Compare the ratio 3:5 and 4:3.

Answer

To compare the ratios 3:5 and 4:3, we can follow these steps:

### Step 1: Convert the Ratios to Decimal Form
First, we will convert each ratio into decimal form.

- For the ratio 3:5:
\[ \frac{3}{5} = 0.6 \]

- For the ratio 4:3:
\[ \frac{4}{3} \approx 1.33 \quad (\text{This is a repeating decimal: } 1.3333...) \]

### Step 2: Compare the Decimal Values
Now we will compare the decimal values obtained:

- \(0.6\) (from \(3:5\))
- \(1.33\) (from \(4:3\))

Since \(1.33\) is greater than \(0.6\), we can conclude that:
\[ 4:3 > 3:5 \]

### Step 3: Convert the Ratios to Fraction Form
Next, we will convert the ratios into fractions and find a common denominator to compare them.

- The fractions are \(\frac{3}{5}\) and \(\frac{4}{3}\).
- The least common multiple (LCM) of the denominators \(5\) and \(3\) is \(15\).

### Step 4: Adjust the Fractions to Have the Same Denominator
Now we will convert both fractions to have a denominator of \(15\):

- For \(\frac{3}{5}\):
\[ \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

- For \(\frac{4}{3}\):
\[ \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \]

### Step 5: Compare the Numerators
Now we can compare the numerators of the two fractions:

- \(9\) (from \(\frac{3}{5}\))
- \(20\) (from \(\frac{4}{3}\))

Since \(20\) is greater than \(9\), we can conclude that:
\[ 4:3 > 3:5 \]

### Final Conclusion
Thus, we have confirmed that:
\[ 4:3 \text{ is greater than } 3:5 \]

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