Fraction with a Whole Number Calculator

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Fraction with a Whole Number Calculator

Add (+) Subtract (-) Multiply (*) Divide (/)

Result:

function gcd(a, b) { return b === 0 ? a : gcd(b, a % b); } function simplifyFraction(num, den) { if (den === 0) return { num: num, den: den }; if (num === 0) return { num: 0, den: 1 }; var common = gcd(Math.abs(num), Math.abs(den)); var sign = (num 0) || (num > 0 && den = Math.abs(finalDen)) { var mixedWhole = Math.floor(Math.abs(finalNum) / finalDen); var mixedNumerator = Math.abs(finalNum) % finalDen; var sign = finalNum < 0 ? "-" : ""; if (mixedNumerator === 0) { mixedString = sign + mixedWhole.toString(); } else { mixedString = sign + mixedWhole + " " + mixedNumerator + "/" + finalDen; } } else if (finalDen !== 0 && finalNum === 0) { mixedString = "0"; } else if (finalDen !== 0) { mixedString = fractionString; // If it's a proper fraction, it's also the mixed number form } fractionResultElement.innerHTML = "Simplified Fraction: " + fractionString; mixedResultElement.innerHTML = "Mixed Number: " + mixedString; decimalResultElement.innerHTML = "Decimal: " + decimalValue.toFixed(4); }

Understanding Fractions and Whole Numbers

Working with fractions and whole numbers is a fundamental skill in mathematics. This calculator helps you perform basic arithmetic operations (addition, subtraction, multiplication, and division) between a whole number and a fraction, providing the result in simplified fraction, mixed number, and decimal forms.

What is a Whole Number?

A whole number is any non-negative number without fractional or decimal parts. Examples include 0, 1, 2, 3, 10, 100, and so on. They are part of the set of integers.

What is a Fraction?

A fraction represents a part of a whole. It consists of two main parts:

  • Numerator: The top number, which indicates how many parts of the whole are being considered.
  • Denominator: The bottom number, which indicates the total number of equal parts the whole is divided into.

For example, in the fraction 3⁄4, 3 is the numerator and 4 is the denominator, meaning three out of four equal parts.

How to Perform Operations with Whole Numbers and Fractions

1. Adding a Whole Number and a Fraction

To add a whole number to a fraction, you can think of the whole number as having a denominator of 1. Then, find a common denominator, convert the whole number to an equivalent fraction, and add the numerators.

Formula: Whole Number + Numerator⁄Denominator = (Whole Number × Denominator) + Numerator⁄Denominator

Example: 3 + 1⁄2

Convert 3 to a fraction with a denominator of 2: 3 = 3 × 2⁄2 = 6⁄2

Now add: 6⁄2 + 1⁄2 = 6 + 1⁄2 = 7⁄2

As a mixed number: 3 1⁄2. As a decimal: 3.5.

2. Subtracting a Fraction from a Whole Number

Similar to addition, convert the whole number into an equivalent fraction with the same denominator as the fraction being subtracted. Then, subtract the numerators.

Formula: Whole Number – Numerator⁄Denominator = (Whole Number × Denominator) – Numerator⁄Denominator

Example: 4 – 3⁄4

Convert 4 to a fraction with a denominator of 4: 4 = 4 × 4⁄4 = 16⁄4

Now subtract: 16⁄4 – 3⁄4 = 16 – 3⁄4 = 13⁄4

As a mixed number: 3 1⁄4. As a decimal: 3.25.

3. Multiplying a Whole Number by a Fraction

To multiply a whole number by a fraction, simply multiply the whole number by the numerator of the fraction. The denominator remains the same.

Formula: Whole Number × Numerator⁄Denominator = Whole Number × Numerator⁄Denominator

Example: 5 × 2⁄3

Multiply the whole number by the numerator: 5 × 2 = 10

The result is 10⁄3

As a mixed number: 3 1⁄3. As a decimal: approximately 3.3333.

4. Dividing a Whole Number by a Fraction

To divide a whole number by a fraction, you multiply the whole number by the reciprocal of the fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.

Formula: Whole Number ÷ Numerator⁄Denominator = Whole Number × Denominator⁄Numerator = Whole Number × Denominator⁄Numerator

Example: 6 ÷ 2⁄5

Find the reciprocal of 2⁄5, which is 5⁄2.

Now multiply: 6 × 5⁄2 = 6 × 5⁄2 = 30⁄2

Simplify the fraction: 30⁄2 = 15

As a mixed number: 15. As a decimal: 15.0.

This calculator simplifies these operations for you, ensuring accurate results in various formats.

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