#### Need Help?

Get in touch with us

# Add Using Mental Math and Partial Sum

## Key Concepts

• Addition of numbers by partial sum using mental math
• Addition of numbers by partial sum using place values

## Introduction

We can add two 2-digit numbers in different ways as given below:

• One way: Add mentally by partial sums using blocks.
• Another way: Add partial sums using ‘mentally break apart as tens and ones.’

### Add mentally by partial sums using blocks

Let’s consider an example to understand the sum of 2-digit numbers by partial sum using place-value blocks.

Example 1:

Find 35 + 37.

Solution:

Step 1:

Represent 35 and 37 as place value blocks

Step 2:

Find the partial sum by adding tens and ones.

3 tens + 3 tens = 6 tens

5 ones + 7 ones = 12 ones

60 and 12 are partial sums.

Step 3:

Find the sum.

So, 35 + 37 = 72.

Example 2:

Find 46 + 15.

Solution:

Step 1:

Represent 46 and 15 as place value blocks

Step 2:

Find the partial sum by adding tens and ones.

4 tens + 1 ten = 5 tens

6 ones + 5 ones = 11 ones

50 and 11 are partial sums.

Step 3:

Find the sum.

So, 46 + 15 = 61.

### Add by partial sums using mentally break apart as tens and ones

Let’s consider another example to understand the sum of 2-digit numbers by mental math.

Example 3:

Find 53 + 18.

Solution:

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

50 + 10 = 60

3 + 8 = 11

60 and 11 are partial sums.

Step 3:

Find the sum.

So, 53 + 18 = 71.

Example 4:

Find the sum of 23 and 71.

Solution:

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

20 + 70 = 90

3 + 1 = 4

90 and 4 are the partial sums.

Step 3:

Find the sum.

So, 23 + 71 = 94.

#### Model question

Question:

Henry has a collection of 18 stamps. Bruce has a collection of 26 stamps. How many stamps do they have in all? Write an addition problem by using partial sums.

Number of stamps with Henry = 18

Number of stamps with Bruce = 26

The total stamps they have in all = 18 + 26

Find the sum of 18 + 26.

Step 1:

Mentally break apart the numbers using tens and ones.

Step 2:

Find the partial sum by adding tens and ones.

10 + 20 = 30

8 + 6 = 14

30 and 14 are partial sums.

Step 3:

Find the sum.

18 + 26 = 44.

So, Henry and Bruce have a collection of 44 stamps in all.

#### Activity

Monica has 28 candies with her, and Simon has 16 candies with him. Help them to find how many candies do have in all. (Use partial sum. Add any way you choose)

## Exercise

• Find the sum of 29 and 28 by partial sums using place value blocks.
• Write the addition problem of 34 and 63. Use partial sum by using mental math.
• Nash has 21 red-colored cards, and Nash has 47 blue-colored cards. How many cards do they have in total?
• Archer has a collection of 16 watches, and August has a collect of 25 watches. How many watches do they have in all?
• On Monday, Diego puts 37 pennies in his bank. On Tuesday, he puts 43 pennies in his bank. How many pennies does he have put in his bank in both days?

### What have we learned

• Add numbers by partial sum using mental math
• Add numbers by partial sum using place value
• Solve model questions related to addition

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […] #### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […] #### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]   