Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Identifying Addition Keywords: In word problems, certain words signal that you need to perform addition. Look for keywords such as 'Total', 'Sum', 'Altogether', 'In all', 'Combined', 'Plus', and 'Increase by'. Imagine these words as a green light on a traffic signal, telling you to join groups together.
Understanding Addends and Sum: The numbers that are being added together are called 'Addends', and the final answer is called the 'Sum'. You can visualize this as two or more separate baskets of fruit being poured into one single, larger basket that represents the sum.
Place Value Alignment: When solving word problems, it is crucial to arrange the numbers in vertical columns according to their place values: Thousands (), Hundreds (), Tens (), and Ones (). Imagine vertical grid lines helping you keep each digit in its correct home so they don't get mixed up.
Regrouping (Carrying Over): If the sum of the digits in one column (like the Ones column) is or more, you must 'regroup' or 'carry over' the tens digit to the next column on the left. Visualize a small '1' sitting on top of the next column's roof, waiting to be added to that group.
The Identity Property of Zero: Adding zero to any number does not change its value (). In a word problem, if one group has zero items, the total remains equal to the other group. Picture a box with toys and another box that is completely empty; when you put them together, you still have exactly toys.
Commutative Property of Addition: The order in which you add the numbers does not change the sum (). In word problems, it doesn't matter if you count the apples first or the oranges first; the total fruit count stays the same. Imagine a see-saw that stays perfectly balanced even if the two people on it switch seats.
Estimating the Sum: Before solving, you can round numbers to the nearest or to get a 'rough idea' of the answer. This helps you check if your final answer makes sense. Think of it as a 'sanity check' to ensure your total isn't way too high or way too low.
📐Formulae
💡Examples
Problem 1:
A flower shop sold roses on Monday and roses on Tuesday. How many roses did the shop sell in total over the two days?
Solution:
Step 1: Identify the numbers (Addends). Roses on Monday = Roses on Tuesday =
Step 2: Arrange the numbers in columns: \begin{array}{r@{\quad}cccc} & Th & H & T & O \\ & 1 & 2 & 4 & 5 \\ + & 2 & 8 & 7 & 6 \\ \hline \end{array}
Step 3: Add the Ones: . Write in the Ones place and carry to the Tens place. Step 4: Add the Tens: . Write in the Tens place and carry to the Hundreds place. Step 5: Add the Hundreds: . Write in the Hundreds place and carry to the Thousands place. Step 6: Add the Thousands: .
Total =
Explanation:
This is a word problem where the keyword 'in total' indicates addition. We align the numbers by place value and use regrouping (carrying) for the Ones, Tens, and Hundreds columns.
Problem 2:
In a school library, there are English books and Mathematics books. What is the sum of books in the library?
Solution:
Step 1: Write down the information provided. English books = Math books =
Step 2: Set up the addition: \begin{array}{r@{\quad}cccc} & Th & H & T & O \\ & 3 & 4 & 5 & 0 \\ + & 2 & 1 & 2 & 0 \\ \hline & 5 & 5 & 7 & 0 \\ \hline \end{array}
Step 3: Add column by column from right to left: Ones: Tens: Hundreds: Thousands:
The sum is .
Explanation:
The keyword 'sum' tells us to add. Since the sum of each column is less than , no regrouping (carrying) is required for this problem.