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Mental Math – Finding Sums and Differences Easily

Key Concepts

  • Finding Sums and Differences with Mental Math
  • Estimate Sums and Differences

Finding Sums and Differences with Mental Math

Mental Math:  

  • Mental math is a group of skills that allow people to do the math ‘in their head’ without using a pencil, paper, or calculator. 
  • Mental math is useful in school and in everyday life. 
  • Mental math can help kids understand math concepts better and get to the answers faster. 
mental math

Solving mental math with the help of properties of addition and subtraction 

Associative Property 

a + (b + c) = (a + b) + c  

Commutative Property 

a + b = b + a 

Identity Property 

a + 0 = a 

Example 1:  

Find $1,985 + 2,595 with mental math. Use addition properties to find the sum 

Using Associative Property: 

Break apart 1,985 to get a number that makes a ten, hundred, or thousand when added to 2,595. Then use the associative property of addition to change the grouping. 

1,985 + 2,595  

= (1,580 + 405) + 2,595 

= 1,580 + (405 + 2,595) 

= 1,580 + 3,000 

= 4,580 

Using Commutative Property: 

Break one addend apart and add on 

Using Commutative Property: 

You can start with either addend because of the commutative property of addition. 

Using Commutative Property: 

Using Identity Property: 

Add 15 to 1,985. Then subtract 15 from 2,595 to compensate. Adding 15 and subtracting 15 is the same as adding zero. Adding zero does not change the sum because of the identity property of addition

1,985 + 2,595 

         = (1,985 + 15) + (2,595 – 15) 

         = 2,000 + 2,580 

         = 4,580 

Example 2: 

Subtract 2,595 – 1,985 with mental math. Use subtraction properties to find the difference  

Count Up 

Count from 1,985 up to 2,595 

Count Up 

Find how much you counted up 

5 + 10 + 595 = 610  

Count Down 

Count down 1,985 from 2,595 

Count Down 

Use compensation 

Adding the same amount to both numbers in a subtraction problem does not change the difference.  

(2,595 + 15) – (1,985 + 15) 

= 2,610 – 2,000 

= 610 

Estimate Sums and Differences 

Estimation is the process of finding an estimate or approximation 

Estimating Sums 

Estimating Sums 

You could also round 5, 387 to the hundreds place, 

Step 1: Rounding is always first decide which place to round to. 

Step 2: Round the first addend to the thousands place and the second addend to the hundreds place. 

Step 3: Now you can add 5, 400 and 400 mentally. 

Estimating Differences 

Estimating Differences 

The actual answer is 33,209, so our estimation is pretty accurate. 

Step 1: Rounding is always first decide which place to round to. 

Step 2: Round each addend to the ten thousands place. 

Step 3: Now you can subtract 20, 000 from 50, 000 mentally. 

Example:  

12,642 books, 4,298 magazines, and 2,149 movies were checked out of the public library. About how many more books were checked out than magazines and movies combined? 

Estimate: Round to the nearest thousand 

Find the number of movies and magazines 

4,298 –> 4,000 

+2,149 –> + 2,000 

= 6,000 

Subtract the number of magazines and movies from the rounded number of books 

13,000 – 6,000 = 7,000 

About 7,000 more books were checked out 

Estimate: Round to the nearest hundreds 

Find the number of movies and magazines 

4,298 —-> 4,300 

+2,149 —-> + 2,100 

= 6,400 

Subtract the number of magazines and movies from the rounded number of books 

12,600 – 6,400 = 6,200 

Exercise:

Read and answer each question: The table shows the number of people visiting an art museum over 3 months.

 JanuaryFebruaryMarch
Child283456
Adult59?55
Senior1522?
Total?139?
  1. What is the total number of people that visited the art museum in January?
  2. Compared to January, how many more children go to the museum in February?
  3. How many adults visited the museum in February?
  4. 16 more seniors visited in March than the number that visited in January and February combined. How many seniors visited the museum in March?
  5. Which month had the highest number of visitors?
  6. Write an equation using x and then solve the equation.
    “In February, there were x museum pass holders admitted to the museum. 68 of the visitors did not have a museum pass.”
  7. Ashley finds a dress that costs $116 and a hat that costs $42. How much does she need to pay if people buying two clothing items get $15 off on the second item?
  8. Estimate and add: 7549 + 3808 + 4261.
  9. Rachel shots baskets each day for a period of 2 weeks. She shot a total of 2260 baskets. Rachel shot 100 more baskets each day during the last 3 days. How many shots per day did she take during the first week?
  10. A school has a total of 1258 students. There are 297 primary students and 364 junior students. How many senior students are there?

What have we learnt:

  • How to add multi-digit numbers using the standard algorithm
  • How to subtract multi-digit numbers using the standard algorithm
  • The different properties of addition
  • Finding sums and differences with mental math
  • Understand how to estimate sums and differences

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Concept Map 
Concept Map 

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