Evaluate Using the Given Value Evaluate 2/5g+3h-6 when g=10 and h=6

Solution:

Step 1:

Insert the value of $g$ as $10$ into the equation. $\frac{2}{5}\cdot 10+3h-6$

Step 2:

Insert the value of $h$ as $6$ into the equation. $\frac{2}{5}\cdot 10+3\cdot 6-6$

Step 3:

Begin simplifying the expression.

Step 3.1:

Eliminate the common factors.

Step 3.1.1:

Extract the factor of $5$ from $10$. $\frac{2}{5}\cdot (5\cdot 2)+3\cdot 6-6$

Step 3.1.2:

Remove the common factor. $\frac{2}{\cancel{5}}\cdot (\cancel{5}\cdot 2)+3\cdot 6-6$

Step 3.1.3:

Reformulate the expression. $2\cdot 2+3\cdot 6-6$

Step 3.2:

Compute $2$ times $2$. $4+3\cdot 6-6$

Step 3.3:

Compute $3$ times $6$. $4+18-6$

Step 4:

Combine the terms by addition and subtraction.

Step 4.1:

Add $4$ to $18$. $22-6$

Step 4.2:

Subtract $6$ from $22$. $16$

Knowledge Notes:

The problem requires evaluating an algebraic expression with given values for the variables. Here are the relevant knowledge points:

1. Substitution: This involves replacing variables with their given numerical values. In this case, $g$ is replaced with $10$ and $h$ is replaced with $6$.

2. Simplifying Expressions: This process includes several steps:

   • Combining like terms: Terms that have the same variable part can be combined by adding or subtracting their coefficients.

   • Multiplying and dividing terms: Apply the correct arithmetic operations to simplify the expression. This includes canceling out common factors in fractions.

3. Arithmetic Operations: Perform basic arithmetic operations such as addition, subtraction, multiplication, and division as required to simplify the expression.

4. Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. However, in this case, the operations are straightforward after substitution.

5. Fractions: When dealing with fractions, look for opportunities to cancel common factors in the numerator and denominator to simplify the calculation.

6. Final Calculation: After simplifying, perform the final arithmetic operations to arrive at the numerical value of the expression.