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Order of operations requires division before subtraction: 12 ÷ 4 = 3, then 7 × 8 = 56, and 56 − 3 = 53. Multiplication and division are performed before addition and subtraction.
The perimeter of a rectangle equals 2 × (length + width). Here 2 × (12 + 5) = 2 × 17 = 34 cm. Perimeter measures the distance around the shape, not the space inside it.
A prime number has exactly two factors, 1 and itself. The number 29 is not divisible by 2, 3, or 5, and no factor below its square root divides it, so it is prime.
Dividing the numerator by the denominator gives 3 ÷ 8 = 0.375. A fraction always represents the numerator divided by the denominator.
The three interior angles of any triangle always add to 180 degrees, regardless of the triangle's shape or size. This follows from drawing a line parallel to one side through the opposite vertex.
Combine like terms separately: 4x − 2x = 2x, and 3y + y = 4y. Unlike terms cannot be merged, so the simplified result is 2x + 4y.
List the factors: 36 has 1, 2, 3, 4, 6, 9, 12, 18, 36, while 48 has 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest shared factor is 12.
Probability equals favourable outcomes divided by total outcomes. There are 5 red marbles out of 8 total, so the probability is 5/8.
Subtract 3x from both sides to get 2x − 7 = 9, then add 7 to obtain 2x = 16, and divide by 2 to find x = 8. Each step keeps the equation balanced.
Average speed equals total distance divided by total time. Dividing 240 km by 3 hours gives 80 km/h.
The area of a circle is πr². Using π ≈ 22/7 and r = 7 gives (22/7) × 49 = 22 × 7 = 154 cm².
A 20% discount reduces the price by 0.20 × 250 = 50 taka. Subtracting that from 250 gives a sale price of 200 taka.
First find the unit price: 18 ÷ 3 = 6 taka per pencil. Multiplying by 7 gives 6 × 7 = 42 taka.
When multiplying powers with the same base, add the exponents: 2³ × 2² = 2^(3+2) = 2⁵. The base stays unchanged.
By Pythagoras' theorem, the hypotenuse squared equals 6² + 8² = 36 + 64 = 100. Taking the square root gives 10 cm.
The total of five numbers averaging 12 is 5 × 12 = 60. The four known numbers sum to 47, so the fifth is 60 − 47 = 13.
Doubling means the interest earned equals the principal. Using I = PRT/100 with I = P and T = 8 gives 100 = 8R, so R = 12.5%.
The differences between consecutive terms are 4, 6, 8, 10, increasing by 2 each time. The next difference is 12, so 30 + 12 = 42.
Adding the equations gives 2x = 14, so x = 7, and then y = 3. The product xy is 7 × 3 = 21.
A cube has six equal square faces, so each face is 96 ÷ 6 = 16 cm², giving an edge of 4 cm. The volume is 4³ = 64 cm³.
Their rates are 1/12 and 1/18 of the tank per minute, summing to 5/36. The combined time is the reciprocal 36/5 = 7.2 minutes.
Let the numbers be n, n+2, and n+4. Their sum 3n + 6 = 84 gives n = 26, so the largest is 26 + 4 = 30.
The semi-perimeter is (13+14+15)/2 = 21. Heron's formula gives area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Downstream speed is 30 ÷ 2 = 15 km/h and upstream speed is 30 ÷ 3 = 10 km/h. The current is half the difference: (15 − 10) ÷ 2 = 2.5 km/h.
Since 8 = 2³, the power rule gives log 8 = 3 × log 2 = 3 × 0.3010 = 0.9030. Multiplying the logarithm by the exponent is the key step.
The decimal 0.25 means 25 hundredths, which is 25/100. Dividing numerator and denominator by 25 gives 1/4. Thus the simplest fractional form is one quarter.
To find 15% of 200, convert the percentage to a decimal (0.15) and multiply by 200. The calculation is 0.15 × 200 = 30. So 15% of 200 is 30.
The perimeter of a rectangle is twice the sum of its length and width. Here, length + width = 8 + 5 = 13 cm, so perimeter = 2 × 13 = 26 cm.
A prime number has exactly two distinct positive divisors: 1 and itself. The number 29 is divisible only by 1 and 29, so it is prime. The others are composite.
To add fractions, first find a common denominator. The least common multiple of 4 and 6 is 12, so 3/4 becomes 9/12 and 1/6 becomes 2/12. Adding gives 11/12.
Multiply 25 by 4 to get 100, then place the decimal point two places from the right because there is one decimal place in each factor. The product is 1.0, or simply 1.
The sequence consists of perfect squares: 1², 2², 3², 4², 5², and so on. The next term is 6², which equals 36.
Subtract 3 from both sides to get 2x = 8. Then divide both sides by 2 to isolate x, giving x = 4.
Dividing by 0.25 is the same as multiplying by 4, because 0.25 is one quarter. So 0.75 × 4 = 3. Alternatively, multiply both numbers by 100 to get 75 ÷ 25 = 3.
Compute each power: 2⁴ = 16 and 3² = 9. Adding these gives 16 + 9 = 25.
The sum of the three numbers must be 3 × 15 = 45. The sum of the two known numbers is 10 + 18 = 28. Therefore, the third number is 45 − 28 = 17.
The total number of parts is 3 + 2 = 5. Each part corresponds to 30 ÷ 5 = 6 students. Therefore, the number of boys is 3 × 6 = 18.
The discount amount is 15% of 800, which is 0.15 × 800 = 120 taka. Subtract the discount from the original price: 800 − 120 = 680 taka.
Multiply the numerators and denominators: (2×9)/(3×4) = 18/12. Simplify by dividing numerator and denominator by 6 to get 3/2.
The factorial of a positive integer n is the product of all positive integers up to n. So 5! = 5 × 4 × 3 × 2 × 1 = 120.
For any polygon with n sides, the sum of interior angles is (n − 2) × 180°. A hexagon has 6 sides, so the sum is (6 − 2) × 180° = 4 × 180° = 720°.
Substitute the values: 2(2²) + 3(3) = 2(4) + 9 = 8 + 9 = 17.
The square root of 144 is 12, and the square root of 25 is 5. Adding these gives 12 + 5 = 17.
Simple interest is calculated as Principal × Rate × Time ÷ 100. So, 5000 × 5 × 2 ÷ 100 = 500 taka.
Substitute y = 1 into the equation: 3x − 2(1) = 7, which simplifies to 3x − 2 = 7. Add 2 to both sides to get 3x = 9, then divide by 3 to find x = 3.
Cubing 0.2 means multiplying 0.2 by itself three times: 0.2 × 0.2 = 0.04, and 0.04 × 0.2 = 0.008.
Let the original number be 100. After a 20% increase, it becomes 120. A 20% decrease on 120 is 24, giving 96. The net change is a decrease of 4 from 100, which is a 4% decrease.
Square both sides of x + 1/x = 3: (x + 1/x)² = x² + 2 + 1/x² = 9. Subtract 2 from both sides to get x² + 1/x² = 7.
The speed of the train is 150 m ÷ 15 s = 10 m/s. To pass a 300 m platform, the train must cover its own length plus the platform length: 150 + 300 = 450 m. Time = 450 m ÷ 10 m/s = 45 s.
log₂ 32 = 5 because 2⁵ = 32. log₃ 9 = 2 because 3² = 9. Adding these gives 5 + 2 = 7.