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A 25% discount removes one quarter of the original price, so the reduction is 80 divided by 4, which equals 20 dollars. Subtracting that reduction from 80 gives 60 dollars. Equivalently, the buyer pays 75% of 80, and 0.75 times 80 is also 60.
Each term is double the term before it, so the pattern is multiplication by 2. Doubling the last shown term, 24, gives 48. Checking earlier steps confirms this rule holds throughout the sequence.
Average speed equals total distance divided by total time. Dividing 240 km by 3 hours gives 80 km per hour. The result is a rate, so the units are kilometres per hour rather than kilometres.
To convert a decimal to a fraction, write it over 1000 as 375/1000 and divide top and bottom by 125. This gives 3/8. Checking by division, 3 divided by 8 equals 0.375, confirming the result.
Perimeter is the total distance around the shape, so it equals twice the length plus twice the width. Twice 12 is 24 and twice 5 is 10, and 24 plus 10 equals 34. The unit stays in centimetres because perimeter measures length.
Fifteen percent means 15 out of every 100, which as a decimal is 0.15. Multiplying 0.15 by 200 gives 30. A quick check: 10% of 200 is 20 and 5% is 10, and 20 plus 10 equals 30.
To compare decimals, line up the place values and compare digits from left to right. All four numbers have zero before the decimal point, so compare tenths: 8 tenths is greater than 7, 6 and 0 tenths. Therefore 0.8 is the largest value.
Probability equals favourable outcomes divided by total outcomes. There are 4 red marbles out of 10 in total, giving 4/10. Simplifying by dividing both parts by 2 gives 2/5.
Fifteen pens is three times as many as five pens, so the cost is also three times as much. Multiplying 12 dollars by 3 gives 36 dollars. This uses proportional reasoning rather than finding the unit price, though both methods agree.
Set up the proportion 8 litres per 100 km, so each 100 km needs 8 litres. For 250 km there are 2.5 lots of 100 km, and 2.5 times 8 equals 20 litres. The unit rate method gives the same answer: 0.08 litres per km times 250.
First expand the bracket by multiplying each term inside by 3, giving 6x + 12. Then subtract 2x from the 6x to get 4x. The constant 12 is unaffected, so the simplified expression is 4x + 12.
If the mean of five numbers is 12, their total must be 5 times 12, which is 60. The four known numbers add to 10 + 14 + 8 + 15 = 47. Subtracting 47 from 60 leaves 13 for the fifth number.
Increasing 60 by 20% gives 60 times 1.2, which is 72. Reducing 72 by 20% means multiplying by 0.8, giving 57.60. The two percentage changes do not cancel because they apply to different base amounts.
The amount per person is 300 divided by 4, which is 75 g. Multiplying 75 g by 10 people gives 750 g. Alternatively, 10 people is 2.5 times 4 people, and 2.5 times 300 also equals 750.
A power tells you how many times to multiply the base by itself. Two to the fifth means 2 x 2 x 2 x 2 x 2. Working through gives 4, then 8, then 16, then 32.
The interior angles of any triangle always add to 180 degrees. The two known angles sum to 45 + 65 = 110 degrees. Subtracting 110 from 180 leaves 70 degrees for the third angle.
Work backwards by reversing each operation in turn. Add 7 to 25 to undo the subtraction, giving 32. Then divide 32 by 4 to undo the multiplication, giving 8. Checking: 8 times 4 is 32, and 32 minus 7 is 25.
A prime number has exactly two factors: 1 and itself. The number 29 is not divisible by 2, 3, 4 or 5, and no factor below its square root divides it, so it is prime. The other options each have a factor of 3.
The volume of a cube is the side length multiplied by itself three times. Three cubed is 3 x 3 x 3, which equals 27. Because three lengths are multiplied, the units are cubic centimetres.
If 18 of the 30 students are girls, then 30 minus 18 equals 12 boys. To express 12 out of 30 as a percentage, divide 12 by 30 to get 0.4 and multiply by 100. This gives 40 percent.
Apply the rule step by step, treating the starting value as the first term. The second term is 2 times 3 minus 1, which is 5. The third term is 5 times 3 minus 1, which is 14. The fourth term is 14 times 3 minus 1, which is 41.
The ratio 3:5 means the total is split into 8 equal parts, since 3 plus 5 equals 8. Each part is 64 divided by 8, which is 8. The larger number takes 5 parts, so 5 times 8 equals 40.
