Estimation: Rounding and Compatible numbers

Estimate: Use Rounding or Compatible Numbers

What is Meant by Estimate?

Estimation of a number is finding a number that is close enough to the actual value to make calculations easier and more realistic.

This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.

Here’s General Rule for Rounding:

• If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

            Example: 39 rounded to the nearest ten is 40.

• If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 32 rounded to the nearest ten is 30.

What Are Compatible Numbers?

Compatible numbers are numbers that are easy to add, subtract, multiply, or divide mentally.

We use compatible numbers to make the problem easier to solve in our head by rounding each number to the nearest ten, twenty, fifty, or hundred.

The below image is an example of compatible numbers:

Estimation of Products Through Rounding

A game rewards a player 13 points every time the player finds a treasure chest. How many points will the players get if Player A finds 25 treasure chests and Player B finds 23 treasure chests? Find the total number of points.

 Solution:

 Step 1: Add 25 + 23 = 48 treasure chests.

  Use rounding to estimate 48 x 13.

  Step 2:   Round 48 to the nearest 10.

              Round 13 to the nearest 10.

Step 3: Multiply 50 x 10 

             50 x 10 = 500

             Players get 500 points.

Example 2:

Robin buys 13 dozen oranges, and his friend buys 14 dozen oranges to give to an old age home. There are 12 oranges in 1 dozen. How many oranges did they buy?

Solution:

 Step 1: Add 13 + 14 = 27 dozen.

            27 dozen oranges were bought in total.

            Use rounding to estimate 27 x 12.

Step 2:   Round 27 to the nearest 10.

              Round 12 to the nearest 10.

Example 3:

 Estimate a product of 18 x 24.

Solution:

Step 1: Use rounding to estimate 18 x 24.

Step 2: Round 18 to the nearest 10.

              Round 24 to the nearest 10.

Step 2: Multiply 20 x 20. 

               20 x 20 = 400

               Product = 400

Estimation of Products Through Compatible Numbers

Example 1:

There are 37 players on each high school football team. If there are 29 teams. Find the total number of players.

Solution:

Use compatible numbers to estimate 37 x 29.

Step 1: Replace the factors with numbers that are close and easy to multiply.

             37 is close to 35                                    29 is close to 30

Step 2:    35x 30 =n

                 1,050 =n

           1,050 players are there in 29 teams.

Example 2:

The Girl Scouts are having their annual cookies sale. Emily sells 68 boxes of cookies each day.

After 76 days, how many boxes of cookies did Emily sell?

Solution:

Use compatible numbers to estimate 68 × 76.

Step 1: Replace the factors with numbers that are close and easy to multiply.

             68 is close to 70                                    76 is close to 75

Step 2:    70× 75 =n

                    5, 250 = n Emily sells 5, 250 boxes in 76 days.             

Exercise:

1. Estimate each product. Explain why you chose the strategy you used to estimate the product.
   • 34 × 56
   • 27 × 34
   • 23 × 12 
2. Estimate the products of 44 and 76.
3. Find the estimated product of 54 and 27 by rounding off to the nearest tens.
4. Ron has a crayon box containing 12 colors. He has 18 such boxes. How many crayons does he have in all?
5. A museum has 21 marble jars. Each jar has 78 marbles. What is the total number of marbles in the museum?
6. Mary eats 14 nuts daily. How many nuts does she eat in 20 days?
7. Use compatible numbers to estimate 23 x 34.
8. Write computable numbers for the following numbers.
9. 76
   • 34
   • 89
   • 58
10. Estimate to check if the given answer is reasonable.

            67 × 41 = 2, 747

            Rounded to ___________ ×   _____________ = _______________

1. Estimate to check if the given answer is reasonable.

34 × 42 = 1, 428

Rounded to ___________ ×   _____________ = _______________

Concept Map:

What Have We Learned:

• Understand an estimation and compatible numbers.
• Understand rules for rounding numbers.
• Understand how to estimate of products through rounding.
• Identify compatible numbers for given numbers.
• Understand how to estimate products through Compatible numbers.