1 2/3 Divided By 26 1/4 As A Fraction

3 min read Jun 17, 2024
1 2/3 Divided By 26 1/4 As A Fraction

Dividing Mixed Numbers: A Step-by-Step Guide

This article will guide you through the process of dividing the mixed number 1 2/3 by 26 1/4 and express the answer as a fraction.

Understanding Mixed Numbers

Before we dive into the division, let's quickly review what mixed numbers are. A mixed number combines a whole number and a fraction, like 1 2/3.

Converting to Improper Fractions

The first step is to convert both mixed numbers into improper fractions. Here's how:

  • 1 2/3: Multiply the whole number (1) by the denominator of the fraction (3) and add the numerator (2). This gives us 5. Keep the same denominator (3). So, 1 2/3 becomes 5/3.

  • 26 1/4: Multiply the whole number (26) by the denominator of the fraction (4) and add the numerator (1). This gives us 105. Keep the same denominator (4). So, 26 1/4 becomes 105/4.

Dividing Fractions

Now we have our improper fractions: 5/3 divided by 105/4. To divide fractions, we flip the second fraction (the divisor) and multiply:

(5/3) ÷ (105/4) = (5/3) x (4/105)

Simplifying the Multiplication

Now, we multiply the numerators and the denominators:

(5 x 4) / (3 x 105) = 20/315

Simplifying the Fraction

Finally, we need to simplify the fraction 20/315. The greatest common factor of 20 and 315 is 5. Dividing both numerator and denominator by 5, we get:

**(20/5) / (315/5) = 4/63

Therefore, 1 2/3 divided by 26 1/4 is equal to 4/63.

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