Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 2 Practice 1 Estimation to finish your assignments.

## Math in Focus Grade 4 Chapter 2 Practice 1 Answer Key Estimation

**Find each sum or difference. Then use rounding to check that your answers are reasonable. Round each number to the nearest hundred.**

Example

534 + 287

534 + 207 = 021

Add: 500 + 300 = 800

821 is close to 800.

So, the answer is reasonable.

Question 1.

515 + 342

Answer:

515 + 342=857

Now we added the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 515:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘1’.

– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 500

The second number is 342:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘4’.

– 4 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 300.

Now add both the numbers:

500+300=800

Therefore, the answer is not reasonable.

For the number 857, the round figure is 900 because in the tens place number ‘5’ is there. According to rule 2, +1 should be added to the hundreds place and the remaining places will become zero. Then it becomes 900. But here we got the estimated value of 800. That’s why it is not reasonable.

Question 2.

681 – 519

Answer:

681 – 519=162

Explanation:

Now we subtracted the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 681:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘8’.

– 8> 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.

– The rounding off number is 700.

The second number 519:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘1’.

– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 500

Now subtract both the numbers:

700-500=200

Therefore, the answer is reasonable.

168 is nearer to 200 according to rule 2.

Question 3.

170 + 725 + 333

Answer:

170 + 725 + 333=1228

Explanation:

Now we added the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 170:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘7’.

– 7 > 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.

– The rounding off number is 200.

The second number is 725:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘2’.

– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 700

The third number is 333:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘3’.

– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 300.

Now add all the three estimated numbers:

200+700+300=1200

Therefore, the answer is reasonable.

Question 4.

2,979 – 814

Answer:

2,979 – 814=2165

Explanation:

Now we subtracted the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 2,979:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘7’.

– 7 > 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.

– The rounding off number is 3000.

The second number is 814:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘1’.

– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 800

Now subtract both the numbers:

3000-800=2200

the answer is reasonable.

2,165 is nearer to 2,200.

**Find each sum or difference. Then use front-end estimation to check that your answers are reasonable.**

Example

Question 5.

7,930 + 2,517

Answer:

7,930 + 2,517=10,447

The answer is 10,447

Explanation:

Now we added the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 7,930:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘3’.

– 3< 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 7900.

The second number is 2,517:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘1’.

– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 2500

Now add the estimated values:

7900+2500=10400

10,447 is close to 10,400

So, the answer is reasonable.

Question 6.

3,166 – 1,625

Answer:

3,166 – 1,625=1541

the answer is 1,541.

Explanation:

Now we subtract the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 3,166:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘6’.

– 6> 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.

– The rounding off number is 3200.

The second number is 1,625:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘2’.

– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 1600

Now subtract the estimated values:

3,200-1,600=1,600

1541 is close to 1500, not 1600

So, the answer is not reasonable.

Question 7.

36,053 + 11,832

Answer:

36,053 + 11,832=47,885

The answer is 47,885

Explanation:

Now we add the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 36,053:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘5’.

– 5 = 5, +1 is added to the rounding digit (hundreds place) and the remaining places will become 0.

– The rounding off number is 36,100.

The second number is 11,832:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘3’.

– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 11,800

Now add the estimated values:

36,100+11,800=47,900

47,885 is close to 47,900

So, the answer is reasonable.

Question 8.

9,705 – 8,250

Answer:

9,705 – 8,250=1455

The answer is 1,455.

Explanation:

Now we subtract the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The first number is 9,705:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘0’.

– 0 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 9,700.

The second number is 8,250:

We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘5’.

– 5 <= 5, +1 is added to the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 8,300

Now subtract the estimated values:

9,700-8,300=1,400

1,455 is close to 1,500, not 1,400

So the answer is not reasonable.

**Find each product. Then use rounding to check that your answers are reasonable. Round the 3-digit number to the nearest hundred.**

Example

Question 9.

233 × 4

Answer:

233 × 4=932

The answer is 932

Explanation:

Now we multiply the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The number is 233:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘3’.

– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 200.

Now multiply the estimated value by 4.

200 × 4 = 800

932 is not close to 800.

932 is close to 900

So, the answer is not reasonable.

