Question

formative assessments unit 2: operations with rational numbers learning target 7 ns 1 i can add and subtract rational numbers. yes no not sure problem 1. complete the equation to make a true statement. use the number bank to fill in the statement. -7 -4 -2 1 2 3 enter your answers in the boxes: 7 - = 7 + error analysis correct incorrect direction error calculation error concept error application error teacher feedback (enter feedback here)

Explanation:

Step1: Recall the rule of subtracting a number

We know that subtracting a number is the same as adding its opposite, i.e., \(a - b=a+(-b)\). So we need to find a number \(x\) such that \(7 - x = 7+ y\), which means \(-x=y\) (by comparing both sides). From the number bank \(-7,-4,-2,1,2,3\), if we take \(x = 2\), then \(y=- 2\) (because \(-x=-2\) when \(x = 2\)) and let's check: \(7-2=5\) and \(7+(- 2)=5\). Also, if we take \(x = 3\), \(y = - 3\) but \(-3\) is not in the number bank. Wait, let's re - examine the number bank. Wait, the number bank is \(-7,-4,-2,1,2,3\). Let's use the rule \(a - b=a+(-b)\). So for the equation \(7-\square=7+\square\), let the first box be \(b\) and the second box be \(-b\). So we need to find a number \(b\) from the number bank such that \(-b\) is also in the number bank. Looking at the numbers: if \(b = 2\), then \(-b=-2\) (both \(2\) and \(-2\) are in the number bank). Let's verify: \(7 - 2=5\) and \(7+(-2)=5\). Similarly, if \(b = 3\), \(-b=-3\) (not in the bank), \(b=-2\), then \(-b = 2\) (also works). Let's check \(7-(-2)=9\) and \(7 + 2=9\). Wait, the problem says "use the number bank to fill in the statement". Let's assume the equation is \(7-\square=7+\square\). Let's take the first blank as \(2\) and the second as \(-2\) (or vice - versa). Let's check with \(b = 2\): \(7-2 = 5\) and \(7+(-2)=5\). So the first box can be \(2\) and the second box can be \(-2\).

Step2: Verify the solution

Left - hand side: \(7 - 2=5\)
Right - hand side: \(7+(-2)=7 - 2 = 5\)
Both sides are equal. Also, if we take the first blank as \(-2\) and the second as \(2\): \(7-(-2)=7 + 2=9\) and \(7+2 = 9\). Both \(2\) and \(-2\) are in the number bank.

Answer:

The first box is \(2\) and the second box is \(-2\) (or the first box is \(-2\) and the second box is \(2\)).