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:
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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.
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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.