# Estimating Products

Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate the sum, difference, etc., to the nearest 10, 100, 1000, etc. Now we have to estimate the products.

In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.

1. Estimate the products of 34 and 86.

34 ⟶ 30 34 is rounded down to 30

86 ⟶ 90 86 rounded up to 90

 34 ⟶ 30 86 ⟶ 90 34 is rounded down to 3086 rounded up to 90

Calculate mentally 30 × 90 = 2700

The estimated product is 2700.

2. Estimate the products of 331 and 267 by rounding to the nearest hundred.

331 ⟶ 300

267 ⟶ 300

300 × 300 = 90000

The estimated product is 90000.

Consider the following examples on estimating products:

1. Estimate the product: 42 × 57

Solution:

4 2 →    4 0

× 5 7 → × 6 0

2 4 0 0

Thus estimated product = 2400

2. Estimate the product: 47 × 84

Solution:

4 7 × 8 4         47 is rounded up to 50

↓       ↓

5 0 × 8 0         84 is rounded down to 80

= 4 0 0 0

The estimated product = 4000

3. Estimate the product: 74 × 85

Solution:

7 4 × 8 5         74 is rounded up to 80

↓       ↓

7 0 × 9 0         85 is rounded down to 90

= 6 3 0 0

6300 is the estimated product

4. Estimate the product: 358 × 326

Solution:

One number is rounded up and the other is rounded down. Here 358 is rounded up to the nearest hundred, i.e., 400 while 326 is rounded down to the nearest hundred, i.e., 300.

3 5 8 × 3 2 6         358 is rounded up to 400

↓         ↓

4 0 0 × 3 0 0        326 is rounded down to 300

= 1 2 0 0 0 0

120000 is the estimated product

5. Estimate the following product by rounding numbers to the nearest;

(i) Hundred

(ii) Ten ‘341 × 267’

Solution:

(i)     3 4 1 × 2 6 7          341 is rounded up to 300

↓         ↓

3 0 0 × 3 0 0           267 is rounded down to 300

= 90,000 & The estimated product is 90,000

(ii)     3 4 1 × 2 6 7         341 is rounded down to 340, the nearest ten

↓         ↓

3 4 0 × 2 7 0           267 is rounded up to 270, the nearest ten

= 91,800 The estimated product is 91,800

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