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To compare the fractions, convert each to a decimal or use a common denominator. 3/4 = 0.75, 5/8 = 0.625, 7/12 is about 0.583, and 2/3 is about 0.667, so 3/4 is the greatest.
The discount is 15% of 80 dollars, which is 0.15 × 80 = 12 dollars. Subtract the discount from the original price: 80 − 12 = 68 dollars.
Order of operations requires multiplication and division before addition and subtraction. First compute 4 × 3 = 12 and 8 ÷ 2 = 4, then evaluate 6 + 12 − 4 = 14.
The ratio 3:5 means the boys represent 3 equal parts. Since 3 parts equal 24 boys, each part equals 8 students. The total is 3 + 5 = 8 parts, so 8 × 8 = 64 students.
The rectangle area is 12 × 5 = 60 cm², and the removed square area is 3 × 3 = 9 cm². Subtract the removed area from the rectangle area: 60 − 9 = 51 cm².
Subtracting a negative number is equivalent to adding its positive value, so the expression becomes −7 + 12 + 5. First −7 + 12 = 5, and then 5 + 5 = 10.
Substitute x = 4 and y = −2 into the expression: 3(4) − 2(−2). This becomes 12 + 4 because multiplying −2 by −2 gives +4, so the value is 16.
Add the five scores: 78 + 85 + 90 + 72 + 80 = 405. Divide the total by the number of scores, 5, so the mean is 405 ÷ 5 = 81.
The added water represents the difference between 2/3 and 1/4 of the tank. Since 2/3 − 1/4 = 8/12 − 3/12 = 5/12, 25 liters equals 5/12 of the capacity. Therefore the full capacity is 25 × 12/5 = 60 liters.
List numbers that leave remainder 3 when divided by 5: 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53. Among these, 53 leaves remainder 2 when divided by 3 and remainder 4 when divided by 7, so it satisfies all three conditions. No smaller positive integer meets all three remainders.
The hundredths digit is 6, and the thousandths digit is 7. Because 7 is 5 or greater, the hundredths digit increases by 1, giving 4.87.
A number is divisible by 9 exactly when the sum of its digits is divisible by 9. For 4,563 the digit sum is 4+5+6+3=18, which is divisible by 9, so 4,563 is divisible by 9.
A fraction is in simplest form when the greatest common factor of its numerator and denominator is 1. The numbers 7 and 9 share no common factor other than 1, so 7/9 is in simplest form.
The area of a triangle is one-half times base times height. Substituting 14 cm for the base and 9 cm for the height gives 0.5 × 14 × 9 = 63 square centimeters.
Divide both sides of 3(x + 4) = 33 by 3 to obtain x + 4 = 11. Subtracting 4 from both sides gives x = 7.
After a 20% increase, the price becomes 60 × 1.20 = 72 dollars. A 25% reduction multiplies that price by 0.75, so the final price is 72 × 0.75 = 54 dollars.
Convert 45 minutes to hours by dividing by 60, which gives 0.75 hours. Average speed is distance divided by time, so 18 kilometers ÷ 0.75 hours = 24 kilometers per hour.
The three interior angles of a triangle add to 180°. The two given angles total 47° + 68° = 115°, so the third angle is 180° − 115° = 65°.
The next shared time is the least common multiple of 8, 12, and 15 minutes. Prime factorization gives 8 = 2³, 12 = 2² × 3, and 15 = 3 × 5, so the LCM is 2³ × 3 × 5 = 120 minutes.
From 1 to 20 there are 6 multiples of 3 and 4 multiples of 5, but 15 is counted in both lists. Using inclusion-exclusion, the favorable count is 6 + 4 − 1 = 9, so the probability is 9/20.
First evaluate each power separately: 2^3 = 8 and 3^2 = 9. Then multiply the results: 8 × 9 = 72.
Since 1 meter equals 1000 millimeters, multiply 3.5 by 1000. Moving the decimal point three places to the right gives 3500 millimeters.
To convert 3/8 to a decimal, divide the numerator by the denominator: 3 ÷ 8 = 0.375. The decimal terminates after three places.
Use the simple interest formula I = P × r × t. Substitute P = 800, r = 0.05, and t = 3: 800 × 0.05 × 3 = 120 dollars.
