## Tuesday, 3 February 2015

### Balanced equations

On Monday we looked at balanced equations using the number scales.  Like this one:
10 + 8 + 6 + 4 + 2  = 30 =  (5 x 2) + (4 x 2) + (3 x 2) + (2 x 2) + (1 x 2)

Can you say what the equation would be for any of these balances?
 A.
 B.
 C.

1. A. 10 + 10 + 2 + 2 + 4 + 4 = 32
B. 10 + 6 +2 = 18
C. 2 + 2 + 2 + 4 = 10

1. Sebastian, thank you so much for being the first to reply.
However, these are not quite correct. Have a look at Aditi's and Marie's below.

2. A..(10x2)=20=(2x4)+(4x3)

B..10+2=12=(6x2)

C..(4x1)=4=(2x2)

1. That would work, yes!

3. A. ( 2x10)=(2x2)+(4x4)
B.10+2=(6x2)
C.4=(2x2)

1. And that would work too, yes!
(Notice how you've got a different answer to Aditi for A - but both could work!)

4. A. 10 x 3 = 30 = (2 x 5) + (4 x 5)
B. (10 x 3) + ( 2 x 3) = 36 = 6 x 6
C. 4 x 3 = 12 = 2 x 6

5. A. 10 x 2 = 20 = (2 x 4) + (4 x 3)
B. (10 x 4) + (2 x 4) = 48 = 6 x 8
C. 5 x 4 = 20 = 2 x 10

6. A.10x2=20=( 2x2 ) + ( 4x4 )
B. ( 10x1 ) + ( 2x1 )=12=( 6x2 )
C.( 4x1 ) =4=( 2x2 )

7. a.(10*2)=(2*2)+(4*4)
b. (10+2)= (6*2)
c. 4=(2*2)

8. Isn't it interesting how there are different ways to write this equation! Well done everyone!

9. This comment has been removed by the author.

1. here below my own examples...
(2x4)+(3x2)=(2x5)+(2x2)
(3x3)+(1x2)=(2x2)+(2x2)
(7x2)+(2x2)=(2x5)+(2x4)

10. A. (10x2) = (2x4) + (4x3)
20 = 20

B. (10x1) + (2x1) = 6x2
12 = 12

C. 4x1 = 2x2
4 = 4