A basic concrete mix is prepared by mixing cement, sand and gravel. The masses of cement and sand used are in the ratio $2 : 5$ , and the mass of sand to gravel is in the ratio $1 : 2$ . Find the ratio of the mass of cement to the mass of gravel in the form $a : b$ in its simplest terms. Express this ratio as a fraction $\frac{a}{b}$ .

Worked solution

1. 统一中间量沙子的比，求出水泥、沙子与碎石的连比

已知水泥与沙子的质量比为 $2 : 5$ ，沙子与碎石的质量比为 $1 : 2$ 。
将沙子与碎石的比扩大 $5$ 倍，得：
$\text{沙子} : \text{碎石} = 5 : 10$
因此，水泥 : 沙子 : 碎石 $= 2 : 5 : 10$ 。

2. 求水泥与碎石的最简质量比

水泥与碎石的质量比为 $2 : 10$ 。
化简为最简比得：
$2 : 10 = 1 : 5$

3. 将最简比表示为分数形式

将比 $1 : 5$ 改写成分数形式得：
$\frac{1}{5}$

Answer

最简比为 $1 : 5$ ，分数形式为 $\frac{1}{5}$

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