The ratio 5:2 means flour is 5 parts and sugar is 2 parts. Since 5 parts equal 350 g, one part is 70 g, so sugar is 2 × 70 = 140 g.
Subtract 6 from both sides to get x/4 = 5. Then multiply both sides by 4, giving x = 20.
Circumference equals 2πr. Using π ≈ 22/7 and r = 7 m gives 2 × (22/7) × 7 = 44 m.
Arrange the six values in order: 7, 8, 9, 10, 12, 15. With an even number of values, the median is the mean of the two middle values, (9 + 10) ÷ 2 = 9.5.
Multiples of 4 below 100 are 4 through 96, giving 24 numbers. Multiples of both 4 and 6 are multiples of 12, giving 8 numbers; subtract to get 24 − 8 = 16.
There are 12 balls total, with 4 red. The probability the first is red is 4/12; without replacement, the second red probability is 3/11. Multiply: (4/12) × (3/11) = 1/11.
Write 36 = 2^2 × 3^2 and 48 = 2^4 × 3. The greatest common divisor uses the smaller power of each shared prime, so 2^2 × 3 = 12. Both numbers are divisible by 12, and no larger integer divides both.
The perimeter of a rectangle is 2(length + width). Here that is 2(12 + 7) = 2 × 19 = 38 m. The value 84 m would be the area, not the distance around the edge.
Find the total first: 4 + 8 + 10 + 14 + 14 = 50. Dividing this total by the five numbers gives 50 ÷ 5 = 10. The mean is therefore 10.
The area of a parallelogram is base × perpendicular height. Multiplying 15 cm by 8 cm gives 120 cm². Unlike a triangle, there is no factor of one-half in this formula.
Add 5 to both sides to get 3x < 15. Then divide both sides by the positive number 3, which preserves the inequality direction, giving x < 5. Checking x = 4, for example, gives 7 < 10, which is true.
Distribute the 2 to get 6x - 8, then add 5x. The x-terms combine as 6x + 5x = 11x, while the constant stays -8, giving 11x - 8.
The volume of a rectangular prism is length × width × height. Substituting gives 6 × 4 × 5 = 120 cm³. The units are cubic centimetres because three lengths are multiplied.
Dividing by a fraction is the same as multiplying by its reciprocal. So 2/5 ÷ 3/4 = 2/5 × 4/3 = (2 × 4)/(5 × 3) = 8/15. The result is already in simplest form.
A cube has six congruent square faces, so each face has area 294 ÷ 6 = 49 cm². The edge length is 7 cm because 7² = 49. The volume is then 7³ = 343 cm³.
The outer square has side length 12 m because 12² = 144. Removing a 1 m strip on each side shortens each side by 2 m, so the inner square has side 10 m and area 100 m². The path area is 144 - 100 = 44 m².
First simplify inside the parentheses: 8 − 3 = 5. Squaring gives 25, then multiply by 2 to get 50, and finally add 5, so the value is 55.
The digit in the hundredths place is 8, so the tenths digit 3 rounds up to 4. Therefore 47.386 rounded to the nearest tenth is 47.4.
A prime number has exactly two positive factors: 1 and itself. Among the choices, 61 has no factor other than 1 and 61, while the others are divisible by 3.
A 25% discount leaves 75% of 80 dollars, which is 60 dollars. Adding 10% tax to 60 dollars gives 6 dollars, so the final cost is 66 dollars.
Subtract 7 from both sides to get −2x ≥ −6. Dividing by −2 reverses the inequality sign, giving x ≤ 3.
The area of a trapezoid is the average of its parallel bases times the height. Here the average of 12 cm and 8 cm is 10 cm, and multiplying by 5 cm gives 50 cm².
Each centimeter on the map represents 4 kilometers in reality. Multiplying 7.5 cm by 4 km/cm gives 30 km.
The favorable outcomes are the multiples of 3 (3 and 6) and the even numbers (2, 4, 6, and 8). Their union has 5 outcomes, so the probability is 5/8.
Numbers that leave remainder 3 when divided by 7 have the form 7a + 3. Combining this with remainder 4 modulo 9 gives n = 31 + 63k, and the smallest such value above 500 is 535.
Total surface area of a cylinder is 2πr² + 2πrh. Using r = 3 cm, h = 10 cm, and π ≈ 3.14 gives 56.52 + 188.4 = 244.92 cm².