# Comparing Fractions Calculator

## Compare Fractions

Try integers, decimals, fractions, mixed numbers, or percents.

Compare: and

### Step-by-Step Explanation:

1. Input Types Supported:

• Integers: Example: 2, 10
• Decimals: Example: 1.75, 2.5
• Fractions: Example: 3/4, 7/8
• Mixed Numbers: Example: 1 1/2, 2 3/4
• Percentages: Input should be converted to decimals manually, e.g., 75% as 0.75.
2. Conversion to Decimal Format:

• For fractions, such as 3/4, the calculator divides the numerator (3) by the denominator (4): $\frac{3}{4}=0.75$
• For mixed numbers, like 1 1/2, it converts the whole number and fraction separately: $1+\frac{1}{2}=1+0.5=1.5$
• For decimals, the input is used as-is, e.g., 1.875 is already in decimal form.
3. Comparison of Values: Once both numbers are converted into decimal format, the comparison is made using standard mathematical symbols:

• Greater than (>): When the first value is larger than the second value.
• Less than (<): When the first value is smaller than the second value.
• Equal to (=): When both values are equal.

### Example 1:

#### Input:

• First value: 1 3/4
• Second value: 1.875

#### Steps:

1. Convert 1 3/4 to decimal: $1+\frac{3}{4}=1+0.75=1.75$
2. Use the second value 1.875 as-is (decimal format).

#### Comparison:

Since 1.75 < 1.875, the result is:

$13\mathrm{/}4<1.875$

### Example 2:

#### Input:

• First value: 2/5
• Second value: 0.4

#### Steps:

1. Convert 2/5 to decimal: $\frac{2}{5}=0.4$
2. The second value 0.4 is already in decimal format.

#### Comparison:

Since 0.4 = 0.4, the result is:

$\frac{2}{5}=0.4$

### Example 3:

#### Input:

• First value: 3 1/2
• Second value: 3.75

#### Steps:

1. Convert 3 1/2 to decimal: $3+\frac{1}{2}=3+0.5=3.5$
2. Use 3.75 as-is (decimal format).

#### Comparison:

Since 3.5 < 3.75, the result is:

$3\frac{1}{2}<3.75$

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### Formula for Comparison:

Let the two fractions or mixed numbers be $\text{Value}_1$ and $\text{Value}_2$, respectively. The comparison is based on:

Where:

• If $\text{Decimal Value}_1 > \text{Decimal Value}_2$, then $\text{Value}_1 > \text{Value}_2$
• If $\text{Decimal Value}_1 < \text{Decimal Value}_2$, then $\text{Value}_1 < \text{Value}_2$
• If $\text{Decimal Value}_1 = \text{Decimal Value}_2$, then $\text{Value}_1 = \text{Value}_2$
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