Find the rate of each pipe as a fraction of the tank per hour. Pipe A fills 1/6 and pipe B fills 1/3, and together they fill 1/6 + 2/6 = 3/6 = 1/2 of the tank each hour. At half a tank per hour, a full tank takes 2 hours.
Simple interest equals principal times rate times time. Here 90 = P times 0.05 times 3, so 90 = P times 0.15. Dividing 90 by 0.15 gives a principal of 600 dollars.
The probability the first counter is red is 5/10. After removing one red, 4 red remain out of 9, so the second probability is 4/9. Multiplying gives 20/90, which simplifies to 2/9.
Average speed is found by dividing total distance by total time, so 240 divided by 3 equals 80 kilometres per hour. This measures the steady rate that would cover the same distance in the same time.
A fraction becomes a decimal when the numerator is divided by the denominator, so 3 divided by 4 equals 0.75. The result is three quarters of one whole.
The perimeter of a rectangle is twice the sum of its length and width, so 2 times (12 plus 5) equals 34 cm. This adds all four sides around the shape.
The decimal 0.6 means six tenths, and the fraction 3/5 simplifies to six tenths when both parts are multiplied by two. Equivalent fractions keep the same value.
After a 25% increase the new value is 125% of the original, so the original equals 50 divided by 1.25, which is 40. Checking, 40 plus 25% of 40 gives 50.
The differences between consecutive terms are 4, 6, 8 and 10, increasing by two each time. The next difference is 12, so 30 plus 12 equals 42.
There are 10 counters in total and 3 of them are green, so the probability is 3 out of 10. Probability compares favourable outcomes with all equally likely outcomes.
Ordering the values gives 2, 4, 5, 7, 9, and the median is the middle value of an odd-sized list. The middle value here is 5.
Total pay equals the hourly rate multiplied by the hours worked, so 18 times 6.5 equals 117 dollars. The half hour contributes 9 dollars on top of six full hours.
Fuel use per kilometre is 12 divided by 150, which is 0.08 litres. Multiplying by 400 gives 32 litres for the longer journey.
The sale price is 70% of the original, so the original equals 84 divided by 0.7, which is 120 dollars. Checking, 30% of 120 is 36, and 120 minus 36 gives 84.
Expanding the bracket gives 10x minus 15, and adding 4x combines the like terms to give 14x minus 15. Like terms are collected only when the variable part matches.
The original total is 8 times 15, which is 120, and the new total is 7 times 14, which is 98. The removed number is the difference, 120 minus 98, giving 22.
Each ratio part equals 36 divided by 4, which is 9. The larger number is 7 parts, so 7 times 9 equals 63.
The side length is the square root of 81, which is 9 cm. The diagonal of a square is the side multiplied by the square root of 2, giving about 12.7 cm.
The first white has probability 6/10, and with one white removed the second has probability 5/9. Multiplying gives 30/90, which simplifies to 1/3.
After one year the value is 2000 times 1.04, which is 2080, and after two years it is 2080 times 1.04, giving 2163.20 dollars. Compound interest earns interest on the first year's interest as well.
Adding the two equations gives 2x = 14, so x is 7, and then y is 3. Their product is 7 times 3, which equals 21.
The volume of a cylinder is pi times the radius squared times the height. That gives 3.14 times 4 times 5, which equals 62.8 cubic metres.
Tea and coffee together account for 75%, so juice represents 25% of the total. Since 25% equals 50 people, the whole total is 50 divided by 0.25, which is 200.
Continuing the rule gives 1, 3, 4, 7, 11, 18, 29, so the sixth term is 18 and the seventh is 29. Reading the position carefully, the sixth term is 18, but the list extended to the seventh is 29.
The train's speed is 200 divided by 10, which is 20 metres per second. To clear a 300 m platform it must cover 200 plus 300 metres, so 500 divided by 20 gives 25 seconds.
Their combined rate is 1/12 plus 1/18, which is 5/36 of the job per day. In 4 days they complete 20/36, leaving 16/36, and B at 1/18 per day needs 8 more days.
Multiplying the factors gives 1.20 times 0.75, which equals 0.90. The final price is therefore 90% of the original, a net fall of 10%.
The volume of a cone is one third of pi times the radius squared times the height. That is one third of 3.14 times 9 times 7, giving about 65.9 cubic centimetres.