In the flag shown below, assume there are about 1500 plants in each of the 50 stars of the flag. And also, assume that there are 64000 plants in each of the 7 short stripes and 105000 plants in each of the 6 long stripes. The blue region contains about 200000.

We can approximate the total number of plants by evaluating the following expression :

50 ⋅ 1500 + 7 ⋅ 64000 + 6 ⋅ 105000 + 200000

To evaluate expressions involving more than one operation, mathematicians have agreed on a set of rules called the order of operations.

1. Evaluate expressions inside grouping symbols.

2. Evaluate powers.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

**Example 1 : **

To approximate the total number of plants described above, use the order of operations to evaluate the expression :

50 ⋅ 1500 + 7 ⋅ 64000 + 6 ⋅ 105000 + 200000

**Solution : **

= 50 ⋅ 1500 + 7 ⋅ 64000 + 6 ⋅ 105000 + 200000

Multiply.

= 75,000 + 448,000 + 630,000 + 200,000

Add.

= 1,353,000

There are approximately 1,353,000 plants in the flag.

**Example 2 : **

Evaluate the expression :

9(16 - 3.2)

**Solution : **

= 9(16 - 3.2)

Subtract within parentheses.

= 9(12.8)

Multiply.

= 115.2

**Example 3 : **

Evaluate the expression :

(18 + 2) / (13 - 8)

**Solution : **

= (18 + 2) / (13 - 8)

Rewrite fraction as division.

= (18 + 2) ÷ (13 - 8)

Evaluate within parentheses.

= 20 ÷ 5

Divide.

= 4

**Example 4 : **

Evaluate the expression :

4 ⋅ [38 - (15 + 7)]

**Solution : **

= 4 ⋅ [38 - (15 + 7)]

Add within parentheses.

= 4 ⋅ [38 - 22]

Subtract within brackets.

= 4 ⋅ 16

Multiply.

= 64

**Example 5 : **

Evaluate the following expression when x = 3 and y = 4.

5(x + y)

**Solution : **

= 5(x + y)

Substitute 3 for x and 4 for y.

= 5(3 + 4)

Add within parentheses.

= 5(7)

Multiply.

= 35

**Example 6 : **

Evaluate the following expression when x = 4 and y = 6.

7(x + y)^{2}

**Solution : **

= 7(x + y)^{2}

Substitute 4 for x and 6 for y.

= 7(4 + 6)^{2}

Add within parentheses.

= 7(10)^{2}

Evaluate power.

= 7(100)

Multiply.

= 700

**Example 7 :**

A pattern and enough material are bought to make two pillows. The pattern costs $6. Each pillow requires $4.25 worth of fabric and a button that costs $0.80. Find the total cost.

**Solution : **

**Read and Understand :**

One pattern plus fabric and buttons are bought to make pillows. You have to find the total cost.

**Make a Plan :**

Write a verbal model.

Total cost

=

Cost of pattern

+

Number of pillows

x

Cost of each pillow

**Solve the Problem : **

Write and evaluate the expression.

Substitute values into verbal model.

Total cost :

= 6 + 2(4.25 + 0.80)

= 6 + 2(5.05)

= 6 + 10.10

= 16.10

The total cost is $16.10.

**Look Back : **

Use estimation to check that the answer is reasonable. The cost of material for each pillow is about

$4 + $1 = $5

The total cost is about

$6 + 2($5) = $16

The answer is reasonable.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**