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Lesson 2 of 15

Joining terms of one kind

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7 min

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Pick a 2 by 2 square on a calendar. Add its four dates. Can you name them from the sum alone?

Pick a square. Its top-left date is a.
Step 1 of 4
  1. Pick a square. Its top-left date is a.
  2. The others are a + 1, a + 7 and a + 8.
  3. Add all four dates.
  4. Join like terms: 4a + 16.

Yes. Subtract 16 from the sum, then divide by 4 to find a.

Like terms — terms with the same letter part.

Rule: join by adding their coefficients. The letter part stays as it is.

Here a + a + a + a = 4a, and 1 + 7 + 8 = 16. At a = 9 the dates are 9, 10, 16 and 17. They add to 52. And 4a + 16 is 4 × 9 + 16 = 36 + 16 = 52. Check back: 52 − 16 = 36, and 36 ÷ 4 = 9.

Taking away works the same way. Take 3a away from 7a. Four a are left: 7a − 3a = 4a.

Slide the square across the calendar. Watch the sum.

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