Estimate Products

Key Concepts

• Estimation of products
• Underestimation of products
• Overestimation of products

What is the meaning of estimate? 

Estimation means approximating a quantity to the required accuracy.  

Estimation of a number is a reasonable guess of the actual value to make calculations easier and realistic.  

• To estimate products, we round the given factors to the required place value.  
• To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers. 

Example: Estimate the product of 272 x 21. 

Here, 272 rounded to 300. 

21 rounded to 20 

Product is 6,000 

Estimation of products   

Example 1: 

73 injections of vaccination were sent to 389 hospitals each. Estimate how many total vaccination injections were sent out?  

Solution: 

Estimate 73 × 389. 

Step 1: 73 rounded to the nearest ten 

70 

Step 2: 389 rounded to the nearest hundred  

400 

Step 3: Add 3 zeros to get the estimated product. 

28,000 

This means 73 × 389 is about 28,000. 

Underestimation of products 

Example 1: 

A factory produces 612 shirts each day. Estimate how many shirts are produced in 42 days?  

Solution: 

Use rounding to estimate. 

Step 1: 

$ 612 rounds to $ 600. 

Step 2: 

42 rounds to 40. 

Step 3: 

Find 40 x 600. 

We know that 4 x 6 =24 

Step 4: 

Add 3 zeros to get the estimated product. 

40 x 600 =24, 000  

Both numbers used to estimate were less than the actual number. 

So, 24, 000 is an underestimate. 

Example 2: 

713 lunch trays are used every day during school lunchtime. Estimate how many lunch trays are used in 62 days?  

Step 1: 

713 rounds to 700. 

Step 2: 

62 rounds to 60. 

Step 3: 

Find 60 x 700. 

We know that 6 x 7 =42 

Step 4: 

Add 3 zeros to get the estimated product. 

60 x 700 =42, 000  

Both numbers used to estimate were less than the actual number. 

So, 42, 000 is an underestimate. 

Overestimation of products 

Example 1: 

Ships with 64 soldiers were sent out during a war. Each ship had 288 soldiers. Estimate how many soldiers in total were sent?  

Solution: 

Estimate 64 x 288. 

65 and 3 are compatible numbers because their product is easy to compute mentally. 

Step 1: 

Multiply 65 x 3=195 

Step 2: 

Add 1 zero 

 65 x 30 = 1950 

Step 3: 

Add 2 zeros. 

65 x 300 = 19,500 

So, 19,500 is a good estimate for 64 x 288. 

Both numbers used to estimate were greater than the actual numbers. 

So, 19, 500 is an overestimate. 

Example 2: 

An ATM machine is used by 498 people each day. Estimate how many people in total use it in 84 days?  

Solution: 

Estimate 84 x 498. 

85 and 4 are compatible numbers because their product is easy to compute mentally. 

Step 1: 

 Multiply 85 x 5=425 

Step 2: 

Add 1 zero  

 85 x 50 = 4, 250 

Step 3: 

Add 2 zeros. 

85 x 500 = 42,500 

So, 42,500 is a good estimate for 84 x 498. 

Both numbers used to estimate were greater than the actual numbers. 

So, 42, 500 is an overestimate. 

Exercise

• Estimate each product.

1. 90 x 136
2. 55 x 312
3. 39 x 256.

• Estimate and tell if your estimate is an overestimate or an underestimate.

1. 28 x 396
2. 42 x 204
3. 49 x 388

• Charmin counted the matches in a matchbox and got 58. How many matches approximately are in 8 boxes?
• One can costs 58 cents, and a boy is going to buy 18 of them. Estimate the cost of 18 Cans.    
• Mercy needs to estimate the product of 62 x 395. Explain two different methods Mercy can use to estimate.

• Round the first number to the nearest ten and multiply.

• A math seminar was conducted in 8 different locations in the country with 48 visitors in each instance. Estimate how many visitors in total attended the seminar throughout the county?
• 21 planes flew from one city to another from an airport. Each plane carried 92 passengers. Approximately how many passengers traveled totally? Choose the better estimate.
• Round each number to the nearest hundred and multiply.

• Estimate and tell estimate is an overestimate or underestimate.

33 x 124.

Concept Map

What have we learned

• Understand estimation.
• Understand overestimate.
• Understand underestimate.
• Estimate the products using rounding.
• Understand how to estimate the products and identify that is over estimate or under estimate.
• Using compatible numbers to estimate the products.