35 5/8 divided by 2

2 min read 28-02-2025

Dividing mixed numbers can seem tricky, but with the right approach, it becomes straightforward. This article will guide you through dividing 35 5/8 by 2, explaining each step clearly. We'll also explore different methods to help you choose the approach that best suits your understanding.

Converting to Improper Fractions: The Foundation of Division

Before we begin dividing, it's crucial to convert the mixed number, 35 5/8, into an improper fraction. This simplifies the division process significantly.

Step 1: Convert the mixed number to an improper fraction.

To do this, multiply the whole number (35) by the denominator (8), add the numerator (5), and keep the same denominator (8).

35 x 8 + 5 = 285

Therefore, 35 5/8 becomes 285/8.

Performing the Division

Now that we have an improper fraction, dividing by 2 becomes a simple matter of multiplying by its reciprocal.

Step 2: Rewrite the division as multiplication.

Dividing by 2 is the same as multiplying by 1/2. So our problem transforms from:

285/8 ÷ 2

to:

285/8 x 1/2

Step 3: Multiply the numerators and denominators.

Multiply the numerators together (285 x 1 = 285) and the denominators together (8 x 2 = 16). This gives us:

285/16

Simplifying the Result

The result, 285/16, is an improper fraction. Let's convert it back into a mixed number to make it easier to understand.

Step 4: Convert the improper fraction to a mixed number.

Divide the numerator (285) by the denominator (16):

285 ÷ 16 = 17 with a remainder of 13

This means that 285/16 is equal to 17 13/16.

Therefore, 35 5/8 divided by 2 equals 17 13/16.

Alternative Method: Decimal Conversion

Another way to solve this problem is by converting the mixed number into a decimal and then dividing.

Step 1: Convert 35 5/8 to a decimal.

Divide 5 by 8: 5 ÷ 8 = 0.625

Add this to the whole number: 35 + 0.625 = 35.625

Step 2: Divide the decimal by 2.

35.625 ÷ 2 = 17.8125

This decimal, 17.8125, is equivalent to 17 13/16.

Conclusion

Whether you prefer working with fractions or decimals, the result remains consistent: 35 5/8 divided by 2 equals 17 13/16. Understanding both methods allows for flexibility and problem-solving confidence. Remember to always convert mixed numbers to improper fractions before dividing to simplify the process. Practice both methods to solidify your understanding and improve your skills in handling mixed number division.