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# 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.

### 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.

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