Cindy says she found a shortcut for doing multiplication problems. When she multiplies 3 x 24 she says,"3 x 4 is 12 ones or 1 ten and 2 ones. Then there's just 2 tens left in 24 ,so add it up, and you get 3 tens and 2 ones .Do you think Cindy shortcut works explain your thinking

Of course it doesn't work, 3 x 24 = 72, not 32 (3 tens and 2 ones)

Step-by-step explanation:

This method is similar to decomposition, but it doesn't work. The problem is that she is mixing multiplication, division and addition all together without any sense at all. The way decomposition works is as follows.

Examples of decomposition:

first you can multiply 3 x 4 = 12

then 3 x 20 = 60

add them and you get 72

for example: 6 x 122

6 x 2 = 12

6 x 20 = 120

6 x 100 = 600

add them together = 732

another example: 9 x 356

9 x 6 = 54

9 x 50 = 450

9 x 300 = 2700

add them to get 3,204

the answer to the expression is 83

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1