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Operations and Calculations - Solving multi-step word problems

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Identifying Keywords: Recognizing words like 'total', 'sum', 'altogether' for addition; 'difference', 'left', 'remain' for subtraction; 'product', 'each', 'times' for multiplication; and 'share', 'average', 'equal parts' for division.

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The RUCSAC Method: A systematic approach—Read the problem, Understand the goal, Choose the operation, Solve the calculation, Answer the question, and Check your work.

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Order of Operations (BODMAS/BIDMAS): Ensuring calculations are performed in the correct sequence (Brackets, Orders/Indices, Division/Multiplication, Addition/Subtraction).

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Interpreting Remainders: Deciding whether to round up, round down, or express a remainder as a fraction/decimal based on the context of the problem.

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Hidden Questions: Identifying the intermediate step that must be solved before the final answer can be found.

📐Formulae

Total Cost=Quantity×Unit Price\text{Total Cost} = \text{Quantity} \times \text{Unit Price}

Change=Amount Paid−Total Cost\text{Change} = \text{Amount Paid} - \text{Total Cost}

BODMAS: Brackets→Orders→Division/Multiplication→Addition/Subtraction\text{BODMAS: } \text{Brackets} \rightarrow \text{Orders} \rightarrow \text{Division/Multiplication} \rightarrow \text{Addition/Subtraction}

Average=Sum of all itemsNumber of items\text{Average} = \frac{\text{Sum of all items}}{\text{Number of items}}

💡Examples

Problem 1:

A school orders 12 boxes of pencils. Each box contains 24 pencils. If the pencils are shared equally among 8 classes, how many pencils does each class receive?

Solution:

36 pencils

Explanation:

Step 1: Find the total number of pencils (12×24=28812 \times 24 = 288). Step 2: Divide the total pencils by the number of classes (288÷8=36288 \div 8 = 36).

Problem 2:

Maya buys 4 notebooks for 3.50eachand2bindersfor3.50 each and 2 binders for 5.25 each. She pays with a $50 note. How much change should she receive?

Solution:

$25.50

Explanation:

Step 1: Calculate the cost of notebooks (4×3.50=14.004 \times 3.50 = 14.00). Step 2: Calculate the cost of binders (2×5.25=10.502 \times 5.25 = 10.50). Step 3: Find the total spent (14.00+10.50=24.5014.00 + 10.50 = 24.50). Step 4: Subtract from the amount paid (50.00−24.50=25.5050.00 - 24.50 = 25.50).

Problem 3:

There are 154 students going on a field trip. Each bus can hold 40 students. How many buses are required to take all the students?

Solution:

4 buses

Explanation:

Step 1: Divide the total students by bus capacity (154÷40=3154 \div 40 = 3 remainder 3434). Step 2: Since 3 buses would leave 34 students behind, we must round up to the next whole number to accommodate everyone. Therefore, 4 buses are needed.