Linear Algebra Examples

$[\begin{array}{c} 1 & 8 & 4 & 9.7 \\ 3 & 5 & 2 & 10.7 \\ 6 & 5 & 3 & 11.9 \\ 1 & 4 & 5 & 7.6 \\ 5 & 6 & 4 & 10.4 \end{array}] + [\begin{array}{c} 9 & 5 & 11 & 18.2 \\ 4 & 1 & 11 & 14.9 \\ 11 & 7 & 15 & 19.4 \\ 2 & 8 & 23 & 12.5 \\ 16 & 1 & 5 & 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 1 + 9 & 8 + 5 & 4 + 11 & 9.7 + 18.2 \\ 3 + 4 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2

Simplify each element.

Tap for more steps...

Step 2.1

Add $1$ and $9$ .

$[\begin{array}{c} 10 & 8 + 5 & 4 + 11 & 9.7 + 18.2 \\ 3 + 4 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.2

Add $8$ and $5$ .

$[\begin{array}{c} 10 & 13 & 4 + 11 & 9.7 + 18.2 \\ 3 + 4 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.3

Add $4$ and $11$ .

$[\begin{array}{c} 10 & 13 & 15 & 9.7 + 18.2 \\ 3 + 4 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.4

Add $9.7$ and $18.2$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 3 + 4 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.5

Add $3$ and $4$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 5 + 1 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.6

Add $5$ and $1$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 2 + 11 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.7

Add $2$ and $11$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 10.7 + 14.9 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.8

Add $10.7$ and $14.9$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 6 + 11 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.9

Add $6$ and $11$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 5 + 7 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.10

Add $5$ and $7$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 3 + 15 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.11

Add $3$ and $15$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 11.9 + 19.4 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.12

Add $11.9$ and $19.4$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 1 + 2 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.13

Add $1$ and $2$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 4 + 8 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.14

Add $4$ and $8$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 5 + 23 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.15

Add $5$ and $23$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 7.6 + 12.5 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.16

Add $7.6$ and $12.5$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 20.1 \\ 5 + 16 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.17

Add $5$ and $16$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 20.1 \\ 21 & 6 + 1 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.18

Add $6$ and $1$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 20.1 \\ 21 & 7 & 4 + 5 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.19

Add $4$ and $5$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 20.1 \\ 21 & 7 & 9 & 10.4 + 17.1 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 2.20

Add $10.4$ and $17.1$ .

$[\begin{array}{c} 10 & 13 & 15 & 27.9 \\ 7 & 6 & 13 & 25.6 \\ 17 & 12 & 18 & 31.3 \\ 3 & 12 & 28 & 20.1 \\ 21 & 7 & 9 & 27.5 \end{array}] + [\begin{array}{c} 8 & 6 & 18 & 17.9 \\ 7 & 1 & 14 & 16.5 \\ 6 & 3 & 21 & 18.2 \\ 1 & 7 & 17 & 10.8 \\ 8 & 2 & 18 & 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 3

Add the corresponding elements.

$[\begin{array}{c} 10 + 8 & 13 + 6 & 15 + 18 & 27.9 + 17.9 \\ 7 + 7 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4

Simplify each element.

Tap for more steps...

Step 4.1

Add $10$ and $8$ .

$[\begin{array}{c} 18 & 13 + 6 & 15 + 18 & 27.9 + 17.9 \\ 7 + 7 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.2

Add $13$ and $6$ .

$[\begin{array}{c} 18 & 19 & 15 + 18 & 27.9 + 17.9 \\ 7 + 7 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.3

Add $15$ and $18$ .

$[\begin{array}{c} 18 & 19 & 33 & 27.9 + 17.9 \\ 7 + 7 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.4

Add $27.9$ and $17.9$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 7 + 7 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.5

Add $7$ and $7$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 6 + 1 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.6

Add $6$ and $1$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 13 + 14 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.7

Add $13$ and $14$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 25.6 + 16.5 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.8

Add $25.6$ and $16.5$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 17 + 6 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.9

Add $17$ and $6$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 12 + 3 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.10

Add $12$ and $3$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 18 + 21 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.11

Add $18$ and $21$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 31.3 + 18.2 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.12

Add $31.3$ and $18.2$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 3 + 1 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.13

Add $3$ and $1$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 12 + 7 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.14

Add $12$ and $7$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 28 + 17 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.15

Add $28$ and $17$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 20.1 + 10.8 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.16

Add $20.1$ and $10.8$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 30.9 \\ 21 + 8 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.17

Add $21$ and $8$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 30.9 \\ 29 & 7 + 2 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.18

Add $7$ and $2$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 30.9 \\ 29 & 9 & 9 + 18 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.19

Add $9$ and $18$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 30.9 \\ 29 & 9 & 27 & 27.5 + 17.1 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 4.20

Add $27.5$ and $17.1$ .

