places, the last subtraction is ...
40 -2 = 40 -10 +8 = 38 . . . . . the difference 8.000 -3.562 is 4.438
This is probably much easier to see using a bead tool such as a soroban or abacus.
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Additional comments
In the first attachment, the signs in the left column are merely to show that the sign of the largest number is attached to the difference. The numbers show subtraction of 3562 from 8000.
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The soroban shown in the second attachment is a sort of hybrid between a 5-bead soroban (3rd attachment) and a 7-bead abacus. An abacus has 5 below and 2 above.
The bead(s) above the bar have a value of 5; the ones below the bar have a value of 1. Their value is counted as part of the represented number when the beads are moved so they touch the bar.
The 6-bead soroban shown can represent the value 5 two different ways:
(5)+(0) or (0)+(1+1+1+1+1)
