Question

find $-6.8 + 2.4$. first, break apart the addends into integer parts and decimal parts. $-6.8 + 2.4 = \boldsymbol{?} + \boldsymbol{?}$ break apart the addends.

Explanation:

Step1: Break -6.8

The integer part of -6.8 is -6, and the decimal part is -0.8. Wait, actually, when breaking into integer and decimal parts for addition, we can also consider the two numbers: -6.8 can be broken into (-6 - 0.8) and 2.4 into (2 + 0.4). But the problem says "break apart the addends into integer parts and decimal parts" for the sum -6.8 + 2.4. So we can rewrite -6.8 as (-6) + (-0.8) and 2.4 as 2 + 0.4. Then combining the integer parts and decimal parts: the integer parts are -6 and 2, and the decimal parts are -0.8 and 0.4. But the equation is -6.8 + 2.4 = (integer part of first addend + integer part of second addend) + (decimal part of first addend + decimal part of second addend)? Wait, no, the problem's format is -6.8 + 2.4 = [?] + [?], where we break each addend into integer and decimal, then combine? Wait, maybe it's (-6 + 2) + (-0.8 + 0.4)? No, the boxes are two, so we need to break each addend into integer + decimal, then for the sum, it's (integer part of -6.8 + integer part of 2.4) + (decimal part of -6.8 + decimal part of 2.4)? Wait, no, the problem says "break apart the addends into integer parts and decimal parts" for the addends. So -6.8 is an addend, 2.4 is the other addend. So break -6.8 into its integer and decimal parts: -6 (integer) and -0.8 (decimal). Break 2.4 into 2 (integer) and 0.4 (decimal). Then, when adding -6.8 + 2.4, we can group the integer parts and decimal parts: (-6 + 2) + (-0.8 + 0.4). But the equation given is -6.8 + 2.4 = [?] + [?], so the two boxes should be the sum of the integer parts and the sum of the decimal parts? Wait, no, maybe the problem is to break each addend into integer and decimal, then write the sum as (integer part of first addend + integer part of second addend) + (decimal part of first addend + decimal part of second addend), but the way the equation is written is -6.8 + 2.4 = [sum of integer parts] + [sum of decimal parts]. Let's calculate the integer parts: -6 (from -6.8) and 2 (from 2.4), so -6 + 2 = -4. The decimal parts: -0.8 (from -6.8) and 0.4 (from 2.4), so -0.8 + 0.4 = -0.4. But that would make -6.8 + 2.4 = (-4) + (-0.4) = -4.4, which is correct. But the problem's format is -6.8 + 2.4 = [?] + [?], so the two boxes are the sum of integer parts and sum of decimal parts. Wait, but maybe the problem is to break each addend into integer and decimal, then combine the integer parts and decimal parts separately. So -6.8 is (-6) + (-0.8), 2.4 is 2 + 0.4. Then -6.8 + 2.4 = [(-6) + 2] + [(-0.8) + 0.4]. So the first box is (-6 + 2) = -4, the second box is (-0.8 + 0.4) = -0.4. Alternatively, maybe the problem is to break the two addends into their integer and decimal components, then write the sum as (integer part of -6.8 + decimal part of -6.8) + (integer part of 2.4 + decimal part of 2.4)? No, that doesn't make sense. Wait, the problem says "First, break apart the addends into integer parts and decimal parts." So addends are -6.8 and 2.4. Break -6.8 into integer part: -6, decimal part: -0.8. Break 2.4 into integer part: 2, decimal part: 0.4. Then, when adding -6.8 + 2.4, we can group the integer parts and decimal parts: ( -6 + 2 ) + ( -0.8 + 0.4 ). So the equation -6.8 + 2.4 = ( -6 + 2 ) + ( -0.8 + 0.4 ). So the two boxes are ( -6 + 2 ) and ( -0.8 + 0.4 ), which are -4 and -0.4. Wait, but let's check: -4 + (-0.4) = -4.4, and -6.8 + 2.4 = -4.4. Yes, that works. So the first box is -6 + 2 = -4, the second box is -0.8 + 0.4 = -0.4. Alternatively, maybe the problem is to write -6.8 as (-6 - 0.8) and 2.4 as (2 + 0.4), then -6.8 + 2.4 = (-6 + 2) + (-0.8 + 0.4), so the two terms are (-6 + 2) and (-0.8 + 0.4), which are -4 and -0.4.

Step2: Verify

Calculate -6.8 + 2.4: 6.8 - 2.4 = 4.4, and since the negative number has a larger absolute value, the result is -4.4. Now, -4 + (-0.4) = -4.4, which matches. So the two boxes should be -4 and -0.4. Wait, but maybe the problem is to break each addend into integer and decimal, then combine the integer parts and decimal parts. So -6.8 is integer part -6, decimal part -0.8; 2.4 is integer part 2, decimal part 0.4. Then the sum is ( -6 + 2 ) + ( -0.8 + 0.4 ) = -4 + (-0.4) = -4.4. So the first box is -4 (sum of integer parts) and the second box is -0.4 (sum of decimal parts).

Answer:

The first box is \(-4\) (which is \(-6 + 2\)) and the second box is \(-0.4\) (which is \(-0.8 + 0.4\)). So filling in the boxes: \(-6.8 + 2.4 = \boldsymbol{-4} + \boldsymbol{-0.4}\)