Ratio Notation and Simplification: แบบฝึกหัด

Simplify the ratio \( 45 : 75 \) to its simplest form.

Simplify the ratio \( 1.5 : 2.25 \) to its simplest form using integers.

If \( A : B = 2 : 3 \) and \( B : C = 4 : 5 \), find the ratio \( A : B : C \).

A student spends 2 hours studying and 1.5 hours playing sports. Find the ratio of the time spent studying to the time spent playing sports in the simplest form.

A wooden board is 2.4 meters long. A carpenter cuts it into three pieces in the ratio \(3:4:5\).
(a) Find the length of the shortest piece in centimeters.
(b) Find the length of the longest piece in centimeters.

A factory produces 480 toys in 8 hours.
(a) Find the ratio of the number of toys produced to the time taken in simplest form.
(b) At this rate, how many toys can be produced in 15 hours?
(c) How many hours are needed to produce 900 toys?