Rapid Fire Mental Calculation Quiz

To find the missing number in the equation 583 = 500 + ? + 3, we start by subtracting 500 and 3 from 583. The calculation is: 583 - 500 - 3 = 80. Therefore, the missing number is 80. This solution involves simple arithmetic subtraction. By isolating the unknown value on one side, we can easily solve for the missing number.

Given that 7 × 6 = 42, the inverse of multiplication is division. Therefore, the corresponding fact is that 42 ÷ 7 = 6. This is a simple application of the division operation, where the result of multiplying 7 by 6 is reversed by dividing 42 by 7. The result of the division is 6. Thus, the other fact is 42 ÷ 7 = 6.

In the number 5628, the underlined digit represents the hundreds place. The digit in the hundreds place is 6, and its place value is 600 because it represents six hundred. To clarify, the place value of each digit in a number is determined by its position, starting from the right (ones, tens, hundreds, etc.). In this case, the 6 in the hundreds place has a value of 600. Therefore, the value of the underlined digit in 5628 is 600.

The number 4001 is an odd number. To find the next lower odd number, we subtract 2 from 4001, which gives us 3999. This is the closest odd number smaller than 4001. Odd numbers always alternate between even numbers, so the number directly before 4001 is the odd number 3999. Therefore, the odd number just before 4001 is 3999.

To find the number that is 300 more than 5762, we simply add 300 to 5762. The calculation is: 5762 + 300 = 6062. Therefore, the number that is 300 more than 5762 is 6062. This solution is based on straightforward addition. By adding the given increment (300) to the original number, we find the result.

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using the Pythagorean theorem, we can find the length of the hypotenuse. In this case, the adjacent side is 5cm and the opposite side is 12cm. So, the length of the hypotenuse can be calculated as √(5^2 + 12^2) = √(25 + 144) = √169 = 13cm.

To solve 765 ÷ 6, we perform the division: 765 divided by 6 equals 127.5. This result comes from the exact division of 765 by 6, where 765 ÷ 6 = 127.5. The quotient is not a whole number because the division does not result in an integer. Therefore, the correct result of 765 ÷ 6 is 127.5.

To calculate 35% of 560, we first determine 10% of 560, which is 56. Then, we calculate 5% of 560 by dividing 56 by 2, which gives us 28. Adding these together, we have 56 + 28 = 84. For the remaining 20%, we multiply 56 by 2 to get 112. Adding all the percentages together, we get 56 + 28 + 112 = 196. Therefore, 35% of 560 equals 196.

This is an arithmetic progression where the first term is 4, the common difference is 2, and the number of terms is 47. The sum of an arithmetic progression is calculated using the formula S = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get S = 47/2 * (4 + 96) = 47/2 * 100 = 47 * 50 = 2350. Therefore, the sum is 5050.

To solve this, we need to square both 18 and 24, and then add the results. First, calculate 18² = 324 and 24² = 576. Now, add them together: 324 + 576 = 468. Therefore, the value of 18² + 24² is 468. This solution involves basic operations of squaring the numbers and then summing the results. It is essential to ensure the correct order of operations to reach the final result.