Mathematics Flashcards

Divide and simplify: ÷ \/

Answer: 2 1\/4

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. Assuming the fractions are 9/10 and 2/5, the operation becomes 9/10 * 5/2. Multiply the numerators (9*5=45) and the denominators (10*2=20) to get 45/20. Simplifying this improper fraction gives 9/4, which converts to the mixed number 2 1/4.

Convert 0.60 to ratio in simplest form

Answer: 3:5

To convert the decimal 0.60 to a ratio in simplest form, first write it as a fraction: 60/100. Then, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20. This reduces the fraction to 3/5, which can be expressed as the ratio 3:5.

A shoe company sends out 7 trucks loaded with nursing shoes that cost the company $1,572 per truck. If they send out 750 boxes per truck, what would be the profit if the cost per box is $ 125.40?

Answer: 647,346.00

First, calculate the total cost for the company: 7 trucks * $1,572/truck = $11,004. Next, determine the total number of boxes: 7 trucks * 750 boxes/truck = 5,250 boxes. Then, calculate the total revenue from selling the boxes: 5,250 boxes * $125.40/box = $658,350. Finally, subtract the total cost from the total revenue to find the profit: $658,350 - $11,004 = $647,346.

Calculate the quotient of 54, 256 \/ 45 (Round to the nearest tenth)

Answer: 1,205.7

To calculate the quotient of 54,256 divided by 45, perform the division: 54,256 ÷ 45 = 1205.6888... To round to the nearest tenth, look at the hundredths digit. Since it is 8 (which is 5 or greater), round up the tenths digit. Therefore, 1205.6888... rounded to the nearest tenth is 1,205.7.

Multiply and reduced to lowest terms 5\/13 x 3 3\/8

Answer: 1 31\/104

To multiply 5/13 by 3 3/8, first convert the mixed number to an improper fraction: 3 3/8 becomes (3*8 + 3)/8 = 27/8. Now multiply the fractions: (5/13) * (27/8) = (5*27) / (13*8) = 135/104. Convert this improper fraction back to a mixed number by dividing 135 by 104, which gives 1 with a remainder of 31, resulting in 1 31/104.

Add: 5 2\/3 + 4\/7

Answer: 6 5\/21

To add 5 2/3 and 4/7, first find a common denominator for the fractions, which is 21. Convert 2/3 to 14/21 and 4/7 to 12/21. Add the fractions: 14/21 + 12/21 = 26/21. Convert 26/21 to a mixed number, which is 1 5/21. Finally, add this to the whole number part of the original mixed number: 5 + 1 5/21 = 6 5/21.

The average speed of a high velocity train is 200 kilometers per hour. The distance between Paris and Naples is 7,346 km (1 mile = 1.609 km). How long will the trip take? (Round to the nearest whole number).

Answer: 37 hours

To find the time the trip will take, use the formula Time = Distance / Speed. The distance is 7,346 km and the speed is 200 km/h. Divide 7,346 by 200, which equals 36.73 hours. Rounding 36.73 to the nearest whole number gives 37 hours. The information about miles to kilometers is extraneous for this calculation.

How many grams in 450 milligrams?

Answer: 0.45 grams

To convert milligrams to grams, you need to know that 1 gram is equal to 1000 milligrams. Therefore, to convert 450 milligrams to grams, you divide 450 by 1000. This calculation yields 0.45 grams.

23\/15 divided by 16\/17 =

Answer: 1 151\/240

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, 23/15 ÷ 16/17 becomes 23/15 * 17/16. Multiply the numerators (23 * 17 = 391) and the denominators (15 * 16 = 240) to get 391/240. Finally, convert this improper fraction to a mixed number: 391 divided by 240 is 1 with a remainder of 151, resulting in 1 151/240.

Convert 25.52 to a reduced fraction

Answer: 25 13\/25

To convert 25.52 to a reduced fraction, separate the whole number (25) from the decimal part (0.52). Write 0.52 as a fraction: 52/100. Then, reduce this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. This simplifies to 13/25. Combine the whole number and the reduced fraction to get 25 13/25.

Convert 3\/5 to a decimal.

Answer: 0.6

To convert a fraction to a decimal, divide the numerator by the denominator. For 3/5, divide 3 by 5. Performing this division, 3 ÷ 5 equals 0.6.

Add 6 1\/4 + 8 1\/3 =

Answer: 14 7\/12

To add the mixed numbers 6 1/4 and 8 1/3, first add the whole numbers: 6 + 8 = 14. Next, add the fractions: 1/4 + 1/3. Find a common denominator for 4 and 3, which is 12, converting them to 3/12 and 4/12 respectively. Adding these gives 7/12. Combine the whole number sum and the fraction sum to get 14 7/12.

A recent online survey published that a hospital needs 9 nurses for every 45 patients. How many nurses a hospital would need in order to take care of 255 patients?

Answer: 51 nurses

The hospital needs 9 nurses for every 45 patients, which simplifies to a ratio of 1 nurse for every 5 patients (9/45 = 1/5). To find out how many nurses are needed for 255 patients, set up a proportion: 1 nurse / 5 patients = x nurses / 255 patients. Solve for x by multiplying 255 by (1/5), which gives 51 nurses.

Convert 5\/8 to a decimal

Answer: 0.625

To convert the fraction 5/8 to a decimal, divide the numerator (5) by the denominator (8). Performing this division, 5 ÷ 8 equals 0.625.

Convert 0.65 to a fraction in lowest term

Answer: 13\/20

To convert the decimal 0.65 to a fraction in lowest terms, first write it as a fraction over 100: 65/100. Then, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5. This reduces the fraction to 13/20.

A book store contains 75,972 books, divided in three sections: Science, Business, and Math. The science section represents 1\/3 of the total books. Of the remaining books, 75% are business. How many books are in the math section?

Answer: 12,662

First, calculate the number of science books: (1/3) * 75,972 = 25,324 books. Subtract these from the total to find the remaining books: 75,972 - 25,324 = 50,648 books. Next, calculate the number of business books: 75% of 50,648 = 0.75 * 50,648 = 37,986 books. Finally, subtract the business books from the remaining books to find the math books: 50,648 - 37,986 = 12,662 books.

During final exams 172 students visited the math lab in total. If 4 out of 11 were male what is the percentage of female students who visited the math lab? (Round to the nearest tenth). a. 63.6%\t

Answer: 63.6%

If 4 out of 11 students were male, then the remaining students are female. This means 11 - 4 = 7 out of 11 students were female. To find the percentage of female students, divide the number of female students by the total number of students in the ratio (7/11) and multiply by 100%. This calculation yields approximately 63.636%, which rounds to 63.6% to the nearest tenth.

0.2 divided by 1.1?

Answer: 0.1818

To divide 0.2 by 1.1, perform the division operation. 0.2 ÷ 1.1 results in a repeating decimal, approximately 0.181818... When rounded to four decimal places, the result is 0.1818.

What is 5 percent of 50?

Answer: 2.5

To find a percentage of a number, first convert the percentage to a decimal by dividing by 100. So, 5% becomes 0.05. Then, multiply this decimal by the given number: 0.05 × 50. This calculation yields 2.5, which is 5 percent of 50.

Solve for x: 44:68::x: 236 (Round to the nearest tenth).

Answer: x=152.7

The problem presents a proportion: 44:68::x:236, which can be written as 44/68 = x/236. To solve for x, cross-multiply, giving 44 * 236 = 68 * x. This simplifies to 10384 = 68x. Dividing 10384 by 68 gives x ≈ 152.70588. Rounding to the nearest tenth, x is 152.7.