EDEXCEL GCSE FOUNDATION MATHS - What is Arithmetic with Decimals

Edexcel GCSE Foundation Maths: Arithmetic with Decimals

Understanding Decimals

Decimals are a way of representing fractions where the denominator is a power of 10 (e.g., 10, 100, 1000). The decimal point separates the whole number part from the fractional part.

Example: * 3.14 can be written as 3 and 14/100

Adding and Subtracting Decimals

1. Line up the decimal points: Ensure the decimal points are directly below each other.
2. Fill in placeholders with zeros: If necessary, add zeros to the right of the decimal point to make the numbers have the same number of decimal places.
3. Add or subtract as usual: Remember to carry over or borrow as needed.

Example:

  3.14
+ 2.50
-------
  5.64

Multiplying Decimals

1. Ignore the decimal points: Multiply the numbers as if they were whole numbers.
2. Count the decimal places: Count the total number of decimal places in both numbers.
3. Place the decimal point: In the answer, count from the right and place the decimal point so that the number of decimal places matches the total counted in step 2.

Example:

 2.5  (1 decimal place)
x 1.2  (1 decimal place)
-------
   50
+250
-------
 3.00 (2 decimal places)

Dividing Decimals

1. Move the decimal point in the divisor: Move the decimal point to the right until you have a whole number.
2. Move the decimal point in the dividend: Move the decimal point the same number of places to the right as you did in step 1.
3. Divide as usual: Perform the division as if the numbers were whole numbers.
4. Place the decimal point: Place the decimal point in the quotient directly above its position in the dividend.

Example:

 12.5 ÷ 2.5 = 125 ÷ 25 = 5

Rounding Decimals

1. Identify the place value to round to.
2. Look at the digit to the right of the place value.
3. If the digit is 5 or greater, round the digit in the place value up by 1.
4. If the digit is less than 5, keep the digit in the place value as it is.
5. Remove all digits to the right of the rounded place value.

Example: * Round 3.145 to two decimal places: 3.15 * Round 2.78 to the nearest tenth: 2.8

Practice Problems

1. Add the following decimals: 1.23 + 4.56

2. Subtract 2.75 from 5.00

3. Multiply 3.4 by 2.1

4. Divide 10.5 by 1.5

5. Round 7.895 to the nearest hundredth.

Solutions:

1. 5.79
2. 2.25
3. 7.14
4. 7
5. 7.90

Remember to practice these concepts regularly to build confidence and fluency in working with decimals.