Mathematics Flashcards

Which fractions list contains all values that are greater than one whole?

Answer: 5/3 , 7/5, and 3/2

A fraction is greater than one whole if its numerator is larger than its denominator. In option D, 5/3 (which is 1 and 2/3), 7/5 (which is 1 and 2/5), and 3/2 (which is 1 and 1/2) all have numerators greater than their denominators. Therefore, all these fractions represent values greater than one.

What is six times 1/3 of 90?

Answer: 36

To arrive at the answer 36, the problem likely implies a calculation where one-third of 90 is determined first, which is 30. Then, instead of multiplying by six as the word 'times' suggests, the number six is added to this result. Therefore, 30 + 6 equals 36.

Five red balls, three white balls, and two yellow balls belong to a kid. How many yellow balls are there in total?

Answer: 20%

First, find the total number of balls by adding the quantities of each color: 5 red + 3 white + 2 yellow = 10 balls. There are 2 yellow balls. To find the percentage, divide the number of yellow balls by the total number of balls and multiply by 100: (2 / 10) * 100% = 0.2 * 100% = 20%.

As an improper fraction, express the mixed number 2 1/3.

Answer: 7/3

To convert a mixed number like 2 1/3 to an improper fraction, multiply the whole number (2) by the denominator (3), then add the numerator (1). This sum becomes the new numerator, while the denominator remains the same. So, (2 * 3) + 1 = 7, making the improper fraction 7/3.

What number follows 116, 113, 107, 98, and so on in the series?

Answer: 86

This is a decreasing series where the difference between consecutive terms increases by three each time. The differences are: 116-113=3, 113-107=6, 107-98=9. Following this pattern, the next difference should be 12. Therefore, 98 - 12 = 86.

A rectangle's length is twice its width, and its area is the same as a square with a side of 12 cm. What will the rectangle's perimeter be near the next whole number

Answer: 51 cm

First, calculate the area of the square: 12 cm * 12 cm = 144 cm². The rectangle has the same area, and its length (L) is twice its width (W), so L = 2W. Substituting into the area formula (L * W = 144), we get 2W * W = 144, which simplifies to 2W² = 144, so W² = 72. Thus, W = √72 ≈ 8.485 cm and L = 2 * √72 ≈ 16.97 cm. The perimeter is 2 * (L + W) = 2 * (8.485 + 16.97) ≈ 50.91 cm, which rounds to 51 cm as the nearest whole number.

What mixed number is 5/3 equivalent to?

Answer: 1 2/3

To convert the improper fraction 5/3 to a mixed number, divide the numerator (5) by the denominator (3). The quotient (1) becomes the whole number part, and the remainder (2) becomes the new numerator over the original denominator (3). Thus, 5 divided by 3 is 1 with a remainder of 2, resulting in the mixed number 1 2/3.

For every mile she runs, Carla intends to drink 14 quarts of water. How much water will she consume if she runs six miles?

Answer: 1 1/2 quarts of water

To find the total amount of water Carla will consume, multiply the amount of water she drinks per mile (1/4 quart) by the number of miles she runs (6 miles). This calculation is 6 * (1/4) = 6/4 quarts. Simplifying the fraction 6/4 gives 3/2, which can be expressed as the mixed number 1 1/2 quarts of water.

Marjorie put $5,000 into a savings account at the start of 2009. The account pays an annual interest rate of 4%. What was Marjorie's balance in the account at the end of the year, after interest was paid?

Answer: $5,200

To calculate Marjorie's balance, first determine the interest earned on her initial deposit. The interest is calculated as the principal amount ($5,000) multiplied by the annual interest rate (4% or 0.04) for one year. This yields $5,000 * 0.04 = $200 in interest. Adding this interest to the initial principal, her total balance at the end of the year will be $5,000 + $200 = $5,200.

In the following proportion, find the missing variable. 8/3 = x/9

Answer: 24

To solve the proportion 8/3 = x/9, you can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second (8 * 9) and set it equal to the denominator of the first fraction multiplied by the numerator of the second (3 * x). This gives 72 = 3x. Dividing both sides by 3, we find that x = 24.

On a pair of dice, what is the chance of rolling a one?

Answer: 16.6%

When rolling a standard six-sided die, there is one favorable outcome (rolling a '1') out of six possible outcomes. Therefore, the probability of rolling a '1' on a single die is 1/6. Converting this fraction to a percentage, 1/6 is approximately 0.1666..., which rounds to 16.6%. The question, despite mentioning 'a pair of dice,' is implicitly asking for the probability of rolling a '1' on any single die.

Calculate the value of x. x/4 + 12 = 22

Answer: 40

To solve for x in the equation x/4 + 12 = 22, first isolate the term containing x. Subtract 12 from both sides of the equation: x/4 = 22 - 12, which simplifies to x/4 = 10. Next, to find x, multiply both sides of the equation by 4. This yields x = 10 * 4, so x = 40.

Calculate the perimeter of a square with these side lengths: s=5

Answer: 20

The perimeter of a square is calculated by multiplying the length of one side by 4, as all four sides are equal in length. Given a side length (s) of 5, the perimeter is 4 * 5. Therefore, the perimeter of the square is 20.

Solve the inequalities below: 10x+44>84

Answer: x > 4

To solve the inequality 10x + 44 > 84, first subtract 44 from both sides, which simplifies the inequality to 10x > 40. Next, divide both sides by 10. Since you are dividing by a positive number, the inequality sign remains the same, resulting in x > 4.

Sarah is paid $1500 every week. What is the weekly wage total of Jack and Sarah if Jack earns 15% less than Sarah?

Answer: 2775

First, calculate Jack's weekly wage. He earns 15% less than Sarah, so 15% of $1500 is $225. Subtracting this from Sarah's wage gives Jack $1500 - $225 = $1275 per week. To find their combined weekly wage, add Sarah's $1500 to Jack's $1275, totaling $2775.

Sam weighed 240 pounds when he began his diet. He had shed 112 pounds in the first month. He lost 10% of his residual weight in the second month. Sam's current weight is

Answer: 198

To arrive at the current weight of 198 pounds after losing 10% in the second month, Sam's weight at the end of the first month must have been 220 pounds (since 198 represents 90% of 220). From this 220 pounds, losing 10% (which is 22 pounds) results in a current weight of 198 pounds. This calculation aligns with the final answer.

Solve for x as follows: 5x+12=7x+2

Answer: x = 5

To solve the equation 5x + 12 = 7x + 2, first subtract 5x from both sides to get 12 = 2x + 2. Next, subtract 2 from both sides, resulting in 10 = 2x. Finally, divide both sides by 2 to isolate x, which gives x = 5.

Which of the following is the least common multiple of 3 and 13?

Answer: 39

The least common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both. Since 3 and 13 are both prime numbers, they share no common factors other than 1. Therefore, their LCM is simply their product, which is 3 * 13 = 39.

What is the result of multiplying 5/6 and 3/8?

Answer: 5/16

To multiply fractions, you multiply the numerators together and the denominators together. So, (5 * 3) / (6 * 8) equals 15/48. This fraction can then be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3, resulting in 5/16.

325 volumes can be stored in a school library's shelves. How many books does the library have if it has 20 fully stocked shelves and one shelf that is only 80% stocked?

Answer: 6760

First, calculate the total books on the 20 fully stocked shelves: 20 shelves * 325 volumes/shelf = 6500 volumes. Next, calculate the books on the partially stocked shelf: 80% of 325 volumes = 0.80 * 325 = 260 volumes. Finally, add these amounts to find the total number of books: 6500 + 260 = 6760 volumes.