Work out the given mathematical expressions and solve the problem

Oct 13, 2025 by recoveryshake.com 11 views

Work out the given mathematical expressions and solve the problem

1. Work out the given mathematical expressions

(a) $1.2 + \frac{1}{8} + \frac{a}{2} + 1 + \frac{1}{2} + 2$

To work out the given mathematical expression, we need to follow the order of operations (PEMDAS):

Evaluate the fractions: $\frac{1}{8} = 0.125$ , $\frac{a}{2}$ is unknown, $\frac{1}{2} = 0.5$
Add the numbers: $1.2 + 0.125 + 1 + 0.5 + 2 = 4.925$
Since $\frac{a}{2}$ is unknown, we cannot simplify the expression further.

However, if we assume that $\frac{a}{2}$ is a constant, we can rewrite the expression as:

$1.2 + 0.125 + \frac{a}{2} + 1 + 0.5 + 2 = 4.925 + \frac{a}{2}$

(b) $16 + 4 + 2 - 1 = (16 + 14 \div 2) - 1$

To work out the given mathematical expression, we need to follow the order of operations (PEMDAS):

Evaluate the division: $14 \div 2 = 7$
Add the numbers: $16 + 4 + 2 = 22$
Subtract 1: $22 - 1 = 21$
Rewrite the expression: $(16 + 7) - 1 = 22 - 1 = 21$

2. State the number of lines of symmetry of the drawn parallelogram

Unfortunately, I don't have the ability to see the drawn parallelogram. However, I can provide some general information about lines of symmetry.

A line of symmetry is a line that divides a shape into two identical halves. A parallelogram has two lines of symmetry, which are the diagonals of the parallelogram.

To determine the number of lines of symmetry of a parallelogram, you can follow these steps:

Draw the diagonals of the parallelogram.
Check if the diagonals intersect at a point.
If the diagonals intersect at a point, the number of lines of symmetry is 2.
If the diagonals do not intersect at a point, the number of lines of symmetry is 0.

Note: The number of lines of symmetry of a parallelogram is always 2, unless the parallelogram is a rectangle, in which case the number of lines of symmetry is 4.

Conclusion

In this article, we worked out two mathematical expressions and solved a problem related to lines of symmetry of a parallelogram. We followed the order of operations (PEMDAS) to evaluate the expressions and determined the number of lines of symmetry of a parallelogram.

References

Keywords

Mathematical expressions
Lines of symmetry
Parallelogram
Order of operations (PEMDAS)
Geometry
Work out the given mathematical expressions and solve the problem: Q&A

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next (e.g., 2^3).
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate a mathematical expression with multiple operations?

A: To evaluate a mathematical expression with multiple operations, follow the order of operations (PEMDAS):

Evaluate any expressions inside parentheses first.
Evaluate any exponential expressions next.
Evaluate any multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What is a line of symmetry?

A: A line of symmetry is a line that divides a shape into two identical halves. A line of symmetry is a line that passes through the center of a shape and divides it into two equal parts.

Q: How do I determine the number of lines of symmetry of a parallelogram?

A: To determine the number of lines of symmetry of a parallelogram, follow these steps:

Draw the diagonals of the parallelogram.
Check if the diagonals intersect at a point.
If the diagonals intersect at a point, the number of lines of symmetry is 2.
If the diagonals do not intersect at a point, the number of lines of symmetry is 0.

Q: What is the difference between a parallelogram and a rectangle?

A: A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. A rectangle is a special type of parallelogram with four right angles and opposite sides that are equal in length.

Q: Can a parallelogram have more than two lines of symmetry?

A: No, a parallelogram can have at most two lines of symmetry, which are the diagonals of the parallelogram.

Conclusion

In this Q&A article, we answered some common questions related to mathematical expressions and lines of symmetry of a parallelogram. We followed the order of operations (PEMDAS) to evaluate mathematical expressions and determined the number of lines of symmetry of a parallelogram.

References

Keywords

Mathematical expressions
Lines of symmetry
Parallelogram
Order of operations (PEMDAS)
Geometry