Today we will see 3 different methods for subtracting a fraction from a whole number. Let’s walk through the examples step by step.
Content:
Before getting into it, just remember that in a fraction, the top number is the numerator, and the bottom number is the denominator. Look at the image below.
1) Classical method
Let’s see this method subtracting 3 — 4/5. First, we convert the whole number 3 to a fraction by putting 1 as the denominator. Then, we multiply this fraction by the fraction 5/5 (don’t forget that 5/5 is equivalent to 1). Next, we multiply the fractions 3/1 and 5/5. We continue by subtracting the fractions with the same denominator.
We have an improper fraction (the numerator is greater than or equal to the denominator), 11/5, which we can convert to a mixed number.
The final answer is 21/5.
2) Mixed number method
In this method, we start by rewrite the whole number 3 as the sum of 2 and 1. Next, we rewrite 1 as the fraction 5/5, we use the number 5 because the fraction has a denominator of 5. We continue by subtracting the fractions 5/5 and 4/5.
Now we have the sum of a whole and a proper fraction, but that is the definition of a mixed number. So, we can rewrite the sum of 2 and 4/5 as the mixed number 24/5. We can also convert this mixed number 24/5 to an improper fraction.
3) Quick method
To subtract a fraction from a whole number with the quick method, we start by multiplying the denominator (5) by the whole number (3), and then, we subtract the numerator (4). Finally, we keep the denominator (5) of the fraction. We can also convert the resulting improper fraction to a mixed number.
As you can see, in the 3 methods the answer is the same, 11/5 or 21/5.
Videos
In this video, we will take a look at the 3 methods.
And here, we will go deeper into the quick method.
References
For this lesson, we have used this book:
- Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 378-382). Cengage Learning.
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