Test: Addition and Subtraction of Whole Numbers - Year 4 MCQ

The correct statement is:

d) Odd + Odd = Even

Explanation:

• d) Odd + Odd = Even — True. Example: 3 + 5 = 8

• b) Even + Odd = Even — false. Example: 2 + 3 = 5

• a) Even + Even = Odd — False. Example: 4 + 6 = 10

Adding three odd numbers always results in an odd number. For example, 1 + 3 + 5 = 9 and 11 + 23 + 35 = 69. This is because each odd number has a remainder of 1 when divided by 2, and the sum of three such remainders (3) is odd, ensuring the total sum is odd. This generalisation holds for all cases, as confirmed by testing multiple examples.

To find the missing number in the equation 30 − _ = 27, rewrite it as a subtraction problem: 30 − 27 = _. This gives 3, so the missing number is 3. Alternatively, using a number line, count from 27 to 30, which requires adding 3. This demonstrates the inverse relationship between addition and subtraction.

A counter-example is an example that disproves a statement. For instance, if someone claims that adding three odd numbers results in an even number (e.g., 50), a counter-example like 1 + 3 + 5 = 9 (odd) disproves it. Counter-examples are essential for testing generalisations about odd and even numbers to ensure their accuracy.

"Compose" means combining parts to form a whole number. For example, if we add 200 + 30 + 5, we compose the number 235. This is the opposite of decomposing, which involves breaking numbers into their place value components.

A blank space is commonly used to represent a missing number in equations, such as 30 − _ = 27. Other symbols like a square or circle can also be used, but the blank space is the most standard choice. This practice introduces algebraic thinking and prepares students for solving equations with unknowns.

To find the missing number in the equation 650 + _ = 1000, you can rewrite the equation as a subtraction problem: 1000 - 650 = _. This gives the answer of 350. This method is effective because it transforms the problem into a more straightforward calculation, demonstrating the inverse relationship between addition and subtraction.

When two odd numbers are added together, the result is always an even number. For example, 3 + 5 = 8 and 7 + 9 = 16. This is because the sum of two odd integers results in a total that can be evenly divided by 2, illustrating a consistent pattern in number theory. This property is crucial for understanding more complex mathematical concepts.

The term used for breaking a number into its place value components is "decomposing." For instance, the number 235 can be decomposed into 200 + 30 + 5. This technique aids in understanding the value of each digit in a number and is especially useful in addition and subtraction calculations, as it simplifies the arithmetic process.

"Regrouping" refers to the process of rearranging numbers during calculations to facilitate addition or subtraction, such as when borrowing in subtraction or carrying in addition. For example, in the subtraction problem 459 - 318, regrouping is necessary to handle the borrowing when subtracting 8 from 9. This method allows students to manage calculations more effectively and enhances their overall numerical skills.