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Order of operations requires multiplication and division before subtraction: 7 × 8 = 56 and 12 ÷ 4 = 3, then 56 − 3 = 53. Working strictly left to right gives a different, incorrect result.
Six notebooks cost 6 × 2 500 = 15 000 FBu. Subtracting this from the 20 000 FBu paid gives 5 000 FBu of change.
A number is divisible by 9 exactly when the sum of its digits is a multiple of 9. The digits of 4 536 sum to 4 + 5 + 3 + 6 = 18, which is divisible by 9.
Dividing 3 by 8 gives 0.375 exactly, since 8 × 0.375 = 3. The decimal terminates after three places.
The diagonal of a rectangle satisfies the Pythagorean relation d² = 12² + 5² = 144 + 25 = 169. Taking the square root gives d = 13 cm.
The divisors shared by 36 and 48 include 1, 2, 3, 4, 6 and 12, and 12 is the largest. Equivalently, 36 = 2² × 3² and 48 = 2⁴ × 3, so the common part is 2² × 3 = 12.
A mean of 14 over five values means the total is 5 × 14 = 70. The four known numbers sum to 53, so the missing value is 70 − 53 = 17.
Collect like terms: the a-terms give 3a − a = 2a and the b-terms give 5b + 2b = 7b. The simplified expression is therefore 2a + 7b.
The average speed is 180 ÷ 3 = 60 km/h. Travelling 300 km at 60 km/h takes 300 ÷ 60 = 5 hours.
Subtracting 3x from both sides gives 2x − 7 = 9, and adding 7 gives 2x = 16. Dividing by 2 yields x = 8, which checks: 5(8) − 7 = 33 and 3(8) + 9 = 33.
The discount is 15% of 12 000 = 0.15 × 12 000 = 1 800 FBu. Subtracting the discount from the original price gives 12 000 − 1 800 = 10 200 FBu.
The angles sum to 180°, and the ratio has 2 + 3 + 4 = 9 equal parts. Each part is 180 ÷ 9 = 20°, so the largest angle is 4 × 20 = 80°.
The area of a circle is πr². Using π ≈ 22/7 and r = 7 gives (22/7) × 49 = 22 × 7 = 154 cm².
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2⁷. Dividing by 2⁵ subtracts exponents, giving 2² = 4.
There are 8 balls in total and 3 of them are blue. The probability of drawing a blue ball is therefore 3/8.
Let the integers be n, n+2 and n+4. Their sum is 3n + 6 = 84, so 3n = 78 and n = 26. The three numbers are 26, 28 and 30.
The hypotenuse is √(9² + 12²) = √(81 + 144) = √225 = 15 cm. The perimeter is the sum of the sides: 9 + 12 + 15 = 36 cm.
The total work is 4 × 9 = 36 worker-days. Dividing by 6 workers gives 36 ÷ 6 = 6 days, illustrating inverse proportionality.
Multiplying each term gives x² − 5x + 3x − 15. Combining the middle terms, −5x + 3x = −2x, so the expansion is x² − 2x − 15.
The volume of a cylinder is πr²h. Here r² = 9 and h = 10, so the volume is 3.14 × 9 × 10 = 282.6 cm³.
The nth term of an arithmetic sequence is a + (n − 1)d. Here a = 5, d = 4 and n = 12, so the 12th term is 5 + 11 × 4 = 5 + 44 = 49.
The new area is (1.20L)(0.80W) = 0.96LW, which is 96% of the original area. The area therefore decreases by 4%, not by zero, because the percentage changes apply to different dimensions.
We need two numbers whose product is 6 and whose sum is 5, namely 2 and 3. Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.
The speed is 150 ÷ 10 = 15 m/s. To clear a 300 m bridge the train must cover 300 + 150 = 450 m, which takes 450 ÷ 15 = 30 seconds.
From log₂(x) = 5 we get x = 32. Then log₂(4x) = log₂(4) + log₂(x) = 2 + 5 = 7, using the product rule for logarithms.
