Multiply Fractions in C++ | A Junior Secondary Math Guide

Understanding the Math Behind Fraction Multiplication | Maths Explanation for C++ Kids

Learning how to multiply fractions in C++ is a great way to combine math skills with coding. This tutorial is designed for junior secondary students who want to understand fraction multiplication using simple C++ classes and constructors.

Multiplying fractions is pretty straightforward:
Cancel out all common factors between numerators and denominators, then multiply whatever is left numerator to numerator and denominator to denominator.

In this lesson, we'll walk through the step-by-step method of multiplying fractions using C++. You'll learn how to define a class, use constructors, and apply logic to find mutual factors and simplify results.

Step-by-Step Explanation of Algorithm to Multiply Fractions in C++

This C++ algorithm for fractions shows how to multiply two fractions and reduce them to their lowest terms. It's a great math coding project for beginners.
Understanding how to multiply multiple fractions in C++ helps students build both computational thinking and math fluency. It's a foundational skill for more advanced topics like algebra and data science.

If we have
⁴/₉ x ²¹/₈;

Step 1:

Find any common factor between any numerator and any denominator.

Step 2:

Cancel out any such common factor.

=		X	7
	4		21
	9		8
	3

Step 3:

Repeat Steps 1 & 2 recursively until there are no more common factors.

=	1	X
	4		7
	3		8
			2

=	7
	6

Create a new C++ class file; call it MultiplyFraction. Type out the adjoining C++ code for multiplying fractions.

Note: You can comment out the LowestTerm C++ object code in the main class from the previous lesson or simply continue from where it stopped.

So! C++ Fun Practice Exercise - Multiply Fractions

As a fun practice exercise, feel free to try out your own fractions with different numerators and denominators, and see how the C++ code multiplies those fractions.

C++ Code for Multiplying Fractions - Header File

#pragma once

#include <vector>
using namespace std;

class MultiplyFraction {
public:
    MultiplyFraction(vector<unsigned>, vector<unsigned>);
    virtual ~MultiplyFraction();
    void doMultiply();

    unsigned int answer[2];
protected:
    vector<unsigned> numerators;
    vector<unsigned> denominators;
    unsigned int n_index, d_index;
    unsigned int trial_factor;
    bool mutual_factor;
};

C++ Code for Multiplying Fractions - Class File

#include "stdafx.h"
#include "MultiplyFraction.h"

MultiplyFraction::MultiplyFraction(vector<unsigned> num, vector<unsigned> denom) {
    numerators = num;
    denominators = denom;
    trial_factor = 0;
    n_index = 0;
    d_index = 0;
    answer[0] = 1;
    answer[1] = 1;

    for (unsigned n : num) {
        if (n > trial_factor) {
            trial_factor = n;
        }
    }
    for (unsigned d : denom) {
        if (d > trial_factor) {
            trial_factor = d;
        }
    }
}

void MultiplyFraction::doMultiply() {
    // STEP 3:
    // We are counting down to test for mutual factors
    while (trial_factor > 1) {
        // STEP 1:
        // iterate through numerators and check for factors
        while (n_index < numerators.size()) {
            mutual_factor = false;
            if ((numerators[n_index] % trial_factor) == 0) { // do we have a factor
                                                             // iterate through denominators and check for factors
                while (d_index < denominators.size()) {
                    if ((denominators[d_index] % trial_factor) == 0) { // is this factor mutual?
                        mutual_factor = true;
                        break; // stop as soon as we find a mutual factor so preserve the corresponding index
                    }
                    d_index++;
                }
                break; // stop as soon as we find a mutual factor so as  preserve the corresponding index
            }
            n_index++;
        }
        // STEP 2:
        // where we have a mutual factor
        if (mutual_factor) {
            numerators[n_index] /= trial_factor;
            denominators[d_index] /= trial_factor;
            continue; // continue with next iteration repeating the current value of trial_factor
        }
        n_index = 0;
        d_index = 0;
        trial_factor--;
    }

    for (int i = 0; i < numerators.size(); i++) {
        answer[0] *= numerators[i];
        answer[1] *= denominators[i];
    }
}

MultiplyFraction::~MultiplyFraction() {
}

C++ Code for Multiplying Fractions - Main Class

// Algebra.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include "MultiplyFraction.h"

#include <iostream>
#include <vector>
#include <exception>

using namespace std;

int main()
{
    cout << "\n    Welcome to our demonstration sequels";
    cout << "\n    Hope you enjoy (and follow) the lessons.\n\n";

    vector<unsigned> numerators;
    vector<unsigned> denominators;

    try {
        /*
        * Multiplying fractions
        */
        numerators = { 16, 20, 27, 20 };
        denominators = { 9, 9, 640, 7 };

        cout << "\n    Solving:\n";
        // Print as fraction
        for (unsigned n : numerators) {
            printf("%13u", n);
        }
        printf("\n%12s", " ");
        for (unsigned i = 0; i < numerators.size() - 1; i++) {
            cout << "-     X      ";
        }
        printf("%1s", "-");
        cout << "\n";
        for (unsigned d : denominators) {
            printf("%13u", d);
        }
        cout << "\n";

        // use the MultiplyFraction class
        MultiplyFraction mul_fract(numerators, denominators);
        mul_fract.doMultiply();

        printf("\n%26u\n", mul_fract.answer[0]);
        printf("%26s\n", "Answer =      -");
        printf("%26u\n", mul_fract.answer[1]);

        cout << "\n\n";

    } catch (exception& e) {
        cout << "\n" << e.what() << "\n";
    }

    return 0;
}

I have a better version / See other versions.