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Decimals – Adding and Subtracting Decimals

📘 Notes

🧮 Adding and Subtracting Decimals (Year 7)

When we add or subtract decimals, the most important rule is to line up the decimal points. This makes sure that each place value (ones, tenths, hundredths, etc.) is in the correct column.

1. ➕ Adding Decimals using Column Method

Step-by-step:

  1. Line up the numbers so that the decimal points are exactly on top of each other.
  2. If one number has fewer decimal places, add zeros to make them the same length.
  3. Add from right to left (just like whole numbers).
  4. Bring the decimal point straight down into the answer.
Example 1: \( 3.45 + 1.2 \) 
   3.45
+  1.20
-------
   4.65

Add each column: \( 5+0=5 \), \( 4+2=6 \), \( 3+1=4 \). Answer: \( 4.65 \)

Example 2: \( 0.8 + 2.34 \) 
   0.80
+  2.34
-------
   3.14

Add zeros if needed to keep columns neat.

2. ➖ Subtracting Decimals using Column Method

Step-by-step:

  1. Line up the decimal points.
  2. Make sure both numbers have the same number of decimal places (add zeros if needed).
  3. Subtract from right to left (borrow if necessary).
  4. Bring the decimal point straight down into the answer.
Example 1: \( 5.60 - 2.35 \) 
   5.60
-  2.35
-------
   3.25

Subtract column by column: \( 0-5 \) (borrow → \( 10-5 = 5 \)), \( 5-3 = 2 \), \( 5-2 = 3 \). Answer: \( 3.25 \)

Example 2: \( 7.1 - 4.85 \) 
   7.10
-  4.85
-------
   2.25

Borrow carefully when subtracting across decimals.

3. ➕➖ Adding and Subtracting Positive and Negative Decimals

When working with negative numbers, think about number lines:

  • Adding a negative number means moving left on the number line.
  • Subtracting a negative number means moving right on the number line.
  • Subtracting a negative is the same as adding a positive.
Example 1: \( 3.4 + (-1.2) \)

Start at \( 3.4 \), move left \( 1.2 \) → Answer: \( 2.2 \). 

   3.40
-  1.20
-------
   2.20
Example 2: \( -2.5 + 1.5 \)

Start at \( -2.5 \), move right \( 1.5 \) → Answer: \( -1.0 \).

Example 3: \( 4.2 - (-1.3) \)

Subtracting a negative is the same as adding: \( 4.2 - (-1.3) = 4.2 + 1.3 = 5.5 \).

📌 Key Points:

  • Always line up decimal points vertically in column addition or subtraction.
  • Add zeros to make decimals the same length if needed.
  • For negative numbers, think of moving left or right on a number line.
  • Subtracting a negative number is the same as adding a positive.
  • Bring the decimal point straight down into the answer.