Program to compare two fractions in C

In C programming, comparing two fractions requires cross-multiplication to avoid floating-point precision issues. Given two fractions with numerators and denominators, we need to determine which fraction has the greater value.

Syntax

struct Fraction {
    int nume, deno;
};

struct Fraction greater(struct Fraction first, struct Fraction second);

Approach

To compare fractions a/b and c/d, we use cross-multiplication: if a*d > b*c, then a/b > c/d. This avoids floating-point division and maintains precision.

Example 1: Basic Fraction Comparison

This example compares 4/5 and 3/4 using cross-multiplication −

#include <stdio.h>

struct Fraction {
    int nume, deno;
};

struct Fraction greater(struct Fraction first, struct Fraction sec) {
    // Cross multiply: first.nume * sec.deno vs first.deno * sec.nume
    int crossProduct = first.nume * sec.deno - first.deno * sec.nume;
    return (crossProduct > 0) ? first : sec;
}

int main() {
    struct Fraction first = {4, 5};
    struct Fraction sec = {3, 4};
    
    printf("Comparing fractions: %d/%d and %d/%d<br>", 
           first.nume, first.deno, sec.nume, sec.deno);
    
    struct Fraction result = greater(first, sec);
    printf("The greater fraction is: %d/%d<br>", result.nume, result.deno);
    
    return 0;
}

Comparing fractions: 4/5 and 3/4
The greater fraction is: 4/5

Example 2: Multiple Fraction Comparison

This example demonstrates comparing different pairs of fractions −

#include <stdio.h>

struct Fraction {
    int nume, deno;
};

struct Fraction compareFractions(struct Fraction f1, struct Fraction f2) {
    // Cross multiplication: f1.nume * f2.deno vs f1.deno * f2.nume
    if (f1.nume * f2.deno > f1.deno * f2.nume) {
        return f1;
    } else {
        return f2;
    }
}

void printComparison(struct Fraction f1, struct Fraction f2) {
    struct Fraction greater = compareFractions(f1, f2);
    printf("%d/%d vs %d/%d: Greater is %d/%d<br>", 
           f1.nume, f1.deno, f2.nume, f2.deno, 
           greater.nume, greater.deno);
}

int main() {
    struct Fraction pairs[][2] = {
        {{2, 3}, {4, 3}},
        {{1, 2}, {4, 3}},
        {{5, 6}, {7, 8}}
    };
    
    int numPairs = sizeof(pairs) / sizeof(pairs[0]);
    
    for (int i = 0; i < numPairs; i++) {
        printComparison(pairs[i][0], pairs[i][1]);
    }
    
    return 0;
}

2/3 vs 4/3: Greater is 4/3
1/2 vs 4/3: Greater is 4/3
5/6 vs 7/8: Greater is 7/8

How It Works

• Cross-multiplication: To compare a/b with c/d, we calculate a×d - b×c
• If positive: First fraction is greater
• If negative: Second fraction is greater
• If zero: Both fractions are equal

Key Points

• Cross-multiplication avoids floating-point precision errors
• The method works for both positive and negative fractions
• Time complexity is O(1) for each comparison
• No division operations are needed

Conclusion

Comparing fractions in C using cross-multiplication is efficient and precise. This approach eliminates floating-point errors and provides reliable results for fraction comparison operations.