$[\begin{array}{c} 18 & 19 & 33 & 45.8 \\ 14 & 7 & 27 & 42.1 \\ 23 & 15 & 39 & 49.5 \\ 4 & 19 & 45 & 30.9 \\ 29 & 9 & 27 & 44.6 \end{array}] + [\begin{array}{c} 7 & 5 & 10 & 15 \\ 0 & 0 & 0 & 0 \\ 6 & 5 & 13 & 15.9 \\ 1 & 3 & 12 & 10.9 \\ 8 & 4 & 5 & 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 5

Add the corresponding elements.

$[\begin{array}{c} 18 + 7 & 19 + 5 & 33 + 10 & 45.8 + 15 \\ 14 + 0 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6

Simplify each element.

Tap for more steps...

Step 6.1

Add $18$ and $7$ .

$[\begin{array}{c} 25 & 19 + 5 & 33 + 10 & 45.8 + 15 \\ 14 + 0 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.2

Add $19$ and $5$ .

$[\begin{array}{c} 25 & 24 & 33 + 10 & 45.8 + 15 \\ 14 + 0 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.3

Add $33$ and $10$ .

$[\begin{array}{c} 25 & 24 & 43 & 45.8 + 15 \\ 14 + 0 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.4

Add $45.8$ and $15$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 + 0 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.5

Add $14$ and $0$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 + 0 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.6

Add $7$ and $0$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 + 0 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.7

Add $27$ and $0$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 + 0 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.8

Add $42.1$ and $0$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 23 + 6 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.9

Add $23$ and $6$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 15 + 5 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.10

Add $15$ and $5$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 39 + 13 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.11

Add $39$ and $13$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 49.5 + 15.9 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.12

Add $49.5$ and $15.9$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 4 + 1 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.13

Add $4$ and $1$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 19 + 3 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.14

Add $19$ and $3$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 45 + 12 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.15

Add $45$ and $12$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 30.9 + 10.9 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.16

Add $30.9$ and $10.9$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 41.8 \\ 29 + 8 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.17

Add $29$ and $8$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 41.8 \\ 37 & 9 + 4 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.18

Add $9$ and $4$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 41.8 \\ 37 & 13 & 27 + 5 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.19

Add $27$ and $5$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 41.8 \\ 37 & 13 & 32 & 44.6 + 13.9 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 6.20

Add $44.6$ and $13.9$ .

$[\begin{array}{c} 25 & 24 & 43 & 60.8 \\ 14 & 7 & 27 & 42.1 \\ 29 & 20 & 52 & 65.4 \\ 5 & 22 & 57 & 41.8 \\ 37 & 13 & 32 & 58.5 \end{array}] + [\begin{array}{c} 4 & 4 & 9 & 12.4 \\ 3 & 1 & 9 & 12 \\ 9 & 5 & 9 & 13.2 \\ 1 & 4 & 14 & 8.9 \\ 12 & 2 & 4 & 13.7 \end{array}]$

Step 7

Add the corresponding elements.

$[\begin{array}{c} 25 + 4 & 24 + 4 & 43 + 9 & 60.8 + 12.4 \\ 14 + 3 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8

Simplify each element.

Tap for more steps...

Step 8.1

Add $25$ and $4$ .

$[\begin{array}{c} 29 & 24 + 4 & 43 + 9 & 60.8 + 12.4 \\ 14 + 3 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.2

Add $24$ and $4$ .

$[\begin{array}{c} 29 & 28 & 43 + 9 & 60.8 + 12.4 \\ 14 + 3 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.3

Add $43$ and $9$ .

$[\begin{array}{c} 29 & 28 & 52 & 60.8 + 12.4 \\ 14 + 3 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.4

Add $60.8$ and $12.4$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 14 + 3 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.5

Add $14$ and $3$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 7 + 1 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.6

Add $7$ and $1$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 27 + 9 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.7

Add $27$ and $9$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 42.1 + 12 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.8

Add $42.1$ and $12$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 29 + 9 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.9

Add $29$ and $9$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 20 + 5 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.10

Add $20$ and $5$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 52 + 9 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.11

Add $52$ and $9$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 65.4 + 13.2 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.12

Add $65.4$ and $13.2$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 5 + 1 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.13

Add $5$ and $1$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 22 + 4 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.14

Add $22$ and $4$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 57 + 14 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.15

Add $57$ and $14$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 41.8 + 8.9 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.16

Add $41.8$ and $8.9$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 50.7 \\ 37 + 12 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.17

Add $37$ and $12$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 50.7 \\ 49 & 13 + 2 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.18

Add $13$ and $2$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 50.7 \\ 49 & 15 & 32 + 4 & 58.5 + 13.7 \end{array}]$

Step 8.19

Add $32$ and $4$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 50.7 \\ 49 & 15 & 36 & 58.5 + 13.7 \end{array}]$

Step 8.20

Add $58.5$ and $13.7$ .

$[\begin{array}{c} 29 & 28 & 52 & 73.2 \\ 17 & 8 & 36 & 54.1 \\ 38 & 25 & 61 & 78.6 \\ 6 & 26 & 71 & 50.7 \\ 49 & 15 & 36 & 72.2 \end{array}]$