35 5/8 divided by 2

Breiz Heurope

2 min read

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11-03-2025

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Dividing mixed numbers can seem tricky, but with the right approach, it's straightforward. This guide will walk you through dividing 35 5/8 by 2, explaining each step clearly. Whether you're a student brushing up on your math skills or an adult needing a refresher, this tutorial will help you master this type of calculation.

Converting the Mixed Number to an Improper Fraction

Before we begin dividing, let's convert the mixed number 35 5/8 into an improper fraction. This makes the division process much easier.

Step 1: Multiply the whole number by the denominator.

35 (whole number) x 8 (denominator) = 280

Step 2: Add the numerator.

280 + 5 (numerator) = 285

Step 3: Keep the same denominator.

Our improper fraction is now 285/8.

Performing the Division

Now that we've converted 35 5/8 to 285/8, we can perform the division. Remember that dividing by a whole number is the same as multiplying by its reciprocal. The reciprocal of 2 is 1/2.

Step 1: Rewrite the division problem as a multiplication problem.

285/8 ÷ 2 becomes 285/8 x 1/2

Step 2: Multiply the numerators together.

285 x 1 = 285

Step 3: Multiply the denominators together.

8 x 2 = 16

Step 4: Simplify the resulting improper fraction.

Our result is 285/16. This is an improper fraction, meaning the numerator is larger than the denominator. We need to convert this back into a mixed number.

Converting Back to a Mixed Number

To convert 285/16 back into a mixed number, we perform the following steps:

Step 1: Divide the numerator by the denominator.

285 ÷ 16 = 17 with a remainder of 13

Step 2: The quotient becomes the whole number.

The quotient is 17, so our whole number is 17.

Step 3: The remainder becomes the numerator.

The remainder is 13, which becomes our new numerator.

Step 4: Keep the same denominator.

The denominator remains 16.

Therefore, 285/16 as a mixed number is 17 13/16.

Final Answer

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

Alternative Method: Dividing the Whole Number and Fraction Separately

You can also divide the whole number and fractional parts of the mixed number separately, then combine the results.

1. Divide the whole number: 35 ÷ 2 = 17 with a remainder of 1.
2. Divide the fraction: (5/8) ÷ 2 = 5/16
3. Combine the results: 17 + 1/2 + 5/16 = 17 + 8/16 + 5/16 = 17 13/16

This method might be easier to visualize for some, leading to the same accurate result. Choose the method that works best for your understanding. Remember to always practice and check your work for accuracy.