Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Translate a grouped purchase into arithmetic.
- Apply multiplication before addition.
- Explain what each intermediate number represents.
Before you start
Multiply whole numbers and distinguish a unit price from a total cost.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A club buys 4 packs containing 6 pens each. Every pen costs $2, and delivery costs $5 for the entire order. What is the total?
Why this math matters
An expression is a compact set of instructions. The order of operations gives those instructions a shared meaning, while parentheses let a writer show a particular grouping. A story helps determine which costs repeat and which occur once.
Set up the model
A useful answer starts with clear assumptions:
- All packs contain exactly six pens at the stated per-pen price.
- Delivery is charged once; there are no other charges.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Read a supply-order expression in the right order
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A club buys 4 packs containing 6 pens each. Every pen costs $2, and delivery costs $5 for the entire order. What is the total?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Count the objects
4 packs × 6 pens/pack = 24 pens
Multiplying packs by pens per pack produces a pen count. The word 'each' points to repeated equal groups.
Price the pens
24 pens × $2/pen = $48
The per-pen price applies to every pen. It does not apply just once to each pack.
Add the one-time charge
4 × 6 × 2 + 5 = 48 + 5 = $53
Multiplication happens before the final addition. Parentheses around 4 × 6 × 2 would clarify the purchase subtotal without changing the value.
The result
The order costs $53, including the single delivery fee.
The expression 4(6 × 2 + 5) would charge $5 delivery four times and total $68. Parentheses should represent the story's grouping, not be inserted merely to make arithmetic look organized.
Common mistakes to catch
- Adding the delivery fee to the per-pack cost repeats a one-time charge.
- Multiplication and division share precedence; neither always comes first.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Three kits each contain a $5 notebook and a $2 folder. Find 3(5 + 2).
Show a hint
Find one kit's cost first.
Reveal answer and explanation
$21
One kit costs $7, so three cost 3 × 7 = $21. The grouping makes both items repeat.
Practice 2
Evaluate 24 ÷ 3 × 2, without inserting new parentheses.
Show a hint
Work left to right through division and multiplication.
Reveal answer and explanation
16
24 ÷ 3 = 8, then 8 × 2 = 16. Dividing by 3 × 2 instead would evaluate a different expression.
Take the idea with you
Annotate each number in an expression with its meaning. Check that every fee repeats the intended number of times.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Make the greatest number of identical kits
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