Integers：練習題

Work out the value of \( (-4) \times (-3) + (-10) \div 2 \).

Calculate the value of the following expression using the correct hierarchy of operations:
\( (15 - 3 \times 2)^2 \div 9 + 4 \)

The integer \( n \) can be written as a product of its prime factors as \( n = 2^3 \times 3^x \times 5^1 \).
Given that \( n \) has exactly 24 factors in total, find the value of the exponent \( x \).

Identify the place value of the digit 7 in the integer 472,305.

Work out the value of the expression:
\( 8 - 2 \times (-3) + (-10) \)

State whether the sum of two odd numbers is always even or always odd, and provide one numerical example to support your answer.

Express 60 as a product of its prime factors. Give your answer in index notation.

At 6:00 am, the temperature was \( -7^{\circ}C \).
By noon, the temperature had risen by \( 12^{\circ}C \).
By 8:00 pm, the temperature had fallen from the noon temperature by \( 9^{\circ}C \).
Work out the temperature at 8:00 pm.

Consider the list of integers given below:
\(15, 23, 27, 31, 39, 47, 51\)

From this list, write down:
(a) a multiple of 9.
(b) a factor of 45.
(c) a prime number that is greater than 40.

A warehouse stores boxes in stacks. Large boxes are 40 cm high and small boxes are 25 cm high.

(a) Express 40 and 25 as products of their prime factors.
(b) Find the Lowest Common Multiple (LCM) of 40 and 25.
(c) Find the lowest height at which a stack of large boxes and a stack of small boxes will be the same height.