the number line models the expression 576 - 388. enter numbers to label each jump; first subtracting the…

the number line models the expression 576 - 388. enter numbers to label each jump; first subtracting the nearest 100 for the second number, then adding back the extra amount. enter the difference between 576 and 388 above the number line. 176 576

the number line models the expression 576 - 388. enter numbers to label each jump; first subtracting the nearest 100 for the second number, then adding back the extra amount. enter the difference between 576 and 388 above the number line. 176 576

Answer

Explanation:

Step1: Subtract nearest 100

The nearest 100 to 388 is 400. So first, we calculate ( 576 - 400 ). ( 576 - 400 = 176 ) (this is the first jump, but wait, actually, the large arc is from 576 to 176? Wait, no, let's re - examine. Wait, the problem says "first subtracting the nearest 100 for the second number, then adding back the extra amount". The second number is 388, nearest 100 is 400. So we do ( 576-400 = 176 ), but then we subtracted 12 more than 388 (since ( 400 - 388=12 )), so we need to add back 12.

Wait, let's break down ( 576 - 388 ). We can rewrite ( 388=400 - 12 ). So ( 576-388=576-(400 - 12)=576 - 400+12 ).

First jump: Subtract 400 from 576. So ( 576-400 = 176 ). But the small jump is adding back the extra. The extra is ( 400 - 388 = 12 ). Wait, no, when we subtract 400 instead of 388, we subtracted 12 too many. So to correct, we add 12. So the small jump (the backward - forward? Wait, the number line has 576 on the right, 176 on the left. The large arc is from 576 to 176 (subtracting 400), and the small arc is from 176 to some number, then back? Wait, no, let's look at the boxes.

The top box (large arc) is the first subtraction: subtract 400 (since 388's nearest 100 is 400), so ( 576-400 = 176 ), but the large arc is labeled with the amount subtracted, so the top box is 400.

Then, we subtracted 12 more than we should (because ( 400-388 = 12 )), so we need to add back 12. The small arc (the lower box) is the amount we added back, which is 12. And the middle box (the number we get after adding back) is ( 176 + 12=188 )? Wait, no, wait ( 576-388 = 188 ). Let's check: ( 388+188=576 ). Yes, ( 388 + 180=568 ), ( 568+8 = 576 ). Wait, ( 388+188=388+(180 + 8)=(388 + 180)+8=568+8 = 576 ).

Wait, let's redo the steps:

  1. First, subtract the nearest 100 of 388 (which is 400) from 576: ( 576-400 = 176 ). So the large arc (top box) is labeled 400 (the amount we subtracted).

  2. Then, we subtracted 12 more than 388 (since ( 400 - 388 = 12 )), so we need to add back 12. So the small arc (lower box) is 12.

  3. Then, ( 176+12 = 188 ), which is the middle box. And the difference ( 576 - 388=188 ).

Step2: Calculate the difference

We know that ( 576-388=(500 + 76)-(300+88)=(500 - 300)+(76 - 88)=200-12 = 188 ). Or using the method above: ( 576-400 + 12=176+12 = 188 ).

Answer:

Top box (large arc): 400; Lower box (small arc): 12; Middle box: 188; Difference: 188