Mathematical expressions on operations, brackets and exponents (powers)

Mathematical expressions on operations, brackets and exponents (powers)

These mathematical expressions are comprised of numbers, mathematical operations and exponents (powers). The acronym BEDMAS is used to express the order of priority of mathematical operations in a mathematical expression with exponents (powers). The following is the order of operations in BEDMAS:

• B represents Brackets
• E represents Exponents (powers)
• D represents Division
• M represents Multiplication
• A represents Addition
• S represents Subtraction

In calculating by using BEDMAS consider the following procedure:

1. Perform the operations in the brackets.
2. Calculate the exponents (powers).
3. Divide from left to right.
4. Multiply from left to right.
5. Add from left to right.
6. Lastly, subtract from left to right.

Example 1

Find the value of $(8 + 3)^2 + (25 - 13) \times 8 - 244 \div 4$.

Solution

Using the BEDMAS rule, follow the steps:

Start by opening brackets: $(8 + 3)^2 + (25 - 13) \times 8 - 244 \div 4$ $= 11^2 + 12 \times 8 - 244 \div 4$

Find the square of 11: $11^2 + 12 \times 8 - 244 \div 4$ $= 121 + 12 \times 8 - 244 \div 4$

Divide: $121 + 12 \times 8 - 244 \div 4$ $= 121 + 12 \times 8 - 61$

Multiply: $121 + 12 \times 8 - 61$ $= 121 + 96 - 61$

Add: $121 + 96 - 61$ $= 217 - 61$

Finally subtract: $217 - 61 = 156$

Therefore, $(8 + 3)^2 + (25 - 13) \times 8 - 244 \div 4 = 156$.

Example 2

Find the value of $(2/3 - 3/7)^2 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2}$.

Solution

Using the BEDMAS rule, follow the steps:

Start by opening brackets: $(2/3 - 3/7)^2 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2} = (5/21)^2 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2}$

Find the square of 5/21: $(5/21)^2 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2} = 25/441 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2}$

Divide: $25/441 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2} = 25/441 + 16 - 1\frac{1}{5} \times 4\frac{1}{2}$

Multiply: $25/441 + 16 - 1\frac{1}{5} \times 4\frac{1}{2} = 25/441 + 16 - 27/5$

Add: $25/441 + 16 - 27/5 = 7,081/441 - 27/5$

Finally subtract: $7,081/441 - 27/5 = 23,498/2,205 = 10\frac{1,448}{2,205}$

Therefore, $(2/3 - 3/7)^2 + 1,984 \div 124 - 1\frac{1}{5} \times 4\frac{1}{2} = 23,498/2,205$ or $10\frac{1,448}{2,205}$.

Example 3

Find the value of $12.45 \times 0.6 + (9.8 - 1.4)^2 - 164 \div 4 + 1.5^2$.

Solution

Using the BEDMAS rule, follow the steps:

Start by opening brackets: $12.45 \times 0.6 + (9.8 - 1.4)^2 - 164 \div 4 + 1.5^2$ $= 12.45 \times 0.6 + 8.4^2 - 164 \div 4 + 1.5^2$

Find the squares of 8.4 and 1.5: $12.45 \times 0.6 + 8.4^2 - 164 \div 4 + 1.5^2$ $= 12.45 \times 0.6 + 70.56 - 164 \div 4 + 2.25$

Divide: $12.45 \times 0.6 + 70.56 - 164 \div 4 + 2.25 = 12.45 \times 0.6 + 70.56 - 41 + 2.25$

Multiply: $12.45 \times 0.6 + 70.56 - 41 + 2.25 = 7.47 + 70.56 - 41 + 2.25$

Add: $7.47 + 70.56 - 41 + 2.25 = 7.47 + 70.56 + 2.25 - 41$ $= 80.28 - 41$

Finally, subtract: $80.28 - 41 = 39.28$

Therefore, $12.45 \times 0.6 + (9.8 - 1.4)^2 - 164 \div 4 + 1.5^2 = 39.28$