Mathematics: Numbers and Operations Flashcards

A bakery sells cookies in packages of 8. A school is planning a party for 126 students. If each student is to receive one cookie, what is the minimum number of packages the school needs to buy?

Answer: 16

To solve this, you need to divide the total number of students (126) by the number of cookies in each package (8). 126 ÷ 8 = 15.75. Since the school cannot buy a fraction of a package, they must round up to the next whole number to ensure every student gets a cookie. Therefore, they need to purchase 16 packages.

Which of the following fractions is equivalent to 0.65?

Answer: 13/20

The decimal 0.65 can be written as the fraction 65/100. To find an equivalent fraction, you simplify 65/100 by dividing both the numerator and the denominator by their greatest common factor, which is 5. 65 ÷ 5 = 13, and 100 ÷ 5 = 20. So, the equivalent fraction is 13/20.

A submarine is located at a depth of -250 feet. It then ascends 85 feet. What is the submarine's new position relative to sea level?

Answer: -165 feet

The initial position is -250 feet. Ascending means moving up, which is represented by adding a positive number. The calculation is -250 + 85. When adding a positive number to a negative number, you find the difference between their absolute values (250 - 85 = 165) and keep the sign of the number with the larger absolute value, which is negative. Therefore, the new position is -165 feet.

What is the result of 42.5 x 10^3?

Answer: 42,500

Multiplying a decimal by a power of 10, such as 10^3 (which is 1,000), involves moving the decimal point to the right. The exponent '3' indicates that the decimal point should be moved 3 places to the right. For 42.5, moving the decimal three places gives 42,500.

A recipe for a batch of muffins requires 3/4 cup of sugar. If you want to make only 1/2 of a batch, how much sugar will you need?

Answer: 3/8 cup

To find the amount of sugar for half a batch, you need to multiply the original amount of sugar by 1/2. The calculation is (3/4) * (1/2). To multiply fractions, you multiply the numerators together (3 * 1 = 3) and the denominators together (4 * 2 = 8). The result is 3/8 cup of sugar.

Which statement correctly compares the two numbers: -4.7 and -4.17?

Answer: -4.7 < -4.17

When comparing negative numbers, the number with the smaller absolute value is greater. On a number line, -4.17 is to the right of -4.7. Therefore, -4.7 is less than -4.17. Another way to think about it is that -4.70 is further from zero in the negative direction than -4.17.