Using Mental Math For Estimation

Key Concepts

• Mental addition
• Mental subtraction
• More mental addition
• Rounding numbers to estimate
• Using front-end estimation.

Introduction 

In this chapter, we will learn about 2-digits addition and subtraction of numbers, and round the numbers up to the nearest estimation of 10 and add on. 

2.1. Mental Addition

Adding 2-digit numbers mentally using regrouping of numbers and separate their place values.

Example 1:  Add mentally 65 + 32 using number bonds. 

Sol:

Step 1: Add 3 tens to 65 => 65 + 30 = 95 

Step 2: Add 2 ones to the result = > 95 + 2 = 97

Example: Add mentally 54 + 42 using number bonds. 

Sol:   

Step 1: Add 4 tens to 54 => 54 + 42 = 94 

Step 2: Add 2 ones to the result => 94 + 2 = 96

2.2 Mental Subtraction

Subtracting 2-digit numbers mentally, using the tens and ones by regrouping numbers.    

Example: Find 97 – 24 

Step 1: Subtract 2 tens from 97 – 20 = 77 

Step 2: Subtract 4 ones from the result 77 – 4 = 73 

So, 97 – 24 = 73 

Example 2:  Subtracting the number using tens, then add the extra one’s strategy. 

53 – 28 

Step 1: Subtract 30 from 53 => 53 – 30 = 23 

Step 2: Add 2 to the result => 23 + 2 = 25 

So, 53 – 28 = 25 

2.3 More Mental Addition

Adding two-digit numbers mentally by adding 100, then subtracting the extra ones. 

Example: Find 49 + 97 

Sol: Add 100, then subtract the extra ones 

Step 1: Add 100 to 49 => 100 + 49 = 149 

Step 2: Subtract 3 from 149 => 149 – 3 = 146 

So, 49 + 97 =146 

Example: Find 95 + 96 

Sol: Add the hundreds, then subtract the extra ones 

Step 1: Add the hundreds 

100 + 100 = 200 

Step 2: Subtract 5 and 4 from 200 

200 – 5 – 4 = 191 

So, 95 + 96 = 191 

2.4 Rounding Numbers to Estimate

2.4.1 Round the number:

2576 is 2600 when rounded to the nearest hundred. 

Estimate:  A number close to the exact number. 

Reasonable: An estimated answer is reasonable when it is close to the actual answer. 

Example: Round 550 to the nearest 100? 

Sol: 

Example: Find 405 + 520 round to the nearest hundred, then add. 

Sol:  405 + 520 = 925 

         405 rounds to 400 

         520 rounds to 500 

         400 + 500 = 900 

         925 is about 900 

So, the answer is reasonable. 

Example: Find 869 – 214 rounds to the nearest hundred, then subtract. 

Sol:  869 – 214 = 655 

         869 rounds to 900 

         214 rounds to 200 

         900 – 200 = 700 

         655 is about 700 

So, the answer is reasonable.

2.5 Using Front-End Estimation

Front-end Estimation: Estimation that uses leading digits to estimate the sum and the digit.

Example: Find the sum of 478 and 96 using front-end estimation? 

Sol: 

Example: Find 465 + 216 use the value of leading digits to add.

Sol:  465 + 216 = 681 

681 is about 700 

So, the answer is reasonable. 

Example: Find 669 – 114. Use the value to the leading digits to subtract. 

Sol: 669 – 114 = 555 

555 is about 600 

So, the answer is reasonable. 

Exercise:

1. Find 26 + 31.
2. Find 28 + 34.
3. Find 46 + 56.
4. Subtract 33 – 23.
5. Subtract 63 – 53.
6. Add 98 and 97, by adding the hundreds and subtracting the ones. 
7. Find 34 + 26.
8. Find 465 + 519 and round to the nearest hundreds.
9. Find 679 – 413 and estimate the nearest value.
10. Find 98 – 33.
11. Subtract mentally 65 – 37.
12. Find the sum (or) difference and round up the answer of 234 and 457.
13. Find 36 + 26.
14. Find 715 – 232.
15. Jack has $66. He saves another $46. Estimate the amount he is having with him.

What we have learnt:

• Add mentally
• Subtract mentally
• Add or subtract, then use rounding to check that their answers are reasonable.
• Use front-end estimation to check their sums and differences.  

Concept Map