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From pre algebra for Dummies

Comutative

When the second number is missing in a subtraction or multiplication problem, just switch around the two values that are next to the equal sign (that is, the blank and the equal sign:

I can’t understand that: just switch around the two values that are next to the equal sign (that is, the blank and the equal sign:

15-.......=8 ——>15-8=.......

The blank and the equal sign ? Explain me more

Guilherme Woolley
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  • commutative has two m's – J. W. Tanner Nov 29 '22 at 04:14
  • I don't understand what there is to not understand. From $a-b=c$ you can add $b$ to both sides to get $a-b+b=c+b$. Now, use that $-b+b=0$ to get $a+0=c+b$ and omit the zero to get $a=c+b$. Now, subtract $c$ from both sides to get $a-c = c+b-c$. Rearrange the right side a bit and use that $c-c=0$ to get that $a-c=b+(c-c)$ simplifying to $a-c=b+0$ and omitting the zero to get $a-c=b$. These all follow from rudimentary properties of addition, subtraction, and zero – JMoravitz Nov 29 '22 at 04:17
  • All they are saying is that $a-b = c\implies a-c=b$. As an example... $15-7=8$ and $15-8=7$ – JMoravitz Nov 29 '22 at 04:18
  • What does it mean by saying to switch the blank and equal sing – Guilherme Woolley Nov 29 '22 at 04:36
  • 15 - x = 8 can become 15 - 8 = x. We are swapping the value to the left of the equals sign (the x) with the value to the right of the equals sign (the 8). We are not swapping the equals sign with anything. – JMoravitz Nov 29 '22 at 19:24

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