Integer Challenge
Calculate: −135 + 78 − 46
−103
Find the HCF of 84 and 126.
42
Calculate: √1764 + ∛1728
42 + 12 = 54
Write an expression for 8 less than five times a number n.
5n − 8
Simplify: 14a + 9b − 6a − 13b + 7
8a − 4b + 7
Calculate: −24 × (−15) ÷ (−8)
360 ÷ (−8) = −45
Find the LCM of 24 and 36.
72
Calculate: √5184 − ∛4096
72 − 16 = 56
One notebook costs x dollars and one pen costs y dollars. Write an expression for the change from $50 after buying 4 notebooks and 3 pens.
50 − 4x − 3y
Expand and simplify: 7(3x − 4) + 5x
21x − 28 + 5x = 26x − 28
Calculate: 84 − (−16) × 5
84 − (−80) = 164
Find both the HCF and LCM of 48 and 72.
HCF: 24. LCM: 144.
Calculate: (√2304 + ∛3375) × 3
(48 + 15) × 3 = 189
Find the value of 7a − 3b + 12 when a = −4 and b = 6.
−28 − 18 + 12 = −34
Expand and simplify: 5(2m − 3n) + 4(m + 2n)
10m − 15n + 4m + 8n = 14m − 7n
nd the missing number: □ ÷ (−12) + 17 = −8.
300, because 300 ÷ (−12) + 17 = −8.
Three lights flash every 18, 24 and 30 seconds. They flash together now. After how many minutes will they next flash together?
LCM = 360 seconds = 6 minutes.
Find the missing positive number: √□ + ∛5832 = 53.
∛5832 = 18, so √□ = 35. □ = 1225.
A rectangle has length 2x + 5 cm and width x − 3 cm. Find its perimeter when x = 9.
Length = 23 cm;
width = 6 cm.
Perimeter = 58 cm.
Expand and simplify: 6(3y − 4) − 2(5y + 7)
18y − 24 − 10y − 14 = 8y − 38
A submarine starts at −125 m relative to sea level. It rises 48 m, dives 3 times that distance, then rises 67 m. What is its final position?
−125 + 48 − 144 + 67 = −154 m
A teacher has 96 pencils and 144 erasers. She makes the greatest possible number of identical packs, using every item. How many packs can she make, and what is in each pack?
48 packs, each containing 2 pencils and 3 erasers.
A square has an area of 2025 cm². A cube has a volume of 3375 cm³. Find the difference between the square’s perimeter and the total length of the cube’s 12 edges.
Square: 4 × 45 = 180 cm.
Cube: 12 × 15 = 180 cm.
Difference: 0 cm.
A taxi charges $4 plus $3 per kilometre. Write an expression for the cost of travelling k kilometres. If the fare is $49, how far did the taxi travel?
Expression: 4 + 3k. Distance: (49 − 4) ÷ 3 = 15 km.
A student writes 4(3x − 5) + 2(x + 6) = 14x − 32. Correct the simplified expression, then find its value when x = −3.
Correct expression: 14x − 8.
Value: −42 − 8 = −50.