Dividing Mixed Numbers: 1 1/4 ÷ 1 2/5 as a Fraction
When we encounter mixed numbers in division problems, it can be a bit tricky to solve them. But don't worry, we're here to help you understand how to divide mixed numbers, specifically 1 1/4 divided by 1 2/5 as a fraction.
Converting Mixed Numbers to Improper Fractions
Before we dive into the division problem, let's convert both mixed numbers to improper fractions.
1 1/4 = 5/4
To convert 1 1/4 to an improper fraction, we multiply the whole number part (1) by the denominator (4) and add the numerator (1). This gives us:
1 × 4 + 1 = 5
So, 1 1/4 is equal to 5/4.
1 2/5 = 7/5
Similarly, to convert 1 2/5 to an improper fraction, we multiply the whole number part (1) by the denominator (5) and add the numerator (2). This gives us:
1 × 5 + 2 = 7
So, 1 2/5 is equal to 7/5.
Dividing Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can divide them.
(5/4) ÷ (7/5)
To divide fractions, we invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
(5/4) × (5/7)
Now, we multiply the numerators and denominators separately:
(5 × 5) / (4 × 7)
Simplifying the multiplication, we get:
25/28
So, 1 1/4 divided by 1 2/5 as a fraction is 25/28.
In conclusion, dividing mixed numbers requires converting them to improper fractions, inverting the second fraction, and then multiplying. By following these steps, we can solve complex division problems like 1 1/4 divided by 1 2/5 as a fraction.
