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Add the donated books to the starting total, then subtract the books given away: 1,248 + 376 = 1,624, and 1,624 - 215 = 1,409. Working left to right through the story keeps the operations in the order they happen.
Compare each number with 3.07 and 3.2 by lining up place values. 3.19 is larger than 3.07 and smaller than 3.20, so it sits between them. Numbers such as 3.02 and 3.007 fall below 3.07.
Find one quarter of 48 by dividing by 4, which gives 12, then multiply by 3 to take three quarters. That gives 36. Alternatively multiply 48 by 0.75.
The perimeter of a rectangle is twice the length plus twice the width, or 2 x (9 + 4). Adding 9 and 4 gives 13, and doubling that gives 26 cm.
Add the hours and minutes separately: 6:45 plus 1 hour is 7:45, and adding 50 minutes moves to 8:35 pm. Regrouping 60 minutes into one hour is needed because 45 + 50 exceeds 60.
A multiple of 6 must be divisible by both 2 and 3, so it is even and its digits add to a multiple of 3. For 42 the digits add to 6 and the number is even, so it is a multiple of 6.
There are 5 + 3 + 2 = 10 counters in total and 3 of them are blue. Probability is favourable outcomes over total outcomes, so the answer is 3/10.
In 4,782 the digit 7 sits in the hundreds place, so its value is 7 hundreds, which is 700. Reading place value from the right gives ones, tens, hundreds and thousands.
Set up a ratio: 250 g for 4 muffins means 62.5 g per muffin. Multiplying 62.5 by 10 gives 625 g. Equivalently, 10 muffins is 2.5 times the base batch, and 250 x 2.5 = 625.
A 25% discount removes one quarter of the price. One quarter of $48 is $12, and subtracting that from $48 leaves $36. The sale price is therefore $36.
Collect like terms separately. The a terms give 4a - 2a = 2a, and the b terms give 3b + 5b = 8b, so the simplified expression is 2a + 8b. Terms with different variables cannot be combined.
If the mean of five numbers is 12, their total must be 5 x 12 = 60. The four known numbers add to 44, so the fifth number is 60 - 44 = 16.
The angles in any triangle add to 180 degrees. The two known angles sum to 115 degrees, and subtracting that from 180 leaves 65 degrees for the third angle.
One kilometre equals 1,000 metres, so multiply the number of kilometres by 1,000. Moving the decimal point three places to the right gives 2,750 metres.
Each term is one more than double the previous term: 3 x 2 + 1 = 7, 7 x 2 + 1 = 15, and so on. Applying the rule to 31 gives 31 x 2 + 1 = 63.
The volume of a cube is the edge length multiplied by itself three times. Here 3 x 3 x 3 = 27, so the volume is 27 cubic centimetres.
Multiply the map distance by the scale factor: 7.5 x 5 = 37.5. Each centimetre stands for 5 kilometres, so the real distance is 37.5 km.
The decimal 0.6 means six tenths, written as 6/10. Dividing the numerator and denominator by 2 gives 3/5, which is the simplest form.
The outer rectangle measures 14 m by 10 m, giving an area of 140 square metres. The garden itself is 12 x 8 = 96 square metres, so the path covers 140 - 96 = 44 square metres.
The chance the first marble is red is 4/10. With one red removed, the chance the second is red is 3/9. Multiplying gives 12/90, which simplifies to 2/15.
Convert 45 minutes to 0.75 hours, then divide distance by time: 18 / 0.75 = 24. The average speed is 24 kilometres per hour.
Subtract 3x from both sides to get 2x - 7 = 9, then add 7 to both sides to get 2x = 16. Dividing by 2 gives x = 8, which checks correctly in the original equation.
Increasing by 20% multiplies the price by 1.2, and reducing by 20% multiplies by 0.8. The combined factor is 1.2 x 0.8 = 0.96, so the final price is 96% of the original, which is 4% lower.
The volume of a cylinder is pi times the radius squared times the height. Here 3.14 x 25 = 78.5, and 78.5 x 10 = 785 cubic centimetres.
For n = 5, the term is 2 x 25 + 1 = 51, and for n = 3 it is 2 x 9 + 1 = 19. Subtracting gives 51 - 19 = 32, which is the required difference.
