Problem 2

Evaluate the expression: \(3(10+3) \div(8+5)+6 \cdot 4^2\)

Short Answer

Expert verified

The given expression can be simplified step-by-step using the order of operations (PEMDAS). The expression is \[3(10 + 3) \div (8 + 5) + 6 \cdot 4^2\] Upon simplification, the expression becomes: \[3(13) \div 13 + 6 \cdot 16\] By following PEMDAS, we get: \[39 \div 13 + 96\] Finally, we compute the value: \[3 + 96 = 99\] Hence, the simplified expression is \(\boxed{99}\).

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Solve expressions inside parentheses first.

We see that there are two sets of parentheses in the expression. We will solve each separately: \[3(10+3) \Rightarrow 3(13)\] and \[(8+5) \Rightarrow 13\]

Step 2: Rewrite expression with simplified terms.

After solving the expressions inside parentheses, we rewrite the overall expression: \[3(13) \div 13 + 6 \cdot 4^2\]

Step 3: Calculate exponents.

Our expression has one exponent term: \(4^2\). We will calculate its value: \[4^2 = 16\]

Step 4: Rewrite expression with calculated exponent.

Now we rewrite the expression with the calculated exponent: \[3(13) \div 13 + 6 \cdot 16\]

Step 5: Perform multiplication and division from left to right.

Now we perform multiplication and division from left to right: \[3 \cdot 13 = 39\] and \[6 \cdot 16 = 96\] Leaving us with: \[39 \div 13 + 96\] Next, we perform division: \[39 \div 13 = 3\]

Step 6: Rewrite expression with simplified multiplication and division terms.

Now, we rewrite the expression with the simplified multiplication and division terms: \[3 + 96\]

Step 7: Perform addition and subtraction from left to right.

Now, we perform addition from left to right: \[3 + 96 = 99\] The final result of the expression is 99.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find Study Materials for

Create Study Materials

Select your language

Chapter 5: Chapter 5

Evaluate the expression: \(3(10+3) \div(8+5)+6 \cdot 4^2\)

Short Answer

Step by step solution

Unlock all solutions

Step 1: Solve expressions inside parentheses first.

Step 2: Rewrite expression with simplified terms.

Step 3: Calculate exponents.

Step 4: Rewrite expression with calculated exponent.

Step 5: Perform multiplication and division from left to right.

Step 6: Rewrite expression with simplified multiplication and division terms.

Step 7: Perform addition and subtraction from left to right.

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Spectrum Critical Thinking for Math, Grade 6’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 7

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Pure Maths

Geometry

Statistics

Mechanics Maths