Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Place Value System in Decimals: In Grade 5 math, decimals extend the whole number system. The decimal point acts as a separator between whole numbers and fractional parts. To the right of the point, the values are Tenths (), Hundredths (), and Thousandths (). Visualise a place value chart where the 'Units' column is on the left of the decimal point and the 'Tenths' column is on the immediate right.
Like and Unlike Decimals: Like decimals have the same number of decimal places (e.g., and ). Unlike decimals have different numbers of decimal places (e.g., and ). For calculations, unlike decimals are often converted into like decimals.
The Role of Placeholder Zeros: You can add zeros to the end of a decimal without changing its value (). Visualise filling empty spaces in a grid with zeros to make all numbers the same length, which helps prevent alignment errors during addition or subtraction.
Vertical Alignment: The most critical step is to align the decimal points vertically in a straight line. Visualise a vertical 'spine' or 'wall' that every decimal point must touch. This ensures that you are adding units to units, tenths to tenths, and so on.
Addition with Regrouping: When the sum in any column (like the hundredths) reaches or more, you must 'carry over' the digit to the column on the left. It is exactly like addition of whole numbers, provided the decimal points remain lined up.
Subtraction and Borrowing: When the digit on top is smaller than the digit below it in the same column, you must borrow from the column to the left. For example, if you have in the hundredths place and need to subtract , borrow from the tenths place.
Decimal Point in the Final Result: Once the digits are added or subtracted, place the decimal point in the answer directly below the column of decimal points used in the problem.
📐Formulae
💡Examples
Problem 1:
Add and .
Solution:
Step 1: Convert to a like decimal by adding a zero: . Step 2: Align the decimal points vertically:
Explanation:
We add a placeholder zero to to make it . In the hundredths place, . In the tenths place, ; we write and carry over to the units place. In the units place, ; we write and carry to the tens place. In the tens place, . The final sum is .
Problem 2:
Subtract from .
Solution:
Step 1: Convert to a like decimal: . Step 2: Align the decimal points:
Explanation:
We add a zero to to get . To subtract from in the hundredths place, we borrow from the tenths place. The in the tenths place becomes , and the in the hundredths becomes . . Now in the tenths place, we have ; we borrow from the units ( becomes after borrowing from tens), making the tenths place . . In the units, . In the tens, . The result is .