Dividing Mixed Numbers: A Step-by-Step Guide
This article will guide you through the process of dividing mixed numbers, using the example of 1 1/4 divided by 1 2/5.
Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. In our example, 1 1/4 represents one whole unit plus one-fourth of another unit.
Converting to Improper Fractions
Before dividing, we must convert our mixed numbers into improper fractions.
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1 1/4: Multiply the whole number (1) by the denominator (4) and add the numerator (1): (1 * 4) + 1 = 5. Keep the same denominator (4). This gives us 5/4.
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1 2/5: Multiply the whole number (1) by the denominator (5) and add the numerator (2): (1 * 5) + 2 = 7. Keep the same denominator (5). This gives us 7/5.
Dividing Fractions
Now, we are left with 5/4 divided by 7/5. Remember that dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of 7/5 is 5/7.
Therefore, our problem becomes: (5/4) * (5/7)
Multiplying Fractions
To multiply fractions, we simply multiply the numerators and the denominators.
(5 * 5) / (4 * 7) = 25/28
Final Answer
The final answer to 1 1/4 divided by 1 2/5 is 25/28.