How to Solve 4 1/5 Divided by 1 1/6: A Step-by-Step Guide
Understanding how to divide mixed numbers, such as 4 1/5 divided by 1 1/6, is a fundamental skill in mathematics that builds confidence in handling fractions. Whether you're a student or a parent helping with homework, mastering this method ensures a strong foundation in arithmetic. This process involves converting mixed numbers to improper fractions, applying division rules, and simplifying results. Below, we’ll break down the steps to solve this problem and explain the reasoning behind each move.
Step-by-Step Solution: Dividing Mixed Numbers
Step 1: Convert Mixed Numbers to Improper Fractions
Mixed numbers combine whole numbers and fractions. To divide them, first convert each into an improper fraction (a fraction where the numerator is greater than the denominator).
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For 4 1/5:
Multiply the whole number (4) by the denominator (5):
$ 4 \times 5 = 20 $.
Add the numerator (1):
$ 20 + 1 = 21 $.
The improper fraction is 21/5. -
For 1 1/6:
Multiply the whole number (1) by the denominator (6):
$ 1 \times 6 = 6 $.
Add the numerator (1):
$ 6 + 1 = 7 $.
The improper fraction is 7/6.
Now the problem becomes:
$ \frac{21}{5} \div \frac{7}{6} $
Step 2: Rewrite Division as Multiplication by the Reciprocal
Division of fractions is equivalent to multiplying by the reciprocal (the flipped version) of the second fraction It's one of those things that adds up..
- The reciprocal of 7/6 is 6/7.
- So, rewrite the problem:
$ \frac{21}{5} \times \frac{6}{7} $
Step 3: Multiply the Fractions
Multiply the numerators together and the denominators together:
$ \frac{21 \times 6}{5 \times 7} = \frac{126}{35} $
Step 4: Simplify the Result
Simplify 126/35 by finding the greatest common divisor (GCD) of the numerator and denominator. Both 126 and 35 are divisible by 7:
$ \frac{126 \div 7}{35 \div 7} = \frac{18}{5} $
If needed, convert this back to a mixed number:
- Divide 18 by 5:
$ 5 \times 3 = 15 $, remainder 3. - The mixed number is 3 3/5.
Final Answer:
$ 4\frac{1}{5} \div 1\frac{1}{6} = \frac{18}{5} \text{ or } 3\frac{3}{5} $
Why This Method Works: The Math Behind It
Understanding Improper Fractions
Mixed numbers represent a combination
