4. In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms. (a) , , , (b) , , , , ,

We find expressions with the same value. We check numbers and their signs. Step 1 — Comparing expressions in set (a) Let us write down each expression. We will identify the numbers and their signs. The first expression is . This means we add 319 and 537. The second expression is . Subtracting 537 is the same as adding -537. So, this expression is . The third expression is . The order of adding numbers does not change the sum. So, this is the same as . The fourth expression is . Subtracting 319 is the same as adding -319. So, this expression is . Now we compare them. These expressions involve adding 319 and -537. They have the same numbers with the same signs. > Step 2 — Comparing expressions in set (b) Let us write down each expression. We will identify the numbers and their signs. The first expression is . This means we add 87 and 46. Then we subtract 109. The second expression is . This expression is exactly the same as the first one. The third expression is . This expression is also exactly the same as the first one. The fourth expression is . This means we subtract 46 from 87. Then we add 109. The fifth expression is . When we have brackets, we do the operation inside first. So, we add 46 and 109. Then we subtract this sum from 87. This is different from the other expressions. Subtracting a sum is like subtracting each number. So, this is . The sixth expression is . Here, we first subtract 46 from 87. Then we add 109 to the result. This is the same as . The brackets just make the order clear. Now we compare them. The expressions (all three instances) are identical. > > Answer > (a) and have the same value. > (b) , , and have the same value. Also, and have the same value.

Arithmetic Expressions

Question 4

In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms.

(a) $319 + 537$ , $319 - 537$ , $-537 + 319$ , $537 - 319$

(b) $87 + 46 - 109$ , $87 + 46 - 109$ , $87 + 46 - 109$ , $87 - 46 + 109$ , $87 - (46 + 109)$ , $(87 - 46) + 109$

Solution

We find expressions with the same value. We check numbers and their signs.

Step 1 — Comparing expressions in set (a)

Let us write down each expression. We will identify the numbers and their signs.

The first expression is $319 + 537$ . $319 + 537$ This means we add 319 and 537.

The second expression is $319 - 537$ . $319 - 537$ Subtracting 537 is the same as adding -537. So, this expression is $319 + (-537)$ .

The third expression is $-537 + 319$ . $-537 + 319$ The order of adding numbers does not change the sum. So, this is the same as $319 + (-537)$ .

The fourth expression is $537 - 319$ . $537 - 319$ Subtracting 319 is the same as adding -319. So, this expression is $537 + (-319)$ .

Now we compare them. These expressions involve adding 319 and -537. They have the same numbers with the same signs.

$\boxed{\text{The expressions 319 - 537 and -537 + 319 have the same value.}}$

Diagram 1

Step 2 — Comparing expressions in set (b)

Let us write down each expression. We will identify the numbers and their signs.

The first expression is $87 + 46 - 109$ . $87 + 46 - 109$ This means we add 87 and 46. Then we subtract 109.

The second expression is $87 + 46 - 109$ . $87 + 46 - 109$ This expression is exactly the same as the first one.

The third expression is $87 + 46 - 109$ . $87 + 46 - 109$ This expression is also exactly the same as the first one.

The fourth expression is $87 - 46 + 109$ . $87 - 46 + 109$ This means we subtract 46 from 87. Then we add 109.

The fifth expression is $87 - (46 + 109)$ . $87 - (46 + 109)$ When we have brackets, we do the operation inside first. So, we add 46 and 109. Then we subtract this sum from 87. This is different from the other expressions. Subtracting a sum is like subtracting each number. So, this is $87 - 46 - 109$ .

The sixth expression is $(87 - 46) + 109$ . $(87 - 46) + 109$ Here, we first subtract 46 from 87. Then we add 109 to the result. This is the same as $87 - 46 + 109$ . The brackets just make the order clear.

Now we compare them. The expressions $87 + 46 - 109$ (all three instances) are identical.

$\boxed{\text{The expressions 87 + 46 - 109 (all three instances) have the same value.}}$ $\boxed{\text{The expressions 87 - 46 + 109 and (87 - 46) + 109 have the same value.}}$

Answer

(a) $319 - 537$ and $-537 + 319$ have the same value. (b) $87 + 46 - 109$ , $87 + 46 - 109$ , and $87 + 46 - 109$ have the same value. Also, $87 - 46 + 109$ and $(87 - 46) + 109$ have the same value.

Question 4

Answer

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