Adding and subtracting fractions with unlike denominators

Adding and subtracting fractions with unlike denominators

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  • ﻿Alex and Mark are walking home from the park when Alex brings up a topic in school that he didn't understand.
  • Today's lesson was confusing. I didn't understand how to add and subtract fractions with unlike denominators.﻿
  • It's actually pretty simple. Let me tell you. Let's try to solve five sevenths plus three fourths.
  • ﻿﻿﻿You know how to add fractions with common denominators? You have to add the numerators and keep the denominators the same. Here, you have to find a common denominator between the two fractions you have, so when you do, you just have to add the numerators.
  • Okay. So how to find the common denominator of 4 and 7?﻿
  • To find a common denominator, you have to find a multiple, which is a number that you get when you multiply your starting number with another number, that is divisible by both numbers and make them that number.﻿
  • 7=7,14,21,28,35﻿
  • 4=4,8,12,16,20,24,28
  • ﻿So the common multiple, or denominator, of 7 and 4 is 28.
  • Now that you have a common denominator that is bigger than your original number, you have to multiply the numerator by the same number you did for the denominator, then you add.﻿
  • So, we multiply ﻿both the 3 and 4 by 7 to get twenty-one twenty-eighths, and we multiply 5 and 7 by 4 to get twenty twenty-eighths. 20 plus 21 is forty-one twenty-eighths, and that turned into a mixed fraction is 1 thirteen twenty eighths! What about subtraction?
  • To subtract fractions, you do the same thing as adding. you find the common denominator but instead of adding, you subtract. What is three fifths minus one third?
  • ﻿The common denominator of 3 and 5 is 15. 3 times 3 is 9 and 1 times 5 is 5, so the fractions now are nine fifteenths minus five fifteenths. 9-5 is 4, so the answer is four fifteenths.
  • 5=5,10,15,20,25
  • 3=3,6,9,12,15﻿
  • ﻿Goodbye!
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