How to Solve 4 Divided by 1 1/3: Visual Proof and Step-by-Step Breakdown

Learn the most effective ways for how to Solve 4 Divided by 1 1/3: Visual Proof and Step-by-Step Breakdown in our detailed walkthrough.

Standard elementary arithmetic resolves fractional division through a clear procedural pipeline: convert, invert, multiply, and reduce.

Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number combines an integer and a proper fraction. Standard multiplication and division rules cannot process these components simultaneously. To convert 1 1/3 into an improper fraction:

Multiply the whole number (1) by the denominator (3), then add the numerator (1):

(1 × 3) + 1 = 4

Place that sum over the original denominator:

1 1/3 = 4/3

Now the original equation reads: 4 ÷ 4/3.

Step 2: Express the Whole Number as a Fraction

Every whole number has an implied denominator of 1. Rewriting 4 as a fraction creates clean symmetry between dividend and divisor:

4 = 4/1

The calculation now sits as: 4/1 ÷ 4/3.

Step 3: Apply the Reciprocal Rule (Keep, Change, Flip)

Division by a fraction is functionally equivalent to multiplication by its reciprocal. The reciprocal is found by swapping the numerator and denominator:

• Keep the first fraction unchanged: 4/1
• Change the division operator (÷) to multiplication (×)
• Flip the divisor (4/3) into its reciprocal: 3/4

This gives: 4/1 × 3/4.

Step 4: Multiply and Simplify

Multiply straight across the numerators and denominators:

Numerator: 4 × 3 = 12

Denominator: 1 × 4 = 4

The resulting fraction is 12/4. Running this through a basic fraction simplifier yields:

12 ÷ 4 = 3

Alternatively, applying cross cancellation in Step 3 removes the shared factor of 4 immediately. Dividing the numerator of the first fraction and the denominator of the second fraction by 4 simplifies the expression to (1/1) × (3/1), reaching 3 instantly without expanding to 12/4.