Calculation of sums

Definition:

The sum is the addition which means joining things together. It can also be defined as combining the collections of objects together into a larger collection is addition. It is represented by the ‘+’ sign. The sum can be obtained by adding the integers using the number line. 

Solved Examples:

Q.1) What is the value of 5 + 5?

Answer: The result is 10. To obtain the result take 5 then add 5 to it.

Q.2) What is the value of 6 + 8?

Answer: The result is 14. To obtain the result take 6 then add 8 to it.

Calculation of difference

Definition:

Difference is the subtraction which means taking things away from a group. The subtraction of integers done using the number line. Add a positive integer by moving to the right on number line or by taking away a given number of objects from a given collection of objects is subtraction. It is represented by the ‘-’ sign. A greater number cannot be subtracted from a smaller number.  

Solved Examples:

Q.1) Subtract 5 from 10?

Answer: The result is 5.  From 10 take away 5 is 5, i.e. 10 - 5 = 5

Q.2) Subtract 255 from 110?

Answer: The result is 145.  From 255 take away 110 is 145, i.e. 255 - 110 = 145

Calculation of product

Definition:

Product is adding a certain number of objects again and again is Multiplication. Multiplication means Counting by number. Counting by 2's means 2, 4, 6, 8...and so on Similarly Counting by 5's means 5, 10, 15, 20...and so on. It is represented by the ‘x’ sign.

Solved Examples:

Q.1) How much is 21 x 2?

Answer: The result is 42. To obtain the result multiply the unit digit 1 in 21 by 2. Write the product 2 in the unit place then multiply the tens digit 2 in 21 by 2 the write the product 4 in the tens place. Hence, the answer is 21 x 2 = 42.

Q.2) How much is 12 x 4?

Answer: The result is 48. To obtain the result multiply the unit digit 2 in 12 by 4. Write the product 8 in the unit place then multiply the tens digit 1 in 12 by 4 the write the product 4 in the tens place. Hence, the answer is 12 x 4 = 48.

Quotient of positive whole numbers

Definition

Subtracting a certain number of objects again and again is division. The quotient is the obtained result from the division. It is represented by the ‘÷’ sign.

Solved Examples:

Q.1) How much is 21 ÷ 7?

Answer: To divide 21 by 7, say the 7 times table up to 21. Hence, 3 is the quotient. Subtract the product of 7 and 3 from 21, the remainder is zero. Hence, 21 ÷ 7 = 3.

Q.2) How much is 44 ÷ 2?

Answer: To divide 44 by 2, say the 2 times table up to 44. Hence, 22 is the quotient. Subtract the product of 2 and 22 from 44 the remainder is zero. Hence, 44 ÷ 2 = 22.

Calculate the result of operations on fractions

Solved Examples:

Multiply the numerators together, then multiply the denominators together.

Simplify complex fractions

Method 1

1. Create a single fraction in the numerator and denominator.
2. Apply the division rule of fractions by multiplying the numerator by the reciprocal or inverse of the denominator.
3. Simplify, if necessary.
4. Find the Least Common Denominator (LCD) of all the denominators in the complex fractions.
5. Multiply this LCD to the numerator and denominator of the complex fraction.
6. Simplify, if necessary.

Method 2

Method 2 is much better than Method 1 because almost always it takes less number of steps to get to the final answer.

Solved Example:

Q.1) Simplify the complex fraction below.

Answer: Using Method 1, both the numerator and denominator of the complex fraction are already expressed as single fractions.