If unequal quantities are subtracted from equal quantities, the remainders are unequal in the opposite order. Since 25=25 and 5>3, then 20<22. If x=y and a>d, then x-a<y-d.
Please show work and explain.
Let's break down the statements step by step:
1. "If unequal quantities are subtracted from equal quantities, the remainders are unequal in the opposite order."
To understand this statement, let's consider an example. Let's say we have two equal quantities, 25 and 25. If we subtract unequal quantities from them, say 5 and 3, the remainders will be different and in the opposite order.
So, when we subtract 5 from 25, we get a remainder of 20. When we subtract 3 from 25, we get a remainder of 22. In this case, 20 < 22, and the remainders are indeed unequal in the opposite order.
2. "Since 25 = 25 and 5 > 3, then 20 < 22."
This statement is applying the principle mentioned in the previous statement. Based on the example we just discussed, we can see that the numbers provided satisfy the condition. 25 is equal to 25, and when we subtract 5 (which is greater than 3) from 25, we get a smaller remainder of 20 compared to subtracting 3 from 25, which gives a remainder of 22. Therefore, the statement is true.
3. "If x = y and a > d, then x - a < y - d."
Using the principles established in the previous statements, we can apply the same logic here. Suppose x = y and a > d.
When we subtract a from x, we get a remainder of (x - a). Similarly, when we subtract d from y, we get a remainder of (y - d).
Based on what we established earlier, if a > d, then (x - a) < (y - d).
So, if x = y and a > d, then (x - a) < (y - d).
That concludes the explanation for the given statements.