Exercise: 1-D
Q1: \(5\left(-6\right)+\left(12\div4\right)\)
Step 1: Solve inside the bracket first → (12 ÷ 4) = 3
So the expression becomes:
5{(-6) + 3}
Step 2: Add the numbers inside the bracket → (-6) + 3 = -3
So the expression becomes:
5 × (-3)
Step 3: Multiply → 5 × (-3) = -15
Answer: -15
Q2: \(10-56\div\left(-16+9\right)\)
Step 1: Solve inside the bracket → (-16 + 9) = -7
So the expression becomes:
10 – {56 ÷ (-7)}
Step 2: Divide → 56 ÷ (-7) = -8
So the expression becomes:
10 – (-8)
Step 3: Subtracting a negative means addition → 10 + 8 = 18
Answer: 18
Q3: \(\left(-6\right)-\left(-28\right)\div\left(-7\right)\)
Step 1: Divide inside the bracket → (-28 ÷ -7) = 4
So the expression becomes:
(-6) – 4
Step 2: Subtract → (-6) – 4 = -10
Answer: -10
Q4: \( 8-{12-(9-\overline{7-4})}\)
Step 1: Simplify innermost bracket → (7 – 4) = 3
Step 2: Now it becomes: 8 – {12 – (9 – 3)}
Step 3: Simplify (9 – 3) = 6
Step 4: Now: 8 – {12 – 6}
Step 5: Simplify (12 – 6) = 6
Answer: 2
Q5: \(11-\left[\left(-8\right)-10-\left(9-\overline{7-4}\ \right)\right]\)
Step 1: Simplify innermost → (7 – 4) = 3
Step 2: Now: 11 – [(-8) – {10 – (9 – 3)}]
Step 3: (9 – 3) = 6
Step 4: Now: 11 – [(-8) – {10 – 6}]
Step 5: (10 – 6) = 4
Step 6: Now: 11 – [(-8) – 4]
Step 7: (-8) – 4 = -12
Step 8: Final: 11 – (-12) = 23
Answer: 23
Q6: \(\left(-9\right)-\left[\left(-5\right)-11-\left(8-\overline{5-2}\ \right)\right]\)
Step 1: Simplify innermost → (5 – 2) = 3
Step 2: Now: (-9) – [(-5) – {11 – (8 – 3)}]
Step 3: (8 – 3) = 5
Step 4: Now: (-9) – [(-5) – {11 – 5}]
Step 5: (11 – 5) = 6
Step 6: Now: (-9) – [(-5) – 6]
Step 7: (-5) – 6 = -11
Step 8: Final: (-9) – (-11) = 2
Answer: 2
Q7: \(10-\left[8-11+30\div\left(4-\overline{5-7}\ \right)\right]\)
Step 1: Innermost: (5 – 7) = -2
Step 2: Now: 10 – [8 – {11 + 30 ÷ (4 – (-2))}]
Step 3: (4 – (-2)) = 6
Step 4: Now: 10 – [8 – {11 + 30 ÷ 6}]
Step 5: 30 ÷ 6 = 5
Step 6: Now: 10 – [8 – {11 + 5}]
Step 7: 11 + 5 = 16
Step 8: Now: 10 – [8 – 16]
Step 9: (8 – 16) = -8
Step 10: Final: 10 – (-8) = 18
Answer: 18
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