Let's solve the math worksheet problems step by step.
1. Prime number between 30 and 40:
To find a prime number between 30 and 40, we look for numbers that have no divisors other than 1 and themselves. Looking through the numbers, 31 and 37 are both primes because no other numbers divide them evenly within that range. We can choose either one of them; let's choose 31 for this answer.
2. (a) Six and a half million in figures:
Six and a half million is written in figures as 6,500,000.
2. (b) 653 correct to the nearest ten:
To round 653 to the nearest ten, we look at the ones digit (3). Since it is less than 5, we round down and the nearest ten would be 650.
2. (c) Work out 6x5+12÷3:
To solve the arithmetic expression, we must follow the order of operations, which is BODMAS/BIDMAS: Brackets first, Orders (i.e., powers and square roots, etc.), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).
Here, we do not have any brackets or orders, so we go directly to division and multiplication.
First, we perform the division:
12 ÷ 3 = 4
Then, the multiplication:
6 * 5 = 30
Now, we add the results:
30 + 4 = 34
2. (d) From this list of numbers, write down:
(i) A factor of 48:
A factor is a number that divides into another number without leaving a remainder. We shall look through the list of numbers provided and find one that can divide 48 evenly.
One such number in the list that is a factor of 48 is 16, because 48 divided by 16 is 3 with no remainder.
(ii) A cube number:
A cube number is a number that can be expressed as the product of an integer multiplied by itself three times (i.e., \(n^3\)). In the provided list, the number 64 is a cube number because it is equal to \(4^3\) (4*4*4).
To neatly write down the final answers from the worksheet,
1. A prime number between 30 and 40 is 31.
2. (a) Six and a half million in figures is 6,500,000.
(b) 653 correct to the nearest ten is 650.
(c) The result of \(6 \times 5 + \frac{12}{3}\) is 34.
(d) From the list of numbers:
(i) A factor of 48 is 16.
(ii) A cube number is 64.
