Conversion of a mixed number into an improper fraction

Any mixed number is the result of isolating the whole part in an improper fraction. For example, consider an improper fraction . If you isolate the whole part of it, you get

But the reverse process is also possible: any mixed number can be converted into an improper fraction. To do this, multiply the whole part by the denominator of the fractional part and add the result to the numerator of the fractional part. The result will be the numerator of the new fraction, and the denominator will remain unchanged.

For example, let's convert a mixed number into an improper fraction. Multiply the whole part of 2 by the denominator of the fractional part:

2 × 3 = 6

Then add the numerator of the fractional part to 6:

6 + 1 = 7

The resulting seven will be the numerator of the new fraction, and the denominator 3 will remain unchanged:

The detailed solution looks like this:

And with the help of variables, the convertion of a mixed number into an improper fraction can be written as follows:

Example 2. Convert a mixed number into an improper fraction.

Multiply the integer part of the mixed number by the denominator of the fractional part and add to the numerator of the fractional part, and leave the denominator unchanged:

Exercises

Task 1. Convert mixed fractions into improper fractions:

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Task 2. Convert mixed fractions into improper fractions without describing how the integer part is multiplied by the denominator of the fractional part and the result is added to the numerator of the fractional part

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