Comparing Numerical Expressions With Parentheses

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Problem 1

Compare

using the symbols <, >, =

Solution

Step 1:

We first simplify the parentheses in first expression.

6 + 4 = 10

Step 2:

So (6 + 4) ÷ 2 = 10 ÷ 2 = 5

Step 3:

Next we simplify the parentheses in second expression

7 2 = 5

Step 4:

So 3 + (7 2) = 3 + 5 = 8

Step 5:

Since 5 < 8, the correct comparison is

(6 + 4) ÷ 2 < 3 + (7 2)

Problem 2

Compare

using the symbols <, >, =

Solution

Step 1:

We first simplify the parentheses in first expression.

13 4 = 9

Step 2:

So (13 4) ÷ 3 = 9 ÷ 3 = 3

Step 3:

Next we simplify the parentheses in second expression

1 + 2 = 3

Step 4:

So 20 6 (1 + 2) = 20 6 3 = 20 18 = 2

Step 5:

Since 3 > 2, the correct comparison is

(13 4) ÷ 3 > 20 6 (1 + 2)