Madison Middle School has a math and science club that holds meetings after school. The club has decided to enter a two-day comp
etition that involves different a math science challenges. The first day of competition involves solving multi-step math problems. Teams will receive two points for every problem they get correct in the morning session and three points for every question they get correct in the afternoon session.
a. Write an equation to represent the situation. Remember to define your variable(s)
b. The team scores four points in the morning session, but finishes the day with 28 points. Solve the equation and interpret the solution in the context of the problem.
c. The second day of the competition the science portion, involving hands-on science problems. Each correct science problem is worth 5 points. If the team started the day with 28 points and ended with 53 points, how many science problems did they get correct? Write and solve the an equation to answer the question.
a. Write an equation to represent the situation. Remember to define your variable(s)
b. The team scores four points in the morning session, but finishes the day with 28 points. Solve the equation and interpret the solution in the context of the problem.
c. The second day of the competition the science portion, involving hands-on science problems. Each correct science problem is worth 5 points. If the team started the day with 28 points and ended with 53 points, how many science problems did they get correct? Write and solve the an equation to answer the question.
1 answer:
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There are a variety of methods of performing this subtraction, and corresponding different methods of regrouping.
If you're taught (as I was) to do the subtraction right-to-left, then the first regrouping you need to do is when you try to subtract 500 from 100. You must regroup the 8 thousands and 1 hundred to 7 thousands and 11 hundreds. Then, when you subtract 5 hundreds, you end with 7 thousands and 6 hundreds.
The next regrouping you need to do is when you try to subtract 6 ten-thousands from 5 ten-thousands. You must regroup the 2 hundred-thousands and 5 ten-thousands to 1 hundred-thousand and 15 ten-thousands. Then, when you subtract 6 ten-thousands, you end with 1 hundred-thousand and 9 ten-thousands.
The end result is
... 258,197 - 64,500 = 193,697
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If you use an abacus or soroban or similar tool to help you keep track of the numbers, you were likely taught to do the subtraction left-to-right. In this case, the first regrouping comes when you want to subtract 6 ten-thousands. Practitioners of this method know that -6 = -10 +4, so the number represented on the tool becomes (2-1) hundred-thousands and (5+4) ten-thousands plus the rest of the initial number, or 198,197 after subtracting the 6 ten-thousands.
The subtraction proceeds until you find you need to subtract 500 from 100. At this point, the tool is representing the partial result as 194,197. Again, if you practice this method, you know that -5 = -10 +5, so you reduce the thousands digit by 1 (to 3) and add 5 to the hundreds digit to get 193,697.
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An attempt is made to show the regroupings in the attachment. In each case there are two of them. However, working left-to-right, the result of the first subtraction of 6 ten-thousands is 19 ten-thousands, so you never actually write down anything else. Of course, if you're using an abacus or soroban, you don't write down anything—you simply change the position of the beads on the tool.
