Test: Special Numbers - Year 4 MCQ

The numbers 5, 10, 15, and 20 are multiples of 5, as they can be obtained by multiplying 5 by the integers 1, 2, 3, and 4, respectively. Understanding multiples is essential for various mathematical concepts, including fractions and ratios.

The even number in the options is 10. Even numbers are defined as those that can be divided by 2 without a remainder. Thus, 10 divided by 2 equals 5, which confirms it is even. In contrast, the other options (3, 7, and 15) are all odd numbers.

The odd number in the options is 21, as it cannot be divided by 2 without a remainder. Odd numbers are significant in various mathematical contexts, including patterns and sequences, often appearing in nature and art, such as in the arrangement of flower petals or in music.

If a number ends in 0, it is divisible by 2, 5, and 10. This is because numbers ending in 0 are even (making them divisible by 2), they end in 5 or 0 (making them divisible by 5), and they end in 0 (making them divisible by 10). Recognizing these rules can simplify many arithmetic operations in real-world applications.

The correct statement is that 50 is not divisible by 100. However, 100 is divisible by 50, as 100 divided by 50 equals 2 with no remainder. This relationship highlights how divisibility works, particularly with larger numbers being multiples of smaller numbers.

The smallest number in the set is -10. When comparing negative numbers, the one with the larger absolute value is actually the smaller number. Therefore, -10 is less than -5, 0, and 5. It's important to remember that on a number line, negative numbers are always to the left of zero, indicating they are smaller.

The number 100 is divisible by 25, as it ends in 00, which is one of the criteria for divisibility by 25. When you divide 100 by 25, the result is 4 with no remainder. Recognizing divisibility rules helps in quickly determining factors of numbers, which can simplify many mathematical calculations.

The correct comparison is -8 < -3. On a number line, -8 is to the left of -3, indicating it is the smaller number. This relationship is crucial for understanding how negative numbers work, as many learners find this concept challenging due to the counterintuitive nature of negative number comparisons.

The first three square numbers are 1, 4, and 9, which correspond to the squares of the integers 1, 2, and 3, respectively (1² = 1, 2² = 4, 3² = 9). Square numbers are important in various areas of mathematics, including geometry and algebra, as they represent areas of squares with integer side lengths.

The greatest common factor (GCF) of 30 and 40 is 10. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, while the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors are 1, 2, 5, and 10, with 10 being the largest. Understanding GCF is essential in simplifying fractions and solving problems involving ratios.

On a number line, numbers increase in value as you move from left to right. Since -3 appears to the right of -5, it signifies a greater value. This understanding is crucial when working with negative numbers, where a number closer to zero is larger than one further away. For example, -1 is greater than -5, while -10 is less than -3.

The common factors of two numbers are those integers that divide both numbers without leaving a remainder. For 30, the factors are 1, 2, 3, 5, 6, 10, 15, and 30. For 40, the factors are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors, therefore, are 1, 2, 5, and 10, which can be used in various mathematical applications, including simplifying fractions.

A number is divisible by 5 if it ends in either 0 or 5. In this case, 55 ends in 5, making it divisible by 5. The other options, 34, 72, and 91, do not meet this criterion, as they do not end in 0 or 5. This rule is particularly useful in quick calculations and checks for divisibility.

To find square numbers that sum to 100, we can calculate the squares of the numbers. 6² equals 36, and 8² equals 64. When added together, 36 + 64 equals 100. The other options do not yield the required sum, demonstrating the interesting property of square numbers and how they can combine to form other numbers through addition.

To order numbers from smallest to largest, we use a number line where numbers increase from left to right.

• For option A, -7 is to the left of -2, so the pair -7, -2 is correctly ordered from smallest to largest.
• For option B, 0 is greater than -5, so 0, -5 is incorrect.
• For option C, -3 is greater than -8, so -3, -8 is incorrect.
• For option D, 4 is greater than 1, so 4, 1 is incorrect.

Thus, option A is the correct pair.