Ratio and Proportion：練習問題

A length of string measuring \(30\text{ cm}\) is cut into two pieces in the ratio \(2:3\). What is the length of the longer piece?

In the diagram below, \(ABCD\) is a square. \(M\) is the midpoint of the side \(CD\). What is the ratio of the area of the shaded triangle \(ABM\) to the area of the square \(ABCD\)?

The ratio of the number of blue marbles to red marbles in a box is \(2:3\). After \(12\) more blue marbles are added to the box, the ratio of the number of blue marbles to red marbles becomes \(1:1\). How many red marbles are in the box?

What is the ratio of \(45\text{ minutes}\) to \(1.5\text{ hours}\) in its simplest form?

The ratio of the number of stickers John has to the number of stickers Mary has is \(7:4\). After Mary buys \(12\) more stickers, the ratio of John's stickers to Mary's stickers becomes \(1:1\). How many stickers did John have?

In a school choir, the ratio of the number of boys to the number of girls is \(3 : 5\). There are 40 girls in the choir.
(a) How many boys are there in the choir?
(b) What is the total number of students in the choir?
(c) If 4 more boys and 2 more girls join the choir, what is the new ratio of the number of boys to the number of girls? Express your answer in the simplest form.