Comparing Fractions Calculator

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:

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

Formula for Comparison:

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

$${\text{Decimal Value}}_1\text{compared to}{\text{Decimal Value}}_{\mathrm{2<span\; style="font-size:\; 15px;\; font-family:\; Verdana,\; BlinkMacSystemFont,\; -apple-system,\; \text{'}Segoe\; UI\text{'},\; Roboto,\; Oxygen,\; Ubuntu,\; Cantarell,\; \text{'}Open\; Sans\text{'},\; \text{'}Helvetica\; Neue\text{'},\; sans-serif;\; color:\; initial;"></span>}}$$

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 $\text{Value}_1 = \text{Value}_2$