MATHS題!!20點

1. Given 2 numbers x and 198. If the H.C.F. is 18 and L.C.F. is 1386, find x.

The product of two numbers = (H.C.F.) x (L.C.M.)
198x = 18 x 1386
x = 126


2.A rectangular sheet of paper 225 cm by 300 cm is cut into squares of equal size, each as large as possible.
a. What will be the length of the side of each square??
b. What will be the area of each square??

a.
225 = 3 x 3 x 5 x 5
300 = 2 x 2 x 3 x 5 x 5
H.C.F. of 225 and 300 = 3 x 5 x 5 = 75

The longest side is the H.C.F. of 225 cm and 300 cm.
Hece, the length of each side of each square = 75 cm

b.
Area of each square
= (75)2 cm2
= 5625 cm2


3.Three bells ring at intervals of 6,18 and 30 minutes respectively.
a.If they all ring at a certain moment,how many minutes wll pass before they do so again??
b.If they all ring at 1:00 p.m. , when will they ring together again in the afternoon??(From 1:00p.m. to 6:00p.m.)

a.
6 = 2 x 3
18 = 2 x 3 x 3
30 = 2 x 3 x 5
L.C.M. of 6, 18 and 30 = 2 x 3 x 3 x 5 = 90

The time required is the L.C.M. of 6 min, 18 min and 30 min.
The time required = 90 minutes

b:
90 min = 1 h and 30 min

1:00 + 1:30 = 2:30
2:30 + 1:30 = 4:00
4:00 + 1:30 = 5:30

They will ring together again in 2:30 p.m., 4:00 p.m. and 5:30 p.m.