The equations with parentheses added to make them true are;
- (4 × (3 + 7 - 6) × 1) + 4 = 20
- (60 - 18) ÷ (2 + 4) + 10÷2 = 12
- 80 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 44
- 3 × (5 + 4) - (2 × (2 + 6) - 4) = 15
<h3>What is the effect of parentheses in a mathematical expression?</h3>
Parentheses indicate that operations within it should be completed first before those that are outside the parentheses.
The given terms of the equations can be regrouped with parentheses to make the equations true as follows;
1. 4 × 3 + 7 - 6 × 1 + 4 = 20
The above equation gives;
3 + 7 - 6 = 4
Therefore;
4 × 3 + 7 - 6 × 1 + 4 = 4 × (3 + 7 - 6) × 1 + 4
4 × (3 + 7 - 6) × 1 + 4 = (4 × 4) × 1 + 4
(4 × 4) × 1 + 4 = 16 × 1 + 4 = 16 + 4 = 20
Which gives;
- (4 × (3 + 7 - 6) × 1) + 4 = 20
2. 60 - 18 ÷ 2 + 4 + 10 ÷ 2 = 12
60 - 18 = 42
2 + 4 = 6
The first four terms, therefore gives;
(60 - 18) ÷ (2 + 4) = 7
10÷2 = 5
Which gives;
60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2
(60 - 18) ÷ (2 + 4) + (10÷2) = 7 + 5 = 12
Which gives;
60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2 = 12
The expression is therefore;
- (60 - 18) ÷ (2 + 4) + 10÷2 = 12
3. 80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 44
80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - 36 ÷ (2 + 6 - 2) × (5 + 1)
(2 + 6 - 2) = 6, and (5 + 1) = 6
Therefore;
80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - ((36 ÷ 6) × 6)
80 - ((36 ÷ 6) × 6) = 80 - ((36 × 6) ÷ 6)
80 - ((36 × 6) ÷ 6) = 80 - (36 × 1) = 44
Therefore;
- 80 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 44
4. 3 × 5 + 4 - 2 × 2 + 6 - 4 = 15
3 × 5 + 4 - 2 × 2 + 6 - 4 = 3 × (5 + 4) - (2 × (2 + 6) - 4)
3 × (5 + 4) - (2 × (2 + 6) - 4) = 3 × 9 - (16 - 4)
3 × 9 - (16 - 4) = 27 - 12 = 15
Therefore;
- 3 × (5 + 4) - (2 × (2 + 6) - 4) = 15
Learn more about the order of mathematical operations here:
brainly.com/question/27146801
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