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1. What are addends and sums?
When two numbers are added, then each of the numbers to be added is called addend and the result obtained is called the sum.
Example: Marry gives £6 to her one friend and £4 to her other friend. How much total money did she give?
£6 + £4 = £10
Total money she gave = £10
Here £6 and £4 are addends and £10 is the sum.
2. Column Addition
2.1 Without carry
Steps:
- Place the numbers on the top of each other, by lining up the hundreds, tens and ones.
- Add them column-wise from right to left. (first, add the ones, then the tens, then the hundreds and so on).
Example: Add 234 and 462.
2.2 WIth carry
Steps:
- Place the numbers on the top of each other, by lining up the hundreds, tens and ones.
- Add them column-wise from right to left.
- If the sum in any column is more than 9, write the one's digit under that particular column, and carry the tens digit to the next column.
- Add up the carry with the addends for the respective column.
Example: Find the sum of 758 and 363.
3. Addition
3.1 Addition of decimals
Steps:
- Arrange the numbers under each other, with the decimal points lined up.
- Put in zeros on empty places.
- Perform the column addition.
- Include decimal in the final result.
Example:
Add 34.56, 67.98 and 12.34
Solution:
Arrange the numbers under each other along with the decimals.
Start adding from right to left.
Include decimal in the final answer.
3.2 Addition of fractions
Steps:
- Check the denominators of the fractions.
- If denominators are the same, add the numerators, keeping the denominators the same.
- If denominators are not the same, make the denominators the same, by finding the LCM of denominators and rationalising them.
- Now, add the numerators, keeping the denominators the same.
- Hence, reduce the fraction to get the final sum.
Example: Add fractions 4 + 3⁄4+ 1⁄2
Solution:
Let us consider 1 as a denominator of 4.
LCM of 4 and 2 is 4.
Rewrite both the fractions as equivalent fractions with 4 as the denominator and then add fractions.
16⁄4 + 3⁄4 + 2⁄4 = 21⁄4
