The Four Operations (Copy)
Practice Questions — 1.6 The Four Operations
Question 1
Evaluate: (−7) + (−12)
Question 2
Simplify: 25 − (−8)
Question 3
Evaluate: (−15) ÷ (−3)
Question 4
Calculate: (−24) ÷ 6
Question 5
Simplify: (−5) × (−4) + (−12)
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
Convert 11/4 into a mixed number and then subtract 2 1/2 from it.
Question 7
Add: 7/12 + 5/18, giving the answer in simplest form.
Question 8
Evaluate: 5/6 ÷ 10/9
Question 9
Simplify: (3 1/5) × (1 2/3), giving answer as an improper fraction.
Question 10
Subtract: 7.25 − 4.68
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
Simplify: (15 − 3²) ÷ 4
Question 12
Evaluate: (20 − 6) × 3 ÷ (2 + 1)
Question 13
If the temperature was −3°C in the morning and it dropped by 7°C, what is the new temperature?
Question 14
If the temperature was −8°C and it increased by 15°C, what is the new temperature?
Question 15
A submarine is 125 m below sea level. It descends a further 60 m, then ascends 90 m. Find its final position relative to sea level.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Calculate: (−2.4) + (5.7) − (8.3)
Question 17
Evaluate: (12.5 ÷ 0.25) − (6.3 × 0.2)
Question 18
Simplify: 2{3 + (5 − 2 × 4)}
Question 19
A person has $500. He spends 2/5 on rent, 1/10 on food, and saves the rest.
(a) How much is spent on rent?
(b) How much is spent on food?
(c) How much is saved?
Question 20
A company makes a profit of $2500 one month, then a loss of $3200 the next, and then a gain of $1500.
Find the overall profit or loss.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.6 The Four Operations
1.
−19
Explanation: Adding two negatives keeps the sign and adds magnitudes: −7 + (−12) = −(7 + 12) = −19.
2.
33
Explanation: Subtracting a negative is addition: 25 − (−8) = 25 + 8 = 33.
3.
5
Explanation: Negative ÷ negative = positive. 15 ÷ 3 = 5.
4.
−4
Explanation: Negative ÷ positive = negative. 24 ÷ 6 = 4, so −24 ÷ 6 = −4.
5.
8
Explanation: Multiply first (order of operations): (−5) × (−4) = 20; then 20 + (−12) = 20 − 12 = 8.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
1/4
Explanation: 11/4 − 2 1/2 = 11/4 − 5/2 = 11/4 − 10/4 = 1/4. (Convert mixed to improper, use a common denominator.)
7.
31/36
Explanation: LCM(12, 18) = 36. 7/12 = 21/36, 5/18 = 10/36, sum = 31/36 (already simplest; 31 is prime).
8.
3/4
Explanation: 5/6 ÷ 10/9 = 5/6 × 9/10. Cancel: 5 with 10 → 1/2; 9 with 6 → 3/2. Result = (1/2) × (3/2) = 3/4.
9.
16/3
Explanation: 3 1/5 = 16/5, 1 2/3 = 5/3. Product = (16/5) × (5/3) = 16/3 (leave as improper fraction as requested).
10.
2.57
Explanation: Align decimals: 7.25 − 4.68 = 2.57.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
1.5 (or 3/2)
Explanation: Evaluate powers first: 3² = 9. Then 15 − 9 = 6. Finally 6 ÷ 4 = 3/2 = 1.5.
12.
14
Explanation: Brackets first: (20 − 6) = 14 and (2 + 1) = 3. Then 14 × 3 ÷ 3 = 42 ÷ 3 = 14.
13.
−10°C
Explanation: Starting at −3°C, a drop of 7°C means −3 − 7 = −10°C.
14.
7°C
Explanation: Starting at −8°C, an increase of 15°C means −8 + 15 = 7°C.
15.
95 m below sea level (i.e., −95 m)
Explanation: Start −125 m, descend 60 m → −185 m, then ascend 90 m → −95 m.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
−5.0 (or −5)
Explanation: (−2.4) + 5.7 = 3.3; then 3.3 − 8.3 = −5.0.
17.
48.74
Explanation: 12.5 ÷ 0.25 = 50 (since 0.25 = 1/4). And 6.3 × 0.2 = 1.26. So 50 − 1.26 = 48.74.
18.
0
Explanation: Inside brackets: 2 × 4 = 8; 5 − 8 = −3; then 3 + (−3) = 0; finally 2{0} = 0.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
19.
Rent: $200; Food: $50; Saved: $250
Explanation: Rent = 2/5 × 500 = 200. Food = 1/10 × 500 = 50. Saved = 500 − (200 + 50) = 250.
20.
Overall profit $800
Explanation: Net change = +2500 − 3200 + 1500 = −700 + 1500 = +800 (profit).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course