# 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.

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.

I. 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.

II. 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.

III. Find the estimated product of 34 and 17 by rounding off to the nearest tens.

Rounding off 34 to nearest tens.

34 is nearer to 30 than 40.

So, 34 is rounded down to 30.

17 is nearer to 20 than 10.

So, 17 is rounded up to 20.

Now 30 × 20 = 600

So, the estimated product of 34 × 17 = 600

IV. Find the estimated product of 148 and 14 by rounding off to the nearest tens.

Rounding off 148 to nearest tens.

148 is nearer to 150 than 140.

So, 148 is rounded up to 150.

14 is nearer to 10 than 20.

So, 14 is rounded down to 10.

Now 150 × 10 = 1500

So, the estimated product of 148 × 14 = 1500

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

Word Problems on Estimating Products:

To solve any word problem, we need to read each word carefully and select numbers carefully from the question to solve it.

1. Ron has a crayon box containing 12 colors. He has 7 such boxes. How many crayons does he have in all?

 Solution:Colors in a crayon box = 15Total number of boxes = 7Total number of crayons in. 7 such boxes = 12 × 7

TRon has 84 crayons in all.

Questions and Answers on Estimation in Multiplication:

1. Find the estimated product for each of the given. First one is done for you.

(b) 70 × 40, 28000

(c) 300 × 100, 30000

(d) 200 × 200, 40000

(e) 700 × 200, 140000

(f) 500 × 400, 200000

(g) 900 × 500, 450000

(h) 3000 × 200, 600000

2. Find the estimated product of the following by rounding off the 2 and 3-digit numbers to the nearest tens.

(i) 121 × 17

(ii) 17 × 14

(iii) 93 × 12

(iv) 189 × 15

(v) 164 × 16

(vi) 335 × 13

2. (i) 2400

(ii) 200

(iii) 900

(iv) 3800

(v) 3200

(vi) 3400

3. Choose the best estimate and tick the right answer.

I. A shopkeeper has 92 packets of chocolates. If each packet has 37 chocolates, then how many chocolates are there in the shop.

(i) 3600                             (ii) 4000

II. A museum has 219 marble jars. Each jar has 178 marbles. What is the total number of marbles in the museum?

(i) 40000                            (ii) 50000

III. There are 76 houses in a locality. Each house uses 278 units of electricity each day. How many units of electricity is used each day in the locality?

(i) 24000                            (ii) 30000

IV. A hotel has 18 water tanks and each tank has the capacity of 4089 litres of water. What is the total quantity of water that can be stored by the hotel?

(i) 80000                            (ii) 16000

3. I. (ii)

II. (i)

III. (ii)

IV. (i)

Worksheet on Word Problems on Estimating Products:

4. Solve the given word problems.

(i)There are 157 pages in a book. How many pages are there in 4 such books?

(ii) Mary eat 6 nuts daily. How many nuts does she eat in 120 days?

(iii) Tina bought a pencil box which has 24 pencils in it. If she gets 5 such boxes then how many pencils will she have in all?

(iv) A packet of nuts contains 233 nuts. There are 3 such packets. How many nuts are there in all?

(v) There are 120 students in one class. How many students are there in 8 classes?

(vi) Shelly and her brother filled a basket with 57 fruits. They both together filled 6 such baskets. How many fruits they have in all the baskets?

4. (i) 628

(ii) 720

(iii) 120

(iv) 699

(v) 960

(vi) 342

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