College

1. What is the value of the smallest share if 360 sweets are divided in the ratio of [tex]$5:3:4$[/tex]?

2. Simplify [tex]$12:36:60$[/tex] to its lowest terms.

Answer :

We start by considering the division of 360 sweets in the ratio
$$5:3:4.$$

**Step 1: Determining the Smallest Share**

1. First, compute the total number of parts:
$$5 + 3 + 4 = 12.$$

2. Each part thus represents:
$$\frac{360}{12} = 30 \text{ sweets}.$$

3. The smallest share corresponds to the smallest number in the ratio, which is $3$. Therefore, the smallest share is:
$$3 \times 30 = 90 \text{ sweets}.$$

**Step 2: Simplifying the Ratio $12:36:60$ to its Lowest Terms**

1. Find the greatest common divisor (GCD) of $12$, $36$, and $60$. The GCD is $12$.

2. Divide each term of the ratio by $12$:
\[
\begin{aligned}
12 \div 12 &= 1, \\
36 \div 12 &= 3, \\
60 \div 12 &= 5.
\end{aligned}
\]

3. Thus, the simplified ratio is:
$$1:3:5.$$

**Final Answer:**
- The smallest share is $\boxed{90}$ sweets.
- The ratio $12:36:60$ in its lowest terms is $\boxed{1:3:5}$.