When we estimate 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 appreciate the products.

In order to assess products, we round the given factors to the required value. Estimation products help us check the appropriateness of an answer.

To estimate the product, we first round the multiplier and 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 **Low** until 30

86 ⟶ 90 86 rounded **above** to 90

34 30 86 90 |
34 is rounded 86 rounded |

Mentally compute 30 × 90 = 2700

The estimated product is 2700.

**II. Estimate the products of 331 and 267 by rounding up 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 up to the nearest tens.**

Round down from 34 to the nearest tens.

34 is more likely to be 30 than 40.

So 34 is rounded down to 30.

17 is closer to 20 than 10.

So 17 is rounded up to 20.

Now 30 × 20 = 600

The estimated product of 34 × 17 = 600

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

Round down from 148 to the nearest tens.

148 is closer to 150 than 140.

148 is rounded up to 150.

14 is closer to 10 than 20.

So 14 is rounded down to 10.

Now 150 × 10 = 1500

The estimated product of 148 × 14 = 1500

Consider the following examples of estimating products:

**1.** Estimate the product: 42 × 57

**Solution:**

4 2 → 4 0

× 5 7 → __× 6 0__

__ 2 4 0 0 __

**So estimated product = 2400**

**2.** Estimate the product: 47 × 84

**Solution: **

4 7 × 8 4 47 becomes 50. rounded up

↓ ↓

5 0 × 8 0 84 becomes 80. rounded

= 4 0 0 0

**The estimated product = 4000**

**3.** Estimate the product: 74 × 85

**Solution: **

7 4 × 8 5 74 becomes 80. rounded up

↓ ↓

7 0 × 9 0 85 becomes 90. rounded

= 6 3 0 0

**6300 is the most valued product**

**4th** 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 becomes 400. rounded up

↓ ↓

4 0 0 × 3 0 0 326 becomes 300. rounded

= 1 2 0 0 0 0

**120000 is the estimated product**

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

(i) Hundred

(ii) Ten ‘341 × 267’

**Solution: **

(i) 3 4 1 × 2 6 7 341 becomes 300. rounded up

↓ ↓

3 0 0 × 3 0 0 267 becomes 300. rounded

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

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

↓ ↓

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

= 91,800 **The estimated product is 91,800**

Word problems when estimating products:

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

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

Colors in a box of crayons = 15 Total number of boxes = 7 Total number of colored pencils in. 7 such boxes = 12 × 7 |

TRon has a total of 84 colored pencils.

Questions and answers about estimating when multiplying:

**1. Find the estimated product for each of the given. The first is done for you.**

**Reply:**

(b) 70 × 40, 28000

(c) 300 × 100, 30000

(d) 200 × 200, 40000

(e) 700 × 200, 140000

(f) 500 × 400, 200000

(g) 900 × 500, 450,000

(h) 3000 × 200, 600000

**2. Find the estimated product of the following numbers by rounding the two and three digit numbers to the nearest tens.**

(i) 121 × 17

(ii) 17 × 14

(iii) 93 × 12

(iv) 189 × 15

(v) 164 × 16

(vi) 335 × 13

**Reply:**

**2.** (i) 2400

(ii) 200

(iii) 900

(iv) 3800

(v) 3200

(vi) 3400

**3. Choose the best estimate and tick the correct answer.**

**I.** A shopkeeper has 92 packets of chocolates. If there are 37 chocolates in each box, how many chocolates are there in the store?

(i) 3600 (ii) 4000

**II.** A museum has 219 marble jugs. Each jar contains 178 marbles. How many marbles are in the museum in total?

(i) 40000 (ii) 50000

**III.** There are 76 houses in one village. Each house uses 278 units of electricity per day. How many electricity units are used in the village every day?

(i) 24,000 (ii) 30,000

**IV.** A hotel has 18 water tanks and each tank has a capacity of 4089 liters of water. How much water can the hotel store in total?

(i) 80000 (ii) 16000

**Reply:**

**3. i. **(ii)

**II. **(I)

**III. **(ii)

**IV. **(I)

Worksheet on Word Problems Estimating Products:

**4. Solve the given word problems.**

(i) A book has 157 pages. How many pages do 4 such books have?

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

(iii) Tina bought a pencil box with 24 pens. If she gets 5 such boxes, how many pencils does she have in total?

(iv) One packet of nuts contains 233 nuts. There are 3 such packages. How many nuts are there in total?

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

(vi) Shelly and her brother filled a basket with 57 fruits. Both together filled 6 such baskets. How many fruits do you have in each of the baskets?

**Reply:**

**4th** (i) 628

(ii) 720

(iii) 120

(iv) 699

(v) 960

(vi) 342

**Related concept**

**● ****additive**

**● ****Word problems adding**

**● ****subtraction**

**● ****Check for subtraction and addition**

**● ****Word problems with addition and subtraction**

**● ****Estimating sums and differences**

**● ****Find the missing digits**

**● ****multiplication**

**● ****Multiply a number by a two-digit number**

**● ****Multiplication of a number by a 3-digit number**

**● ****Multiply a number**

**● ****Appreciating products**

**● ****Word problems with multiplication**

**● ****Multiplication and division**

**● ****Terms used in divisions**

**● ****Division of two-digit by one-digit numbers**

**● ****Division of four-digit numbers by one-digit number**

**● ****Division by 10 and 100 and 1000**

**● ****Share numbers**

**● ****Estimating the quotient**

**● ****Division by two-digit numbers**

**● ****Word problems with the division**

**4th grade math activities**

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