Evaluate Using the Given Value Evaluate 2/5g+3h-6 when g=10 and h=6
The problem presented requires you to perform a substitution and calculation based on the given expressions and values. You are asked to take the algebraic expression 2/5g+3h-6 and substitute the variables 'g' and 'h' with the numbers provided, which are g=10 and h=6, respectively. After substituting these values into the expression, you are then expected to carry out the arithmetic operations to simplify and find the numerical result.
Evaluate$\frac{2}{5} g + 3 h - 6$when$g = 10$and$h = 6$
Answer
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:
Substitution: This involves replacing variables with their given numerical values. In this case, $g$ is replaced with $10$ and $h$ is replaced with $6$.
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.
Arithmetic Operations: Perform basic arithmetic operations such as addition, subtraction, multiplication, and division as required to simplify the expression.
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.
Fractions: When dealing with fractions, look for opportunities to cancel common factors in the numerator and denominator to simplify the calculation.
Final Calculation: After simplifying, perform the final arithmetic operations to arrive at the numerical value of the expression.
