Find the ratio of :
35 min to `1 (1)/(2)` h

Answer

To find the ratio of 35 minutes to \(1 \frac{1}{2}\) hours, we can follow these steps:

### Step 1: Convert 35 minutes to hours
We know that 1 hour = 60 minutes. Therefore, to convert 35 minutes into hours, we can use the formula:

\[ \text{Hours} = \frac{\text{Minutes}}{60} \]

So,

\[ 35 \text{ minutes} = \frac{35}{60} \text{ hours} \]

### Step 2: Simplify \(\frac{35}{60}\)
Now, we simplify \(\frac{35}{60}\):

\[ \frac{35}{60} = \frac{7}{12} \text{ hours} \]

### Step 3: Convert \(1 \frac{1}{2}\) hours to an improper fraction
Next, we convert \(1 \frac{1}{2}\) hours to an improper fraction.

\[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \text{ hours} \]

### Step 4: Write the ratio
Now we can write the ratio of 35 minutes to \(1 \frac{1}{2}\) hours:

\[ \text{Ratio} = \frac{35 \text{ minutes}}{1 \frac{1}{2} \text{ hours}} = \frac{\frac{7}{12}}{\frac{3}{2}} \]

### Step 5: Simplify the ratio
To simplify this ratio, we multiply by the reciprocal of the denominator:

\[ \frac{7}{12} \div \frac{3}{2} = \frac{7}{12} \times \frac{2}{3} = \frac{7 \times 2}{12 \times 3} = \frac{14}{36} \]

### Step 6: Further simplify \(\frac{14}{36}\)
Now, we simplify \(\frac{14}{36}\):

\[ \frac{14}{36} = \frac{7}{18} \]

### Final Ratio
Thus, the ratio of 35 minutes to \(1 \frac{1}{2}\) hours is:

\[ \text{Ratio} = 7 : 18 \]

---