To sum fractions with whole numbers, you can convert the whole number into an equivalent fraction with the same denominator as the fraction you're adding, and then add the numerators. Alternatively, you can convert the mixed number into an improper fraction.
Here's a breakdown of the process:
- Convert the whole number to a fraction: To do this, give the whole number a denominator of 1. For instance, if you want to add 3 and 1/4, rewrite 3 as 3/1.
- Find a common denominator: If the fractions don't already have the same denominator, find the least common multiple (LCM) of the denominators. Convert both fractions to equivalent fractions with this common denominator. In our example, we want to add 3/1 + 1/4. The common denominator is 4. So we convert 3/1 to 12/4 (multiply both numerator and denominator by 4).
- Add the numerators: Once the fractions have the same denominator, add the numerators. The denominator remains the same. So 12/4 + 1/4 = 13/4.
- Simplify (if needed): If the resulting fraction is an improper fraction (numerator is greater than the denominator), convert it to a mixed number. 13/4 can be converted to 3 1/4.
Example:
Let's add 9 + 2/3, as demonstrated in the provided YouTube video excerpt.
- Convert the whole number to a fraction: Think of 9 as 9/1.
- Find a common denominator: The common denominator between 9/1 and 2/3 is 3. Convert 9/1 to 27/3.
- Add the fractions: Now add 27/3 + 2/3. Add the numerators: 27 + 2 = 29. Keep the denominator: 29/3.
- Simplify: So 9 + 2/3 = 29/3. The video excerpt confirms that 9 times 3 (the denominator) gives you 27. Adding that to the numerator 2 gives 29. The denominator remains the same.
Therefore, 9 + 2/3 = 29/3. This can also be expressed as the mixed number 9 2/3.
