How to simplify a mixed arithmetic expression step by step for fifth graders

Learn a clear, friendly method to simplify a complex arithmetic expression. We walk through squaring numbers, handling parentheses, dividing by brackets, and working with cubes, all at a kid-friendly pace. A practical guide that makes order of operations feel natural and approachable.

Powering Through Expressions: A Friendly Look at a Math Problem for 5th Class Engineers

Let’s start with a small, cozy question that feels like a doorway into everyday engineering thinking: what’s the value of this expression? 6² ÷ (2² + 15 - 3 - [6 ÷ 2]) x 1 + 3³. It’s not just about getting the right number—it’s about how you approach it, step by step, like a young engineer checking a schematic before a big build.

First impressions and a quick reality check

If you’re familiar with the general rhythm of numbers, you might hear “PEMDAS” or “BODMAS” in your head. That stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). These rules keep math from turning into chaos, especially when you’re juggling several operations at once. Today’s expression is a nice example: there are exponents, there are brackets, there’s division, multiplication, addition—the whole family showing up in one place. We’ll treat it like a little power plant diagram: clear, orderly steps that lead to a solid result.

Step 1: Gather the parts and identify the order of operations

Let me explain the mental map. The expression is:

6² ÷ (2² + 15 - 3 - [6 ÷ 2]) x 1 + 3³

• We’ve got numbers being squared: 6² and 2² and 3³.

• There are brackets and square brackets containing a nested operation: (2² + 15 - 3 - [6 ÷ 2]).

• There’s a division by that whole bracket, then a multiplication by 1, and finally an addition of 3³.

The first move is to crack the innermost pieces inside the brackets. Once those are settled, the outer operations follow.

Step 2: Do the innermost calculations

Inside the big parentheses, there’s the innermost [6 ÷ 2], which is 3. Substituting that in keeps the flow consistent:

So the expression becomes:

6² ÷ (2² + 15 - 3 - 3) x 1 + 3³

Parallel track—exponents check

We also have 6², 2², and 3³ to compute. It helps to knock those out early so the middle part—the bracketed sum—shines clearly.

• 6² = 36

• 2² = 4

• 3³ = 27

Now we can rewrite the expression with those numbers in place:

36 ÷ (4 + 15 - 3 - 3) x 1 + 27

Step 3: Simplify inside the big parentheses

Now we work inside the parentheses (the heart of the calculation). It’s a simple arithmetic stream, but we must do it in order, left to right for addition/subtraction after we’ve settled the inner sums.

Compute step by step:

• 4 + 15 = 19

• 19 - 3 = 16

• 16 - 3 = 13

So the bracketed expression collapses to 13. The expression now reads:

36 ÷ 13 x 1 + 27

A quick note on notation: x 1 doesn’t change things, but we still treat it as a multiplication to keep the rhythm of operations clean.

Step 4: Finish the division and multiplication in the right order

Here’s where a lot of folks slip up if they’re rushing. Multiplication and division share the same level of priority and are resolved from left to right.

We have 36 ÷ 13, then multiply by 1. Since multiplying by 1 doesn’t change the value, this is basically just 36 ÷ 13.

Compute 36 ÷ 13. That’s a repeating-ish decimal, but for our classroom and power-engineering intuition, we’ll keep enough precision to land at the final answer. 36 ÷ 13 is about 2.769230769…

So after the division (and the harmless multiplication by 1), the expression becomes:

2.769230769… + 27

Step 5: Add the final piece

Now add 27 to the number we just found:

27 + 2.769230769… = 29.769230769…

Rounding for the classroom-friendly result

If your teacher asked for a two-decimal place answer, you’d round 29.769230769… to 29.77. That’s where the neat value in the multiple-choice options comes from. It’s a good habit—engineering calculations often end with a sensible level of precision, especially when you’re communicating results to teammates or drawing a quick diagram.

So, the final result, to two decimals, is 29.77.

Turning the math into a little engineering habit

This problem isn’t just about number-crunching. It’s a tiny, friendly model of how engineers approach real-world tasks:

• Clarity of structure matters. When you break a complex expression into chunks, you reduce the risk of misreading. In projects like electrical circuits or power flow models, you’ll see a similar need to segment problems so each part is well understood.

• Order of operations is your best tool, not a hurdle. If you skip a step or rush through parentheses, the entire result can drift from reality. In engineering, a missed step can ripple into a faulty calculation for a system you’re trusting with real power.

• Precision and communication go hand in hand. Deciding whether to report 29.77 or 29.769 or 29.77 with a little more decimal care depends on the context. In many practical settings, you settle on a reasonable precision that keeps things clear but not cluttered.

A tiny detour into a real-world analogy

Imagine you’re balancing a simple, small-scale power setup in a classroom model—one that uses a few LEDs, some resistors, and a tiny power supply. You might think of the numbers in our expression as components of that model:

• The squared terms could be like calculating the power or energy associated with a surge in a circuit, where higher values indicate more “weight” in the system.

• The bracketed sum acts like a subcircuit: a little module whose output feeds into the bigger circuit.

• The final addition is akin to combining the subcircuit’s output with a constant bias, a common move when you’re adjusting a signal or an offset in a test rig.

Staying curious about the math under the hood

As you grow more comfortable with these steps, you’ll naturally start seeing patterns. For instance, whenever you have a division by a relatively large number and you’re then adding a fairly large cube, you’ll often end up with a fairly tidy result, especially after rounding. It’s not magic—it’s arithmetic that keeps showing up in the same places, like a familiar tune in a workshop.

How to practice this without turning it into a chore

If you’re exploring on your own, try reworking similar expressions with different numbers. Swap 6 with another small integer, or change the 15 to 12, and see how the decimal lands. The process stays the same, and you’ll start to trust your instincts about where to expect quick simplifications and where to expect a little more decimal nuance.

A few tips that help every budding engineer

• Write it out clearly. A neatly written line of steps beats mental gymnastics any day. If you can’t see a step, you’re more likely to miss it.

• Check your work backward. Given a result, can you reconstruct the key operations to land at that number? It’s a great sanity check.

• Don’t fear decimals. In power engineering, decimals and fractions aren’t enemies—they’re tools. Knowing when to round and how to label precision is part of the craft.

A closing thought, with a wink at curiosity

math is a language, and problems like this are little conversations with numbers. They’re not meant to confound you; they’re meant to teach you how to read a situation, pick the right tools, and map a sensible path from a jumble of symbols to something you can trust. And when you land on a clean, convincing result—like 29.77—it feels a bit like finishing a neat circuit layout: everything fits, everything clicks, and you’re ready to move on to the next idea.

If you’re ever unsure about a step, pause for a moment. Revisit the parentheses, re-check the exponents, and walk the sequence again from the top. That calm, methodical approach is exactly what makes a good engineer in training—not just someone who can solve a problem, but someone who can solve it with confidence and clarity.

Finally, a quick recap for memory’s sake:

• Compute innermost parts first (the 6 ÷ 2 inside the brackets).

• Handle exponents next (6², 2², 3³).

• Tackle the parentheses’ sum: 4 + 15 − 3 − 3 = 13.

• Do the division left-to-right with any remaining multiplications: 36 ÷ 13 ≈ 2.769.

• Add the final piece: 2.769 + 27 ≈ 29.769, which rounds to 29.77.

And there you have it—a neat little expression tamed, with a taste of how thoughtful, steady practice builds the confidence to handle real-world problems with poise.