Solve 8a-b(7+a): Evaluating with a=2 and b=1/3

Q: Why do I substitute the values first?

Substituting values for variables transforms the algebraic expression into arithmetic. This makes it much easier to follow the order of operations and avoid mistakes with the variables.

Q: What happens if I don't solve the parentheses first?

You'll get the wrong answer! The expression $ \frac{1}{3}(7+2) $ means multiply $ \frac{1}{3} $ by the sum of 7 and 2, not multiply each term separately.

Q: How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $ \frac{1}{3} \times 9 = \frac{9}{3} = 3 $. The denominator stays the same!

Q: Can I convert the fraction to a decimal first?

Yes! $ \frac{1}{3} \approx 0.333... $ but this creates repeating decimals that are harder to work with. Keep fractions as fractions for exact answers.

Q: What if I get confused with the negative sign?

Remember that $ 8a - b(7+a) $ means $ 8a + (-b)(7+a) $. Since b is positive $ \frac{1}{3} $, we're subtracting a positive result.

Order of Operations with Fractional Coefficients

Solve the following expression:

$8a-b(7+a)$

$a=2,b=\frac{1}{3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:03 Substitute appropriate values according to the given data and solve

00:16 Always solve parentheses first

00:20 Continue solving according to proper order of operations

00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$8a-b(7+a)$

$a=2,b=\frac{1}{3}$

Step-by-step solution

Note that we have two unknowns, a and b, and we are also given values for them,

Therefore, let's start by substituting these values in the equation instead of the unknowns:

8*2-1/3*(7+2)=

When there is a number before parentheses, it's like having a multiplication sign between them.

Let's start solving according to the order of operations, beginning with the parentheses:

8*2-1/3*(9)=

Now let's continue with multiplication and division:

16-9/3=
16-3=

‎‎‎‎‎‎‎13

And that's the solution!

Final Answer

$13$

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace variables with given values before calculating
Order of Operations: Solve parentheses first: (7+2) = 9, then multiply
Verification: Check final calculation: 16 - 3 = 13 ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations with fractions
Don't solve 8×2 - $\frac{1}{3}$ × 7 - $\frac{1}{3}$ × 2 = wrong answer! This breaks up the parentheses incorrectly and gives 16 - $\frac{7}{3}$ - $\frac{2}{3}$ = 13. Always solve what's inside parentheses first, then multiply by the coefficient.

Practice Quiz

Test your knowledge with interactive questions

What will be the result of this algebraic expression:

$$ 5x-6 $$

if we place

$$ x=8 $$

FAQ

Everything you need to know about this question

Why do I substitute the values first?

Substituting values for variables transforms the algebraic expression into arithmetic. This makes it much easier to follow the order of operations and avoid mistakes with the variables.

What happens if I don't solve the parentheses first?

You'll get the wrong answer! The expression $\frac{1}{3}(7+2)$ means multiply $\frac{1}{3}$ by the sum of 7 and 2, not multiply each term separately.

How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $\frac{1}{3} \times 9 = \frac{9}{3} = 3$ . The denominator stays the same!

Can I convert the fraction to a decimal first?

Yes! $\frac{1}{3} \approx 0.333...$ but this creates repeating decimals that are harder to work with. Keep fractions as fractions for exact answers.

What if I get confused with the negative sign?

Remember that $8a - b(7+a)$ means $8a + (-b)(7+a)$ . Since b is positive $\frac{1}{3}$ , we're subtracting a positive result.

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