Adding and Subtracting Fractions and Decimals
Table Of Contents
🎬 Math Angel Video: How to Calculate with Fractions and Decimals
How to Add or Subtract Fractions and Decimals?
⏩️
There are two ways to add or subtract when one number is a fraction and the other is a decimal. You can choose the method you find easier.
🛎️ Method 1: Convert everything to decimals
Example:
$$\frac{3}{5} + 0.75 = ? $$
- Step 1: Convert the fraction into a decimal
$$\frac{3}{5} = 0.6$$ - Step 2: Add the decimals to get the answer
$$0.6+0.75=1.35$$
🛎️ Method 2: Convert everything to fractions
Example:
$$\frac{3}{5} + 0.75 = ? $$
- Step 1: Convert the decimal into a fraction
$$0.75 = \frac{3}{4}$$ - Step 2: Make the denominators the same
$$\frac{3}{5} = \frac{12}{20}, \qquad \frac{3}{4} = \frac{15}{20}$$ - Step 3: Add the fractions to get the answer
$$\frac{12}{20} + \frac{15}{20} = \frac{27}{20}$$
❇️ Key Idea:
You can convert to decimals or convert to fractions, both methods give the same answer.
When to Convert to Fractions or Decimals (Pros and Cons)
⏩️
To add or subtract fractions and decimals, you can convert everything to decimals or convert everything to fractions.
Each method has advantages and disadvantages.
🛎️ Method 1: Convert everything to decimals
- Pros
Makes calculations faster, because you can add or subtract directly. - Cons
Some fractions do not convert neatly and need rounding. For example:
$$ \frac{1}{3} = 0.333\ldots, \qquad \frac{1}{7} = 0.14285\ldots$$
🛎️ Method 2: Convert everything to fractions
- Pros
Gives exact answers with no rounding. - Cons
Takes longer because you must find a common denominator first.
❇️ Key Idea:
Both methods work.
- Choose decimals when the conversion is easy, because you can then add or subtract directly.
- Choose fractions when you want an exact answer without rounding, even though it usually takes more effort to find the common denominator.
Practice: Adding and Subtracting Fractions and Decimals
⏩️
Now, let’s work through an example:
$$\frac{1}{3} + 0.55−0.3 = ? $$
🛎️ Step 1: Simplify the decimals first
It’s easier to combine decimals before converting anything.
$$0.55−0.3=0.25$$
So the question becomes:
$$\frac{1}{3} + 0.25=?$$
🛎️ Step 2: Convert the decimal to a fraction
We can’t convert the fraction to an exact decimal, so it’s better to convert 0.25 to a fraction, so the final answer is precise.
$$0.25 = \frac{1}{4}$$
So the question becomes:
$$\frac{1}{3} + \frac{1}{4} =?$$
🛎️ Step 3: Find a common denominator
Fractions must have the same denominator before you add them:
$$\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}$$
🛎️ Step 4: Add the fractions to get the answer:
$$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$
🍪 Practice: Adding and Subtracting Fractions and Decimals
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