Work out 1 1/5 - 3/10. Give your answer as a fraction.
How to approach this question
1. **Convert the mixed number to an improper fraction:**
1 1/5 = (1 × 5 + 1) / 5 = 6/5.
2. **Rewrite the subtraction with the improper fraction:**
6/5 - 3/10.
3. **Find a common denominator:**
The denominators are 5 and 10. The lowest common multiple is 10.
4. **Convert 6/5 to an equivalent fraction with a denominator of 10:**
To get from 5 to 10, you multiply by 2. So, multiply the numerator by 2 as well: 6 × 2 = 12.
So, 6/5 = 12/10.
5. **Perform the subtraction:**
12/10 - 3/10 = (12 - 3) / 10 = 9/10.
Full Answer
To subtract fractions, they must have a common denominator. First, we need to convert the mixed number into an improper fraction.
**Step 1: Convert mixed number to improper fraction.**
1 1/5 = (1 × 5 + 1) / 5 = 6/5.
So the calculation becomes 6/5 - 3/10.
**Step 2: Find a common denominator.**
The denominators are 5 and 10. The lowest common multiple of 5 and 10 is 10.
The second fraction, 3/10, already has this denominator.
We need to convert 6/5 into an equivalent fraction with a denominator of 10.
To change the denominator from 5 to 10, we multiply by 2. We must do the same to the numerator:
6/5 = (6 × 2) / (5 × 2) = 12/10.
**Step 3: Perform the subtraction.**
Now we can subtract the fractions:
12/10 - 3/10 = (12 - 3) / 10 = 9/10.
The fraction 9/10 cannot be simplified further.
Common mistakes
✗ Subtracting the numerators and denominators separately (e.g., 6/5 - 3/10 = 3/-5).\n✗ Incorrectly converting the mixed number to an improper fraction.\n✗ Making an error when finding the equivalent fraction.
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