Basic Math Examples



\begin{array}{r} h = & 3 \\ l = & 7 \\ w = & 5 \end{array}

$\begin{array}{r} h = & 3 \\ l = & 7 \\ w = & 5 \end{array}$

Step 1

The surface area of a box is equal to the sum of the areas of each side of the box.

2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)

$2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)$

Step 2

Substitute the values of the length

l = 7

$l = 7$ , the width

w = 5

$w = 5$ , and the height

h = 3

$h = 3$ into the formula.

2 \cdot 7 \cdot 5 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3

$2 \cdot 7 \cdot 5 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 7 \cdot 5

$2 \cdot 7 \cdot 5$ .

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Step 3.1.1

Multiply

2

$2$ by

7

$7$ .

14 \cdot 5 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3

$14 \cdot 5 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3$

Step 3.1.2

Multiply

14

$14$ by

5

$5$ .

70 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3

$70 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3$

70 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3

$70 + 2 \cdot 7 \cdot 3 + 2 \cdot 5 \cdot 3$

Step 3.2

Multiply

2 \cdot 7 \cdot 3

$2 \cdot 7 \cdot 3$ .

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Step 3.2.1

Multiply

2

$2$ by

7

$7$ .

70 + 14 \cdot 3 + 2 \cdot 5 \cdot 3

$70 + 14 \cdot 3 + 2 \cdot 5 \cdot 3$

Step 3.2.2

Multiply

14

$14$ by

3

$3$ .

70 + 42 + 2 \cdot 5 \cdot 3

$70 + 42 + 2 \cdot 5 \cdot 3$

70 + 42 + 2 \cdot 5 \cdot 3

$70 + 42 + 2 \cdot 5 \cdot 3$

Step 3.3

Multiply

2 \cdot 5 \cdot 3

$2 \cdot 5 \cdot 3$ .

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Step 3.3.1

Multiply

2

$2$ by

5

$5$ .

70 + 42 + 10 \cdot 3

$70 + 42 + 10 \cdot 3$

Step 3.3.2

Multiply

10

$10$ by

3

$3$ .

70 + 42 + 30

$70 + 42 + 30$

70 + 42 + 30

$70 + 42 + 30$

70 + 42 + 30

$70 + 42 + 30$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

70

$70$ and

42

$42$ .

112 + 30

$112 + 30$

Step 4.2

Add

112

$112$ and

30

$30$ .

142

$142$

142

$142$