Class 4 Math Marvels: A Quiz Adventure!

Explanation
The Roman numeral for 18 is XVIII. Roman numerals are represented by combinations of letters from the Latin alphabet, primarily I, V, X, L, C, D, and M. To form the numeral for 18, 'X' (which stands for 10) is followed by 'VIII' (which stands for 8). When these values are added together—10 + 8—you get 18. This numeral system does not use repetitive or consecutive characters that would sum negatively when placed before larger values, except in specific cases (such as IV for 4 or IX for 9), thus XVIII is the correct notation for 18.

Explanation
To find the smallest 4-digit number using the digits 0, 3, 5, and 6, we need to consider the place values:

 

Thousand's place: Since it's a 4-digit number, we cannot start with 0, so the smallest possible digit for the thousand's place is 3.

Remaining digits: After placing 3 in the thousand's place, the remaining digits are 0, 5, and 6.

Ordering for smallest number: Arrange the remaining digits in ascending order after 3, which would be 0, 5, and 6.

Final number: Combining these, the smallest number is 3056.

 

Thus, the smallest 4-digit number you can form with the digits 0, 3, 5, and 6 is: 3056

Explanation
The smallest 5-digit number is 10000. The predecessor of a number is the number that comes immediately before it. Therefore, the predecessor of 10000 is 9999. This number, 9999, is the largest 4-digit number and directly precedes the smallest 5-digit number, completing the transition from four digits to five.

Explanation
A composite number is defined as a positive integer that has at least one positive divisor other than one or itself. The smallest single-digit composite number is 4. This is because 4 can be divided evenly by 1, 2, and 4, making it the first single-digit number that fits the definition of a composite number. Numbers like 2 and 1 are not composite; 2 is a prime number and 1 is neither prime nor composite as it only has one divisor, which is itself.

Explanation
The sum of the interior angles of any triangle is always 180 degrees. This is a fundamental principle in geometry, applicable to all triangles, regardless of their type (scalene, isosceles, or equilateral). Understanding this property is crucial for solving various geometric problems, and constructing accurate figures, and is foundational in proving more complex theorems in the field of geometry.

Explanation
Multiplying 8 by 12 gives the product of 96. This basic arithmetic operation, multiplication, is used to calculate the total when a particular item or value is grouped into equal parts, such as calculating the total number of objects in multiple groups or determining the total cost when multiple items are priced the same. Mastery of multiplication is essential for both everyday tasks and more complex mathematical calculations.

Explanation
To find how many one-sixths make up the number 2, you divide 2 by 1/6. This is equivalent to multiplying 2 by the reciprocal of 1/6, which is 6. So, 2 times 6 equals 12. This means there are twelve one-sixths in 2. Understanding how to convert whole numbers to fractions and vice versa is crucial in fractional arithmetic, helping clarify relationships between different quantities and making calculations more straightforward.

Explanation
Three hundredths, expressed as a decimal, is written as 0.03. In decimal notation, the term "hundredths" refers to the second place after the decimal point, where each place value represents a power of ten. The first place after the decimal is tenths (1/10), and the second is hundredths (1/100). Therefore, three-hundredths means three parts out of one hundred, which translates directly to 0.03 in decimal form. Understanding decimal place values is essential for accurate representation of fractions and decimals in mathematical calculations.

Explanation
The decimal 0.07 represents seven hundredths, which can be directly converted into a fraction as 7/100. This fraction reflects the decimal point's position, indicating that the number is seven parts out of a hundred. Understanding decimal-to-fraction conversions involves recognizing the place value of each digit in a decimal. Here, the 7 is in the hundredths place, meaning it is the second digit to the right of the decimal point, thus making the equivalent fraction 7/100. This skill is fundamental in math for accurately interpreting and using decimal values in various applications.

Explanation
To find the total number of minutes in 3 hours and 40 minutes, you first convert the hours into minutes and then add the remaining minutes. Since there are 60 minutes in an hour, 3 hours equals 180 minutes (3 hours x 60 minutes/hour). Adding the 40 minutes gives a total of 220 minutes. This calculation is straightforward and essential for converting time units, allowing for easier computation and understanding of time durations in different formats.