## 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.

- 90 x 136
- 55 x 312
- 39 x 256.

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

- 28 x 396
- 42 x 204
- 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.

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