Insert brackets to make each statement true
a) 15 ÷ 3 + 2 × 42 – 5 = 43 b) 15 ÷ 3 + 2 × 42 – 5 = 107
To insert brackets and make each statement true, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
a) 15 ÷ 3 + 2 × 42 - 5 = 43
To solve this equation correctly, we need to add brackets to indicate the order of operations. Using PEMDAS, we will first perform the multiplication and division operations, then addition, and finally subtraction:
15 ÷ (3 + (2 × 42)) - 5 = 43
Now let's simplify it:
15 ÷ (3 + 84) - 5 = 43
15 ÷ 87 - 5 = 43
0.172 - 5 = 43
-4.828 = 43
As you can see, with the inserted brackets, the equation becomes mathematically incorrect. Therefore, it is not possible to insert brackets to make statement a) true.
b) 15 ÷ 3 + 2 × 42 - 5 = 107
Similarly, let's add brackets to indicate the order of operations:
(15 ÷ 3) + (2 × 42) - 5 = 107
Now let's simplify it:
5 + 84 - 5 = 107
89 - 5 = 107
84 = 107
Again, with the inserted brackets, the equation becomes mathematically incorrect. Therefore, it is not possible to insert brackets to make statement b) true.