Converting Mixed Numbers to Improper Fractions
Actually, we convert them almost in the same way as we add fractions with unlike denominators.
Recall that every integer `m` can be expressed as fraction `m/1`.
Mixed number, as known, is a sum of integer and fraction, so mixed number `m n/q` is `m+n/q=m/1+n/q`.
Now, we perform addition of fractions with unlike denominators: `m/1+n/q=(mq)/q+n/q=(mq+n)/q`.
To convert mixed number into improper fraction following formula is used: `color(green)(m n/q=(mq+n)/q)`.
Example 1. Convert `5 3/7` to improper fraction.
Let's first do converting step-by-step:
Example 2. Convert `9 2/5` to improper fraction.
Now, we use direct formula:
Example 3. Convert `-2 8/11` to improper fraction.
In case of negative mixed number way of converting isn't changed.
First we just ignore minus sign: `2 8/11=(2*11+8)/11=30/11`.
Now, add ignored minus sign: `-30/11`.
Now, it is time to practice.
Exercise 1. Convert `1 7/8` to improper fraction.
Exercise 2. Convert `9 2/3` to improper fraction.
Exercise 3. Convert `-5 7/9` to improper fraction.