Dividing the total number of books by the number of shelves gives the number per shelf: 1,248 divided by 8 equals 156. Checking by multiplication, 156 times 8 is 1,248, which confirms the division is correct.
A fraction is converted to a decimal by dividing the numerator by the denominator. Dividing 3 by 4 gives 0.75 exactly, because four lots of 0.75 make 3.
Adding 100 increases the hundreds digit by one while the tens and ones digits stay the same. So 4,096 plus 100 equals 4,196.
A prime number has exactly two factors, 1 and itself. The number 29 cannot be divided evenly by any whole number other than 1 and 29, so it is prime.
Adding 1 hour to 6:45 pm gives 7:45 pm, then adding 40 minutes gives 8:25 pm. Since 45 plus 40 minutes is 85 minutes, this is 1 hour and 25 minutes, giving the same result.
Each term is found by multiplying the previous term by 3: 2 times 3 is 6, 6 times 3 is 18, and 18 times 3 is 54. So the next term is 54 times 3, which equals 162.
The numbers greater than 5 on the spinner are 6, 7 and 8, which is 3 favourable outcomes. With 8 equally likely sections, the probability is 3 out of 8, written as 3/8.
There are 1,000 millilitres in one litre, so converting litres to millilitres means multiplying by 1,000. Thus 4.5 times 1,000 equals 4,500 mL.
To find 40% of 25, multiply 25 by 0.40, which equals 10. Equivalently, 10% of 25 is 2.5, so 40% is four lots of 2.5, which is 10.
Like terms are combined separately: the m terms 7m and 2m add to 9m, and the numbers -3 and +8 add to +5. The simplified expression is therefore 9m + 5.
If the mean of four numbers is 15, their total must be 4 times 15, which is 60. The three known numbers add to 44, so the fourth number is 60 minus 44, which equals 16.
The volume of a rectangular prism is length times width times height. Multiplying 6 by 4 gives 24, and 24 by 5 gives 120 cubic centimetres.
Subtract 9 from both sides to get 4x = 24, then divide both sides by 4 to get x = 6. Substituting back gives 4 times 6 plus 9, which equals 33.
A 15% reduction means the customer pays 85% of the original price. Multiplying 80 by 0.85 gives 68 dollars, which is also 80 minus the 12-dollar discount.
Each centimetre represents 7 divided by 2, which is 3.5 km. Multiplying 9 cm by 3.5 km per cm gives 31.5 km.
The angles in any triangle add to 180 degrees. The two known angles add to 120 degrees, so the third angle is 180 minus 120, which equals 60 degrees.
The first red has probability 6/10, and after removing one red there are 5 reds left among 9 counters, giving 5/9. Multiplying 6/10 by 5/9 gives 30/90, which simplifies to 1/3.
Order of operations requires evaluating the exponent first: 3 squared is 9. Then multiply 2 by 9 to get 18, and finally add 5 to get 23.
Working backwards, add 7 to 29 to get 36, then divide by 4 to get 9. Checking forward, 9 times 4 is 36, and 36 minus 7 is 29.
A square has four equal sides, so each side is 36 divided by 4, which is 9 cm. The area is the side length squared, and 9 times 9 equals 81 square centimetres.
Increasing by 20% multiplies the price by 1.2, and reducing by 20% multiplies it by 0.8. The combined factor is 0.96, so the final price is 96% of the original, which is 4% lower.
The volume of a cylinder is pi times radius squared times height. The radius squared is 16, and 3.14 times 16 times 9 equals 452.16, which rounds to 452 cubic centimetres.
For n = 4, the term is 3 times 16 minus 2, which is 46. For n = 2, the term is 3 times 4 minus 2, which is 10, so the difference is 46 minus 10, equal to 36.
Adding the sum and the difference gives twice the larger number: 20 + 6 = 26, so the larger number is 13. The smaller number is then 7, and 13 plus 7 is 20 while 13 minus 7 is 6.
A cube has six identical square faces, so each face has area 150 divided by 6, which is 25 cm². The edge is the square root of 25, which is 5 cm, and the volume is 5 cubed, equal to 125 cm³.