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Fractions can seem like a puzzle, especially when you're trying to add or subtract them. It's like trying to fit together puzzle pieces that don't quite match! But don't worry, there's a secret weapon to make it all click: the least common multiple, or LCM.
Let's say you're faced with this problem: 1/4 + 2/5 - 1/10. You can't just add the numerators (the top numbers) because the denominators (the bottom numbers) are different. They need a common ground!
Here's where the LCM swoops in to save the day:
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Identify the denominators: In our example, they are 4, 5, and 10.
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Find the least common multiple: This is the smallest number that all three denominators divide into evenly. You can find it by listing out the multiples of each denominator until you find a match.
- Multiples of 4: 4, 8, 12, 16, 20, 24...
- Multiples of 5: 5, 10, 15, 20, 25...
- Multiples of 10: 10, 20, 30...
See how 20 is the smallest number that appears in all three lists? That's our LCM!
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Rewrite each fraction with the LCM as the denominator:
- 1/4 becomes 5/20 (multiply numerator and denominator by 5)
- 2/5 becomes 8/20 (multiply numerator and denominator by 4)
- 1/10 becomes 2/20 (multiply numerator and denominator by 2)
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Now you can add and subtract the fractions easily: 5/20 + 8/20 - 2/20 = 11/20
Think of it like this: You've given all the fractions the same-sized pieces so you can combine them fairly. The LCM is your key to unlocking fraction addition and subtraction!
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