In a base-ten number each position is worth ten times the position on its right. The 7 sits in the hundreds place, so its value is 7 × 100 = 700.
A whole number is divisible by 9 exactly when the sum of its digits is a multiple of 9. For 4 527 the digit sum is 4 + 5 + 2 + 7 = 18, which is 2 × 9.
The profit is 54 000 − 45 000 = 9 000 FBu. Percentage profit compares this gain with the cost price, so 9 000 ÷ 45 000 = 0,2, which is 20%.
The absolute value of a number is its distance from zero on the number line, so it is never negative. Thus |−8| = 8 and |3| = 3, and their sum is 11.
A cube is a solid bounded by six congruent square faces, one on each side. The eight points where edges meet are vertices, and the twelve line segments are edges.
The decimal 0,75 means 75 hundredths, that is 75/100. Dividing numerator and denominator by 25 gives 3/4, which cannot be reduced further.
Rising means moving to the right on the number line, so we compute −4 + 11. Starting at −4 and counting 11 steps right lands on 7.
A prime has exactly two divisors, 1 and itself. The number 29 is not divisible by 2, 3 or 5, and 5² = 25 < 29 < 7², so no further test is needed.
A square has four equal sides, so each side measures 36 ÷ 4 = 9 cm. The area is the side squared, 9 × 9 = 81 cm².
This is a direct proportion: the amount per person is 300 ÷ 4 = 75 g. Multiplying by 10 people gives 75 × 10 = 750 g.
Dividing by a fraction is the same as multiplying by its reciprocal. So 2/3 × 9/4 = 18/12, which simplifies to 3/2.
Squaring a binomial gives the square of the first term, twice the product of the two terms, and the square of the last term. Here that is a² − 2·4·a + 16, since the middle term is negative.
The ladder, wall and ground form a right triangle with the ladder as hypotenuse. By Pythagoras, height² = 13² − 5² = 169 − 25 = 144, so the height is 12 m.
The first six numbers total 6 × 12 = 72. Seven numbers with mean 13 total 7 × 13 = 91, so the added number is 91 − 72 = 19.
After the rise the price is 20 000 × 1,10 = 22 000 FBu. The reduction applies to this new price, so 22 000 × 0,90 = 19 800 FBu, slightly below the starting price.
By inclusion–exclusion the number studying at least one language is 24 + 18 − 8 = 34. The remaining pupils, 40 − 34 = 6, study neither.
The differences between consecutive terms are 4, 6, 8, 10, increasing by 2 each time. The next difference is therefore 12, giving 30 + 12 = 42.
The volume of a cone is one third of the base area times the height. The base area is (22/7) × 36 = 792/7 cm², so the volume is (1/3) × (792/7) × 7 = 264 cm³.
Multiply the numerical coefficients, 3 × 2 = 6. For each variable add the exponents: x² · x = x³ and y · y³ = y⁴, giving 6x³y⁴.
An exterior angle of a triangle equals the sum of the two interior angles that are not adjacent to it. Hence it measures 47° + 68° = 115°, which also equals 180° minus the third interior angle of 65°.
Simple interest is capital × rate × time, so 7 500 = C × 0,05 × 3 = 0,15C. Dividing gives C = 7 500 ÷ 0,15 = 50 000 FBu.
A fraction is undefined when its denominator equals zero, since division by zero is not allowed. Solving x + 5 = 0 gives x = −5, while the numerator may be zero without causing trouble.
The three pens cost 3 × 250 = 750 FBu, leaving 3 950 − 750 = 3 200 FBu for notebooks. Dividing by 800 gives 3 200 ÷ 800 = 4 notebooks.
The nth term equals Sₙ − Sₙ₋₁. Here S₁₀ = 100 + 20 = 120 and S₉ = 81 + 18 = 99, so the 10th term is 120 − 99 = 21, matching the formula 2n + 1.
If the sides are a and b, then ab = 60 and a + b = 17. The numbers 12 and 5 satisfy both conditions, since 12 × 5 = 60 and 12 + 5 = 17, so the longer side is 12 cm.