Question 10.

485 × 2

Answer:

485 × 2 = 970

The answer is 970

Explanation:

Now we multiply the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The number is 485:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘8’.

– 8 > 5, +1 is added to the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 500.

Now multiply the estimated value by 2.

500 × 2 = 1000

970 is close to 1000.

So, the answer is reasonable.

Question 11.

117 × 5

Answer:

117 × 5 = 585

The answer is 585.

Explanation:

Now we multiply the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The number is 117:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘1’.

– 1 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 100.

Now multiply the estimated value by 5.

100 × 5 = 500

585 is not close to 500

585 is close to 600

So, the answer is not reasonable.

Question 12.

276 × 3

Answer:

276 × 3 = 828

the answer is 828

Explanation:

Now we multiply the above-given numbers.

We have to estimate the numbers and then add the estimated numbers to know the above result is correct or not.

In Maths, rounding numbers is a kind of estimating the numbers in the rounded form rather than the exact form. There are some procedures to round off the whole numbers. To round off whole numbers, find the place value that you want to round, and just see the digit just right to it.

RULE 1: If that digit number is less than 5, don’t change the rounding figure, but replace all the digits right to the rounding digits to “zero”.

RULE 2: If it is greater than 5, add 1 to the rounding digit, and replace all the digits right to the rounding digits to “zero”.

The number is 276:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘7’.

– 7 > 5, +1 is added to the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 300.

Now multiply the estimated value by 3.

300 × 3 = 900

828 is not close to 900

828 is close to 800

So, the answer is not reasonable.

**Find each product. Then use front-end estimation to check that your answers are reasonable.**

Example

Question 13.

108 × 3

Answer:

108 × 3 = 324

The answer is 324

Explanation:

Front end rounding is taking the number farther to the left and rounding it. So with our number, 108, we will be rounding to the hundreds since the farthest number to the left is a 1 and it’s in the hundredth place. The front end means the front or first digit in the number.

secondly, how do you round a number? Here’s the general rule for rounding:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The number 108:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘0’.

– 0 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 100.

Now multiply the estimated value by 3.

100 × 3 = 300

324 is close to 300

So, the answer is reasonable.

Question 14.

121 × 5

Answer:

121 × 5 = 605

the answer is 605

Explanation:

Front end rounding is taking the number farther to the left and rounding it. So with our number, 121, we will be rounding to the hundreds since the farthest number to the left is a 1 and it’s in the hundredth place. The front end means the front or first digit in the number.

secondly, how do you round a number? Here’s the general rule for rounding:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The number 121:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘0’.

– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 100.

Now multiply the estimated value by 5.

100 × 5 = 500

605 is close to 600, not 500

So, the answer is not reasonable.

Question 15.

439 × 2

Answer:

439 × 2 = 878

the answer is 878

Explanation:

Front end rounding is taking the number farther to the left and rounding it. So with our number, 439, we will be rounding to the hundreds since the farthest number to the left is a 4 and it’s in the hundredth place. The front end means the front or first digit in the number.

secondly, how do you round a number? Here’s the general rule for rounding:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The number 439:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘0’.

– 3 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 400.

Now multiply the estimated value by 2.

400 × 2 = 800

878 is close to 800

So, the answer is reasonable.

Question 16.

227 × 4

Answer:

227 × 4 = 908

the answer is 908.

Explanation:

Front end rounding is taking the number farther to the left and rounding it. So with our number, 439, we will be rounding to the hundreds since the farthest number to the left is a 4 and it’s in the hundredth place. The front end means the front or first digit in the number.

secondly, how do you round a number? Here’s the general rule for rounding:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The number 227:

– We need to round off nearest to hundred so check the tens place.

– The tens place is having the digit ‘2’.

– 2 < 5, we don’t change the value of hundreds of places and the remaining places will become 0.

– The rounding off number is 200.

Now multiply the estimated value by 4.

200 × 4 = 800

908 is not close to 800

So, the answer is not reasonable.

**Find each quotient. Then use related multiplication facts to check that your answers are reasonable.**

Example

85 ÷ 5

85 ÷ 5 = 17

The answer is 17.

since division is the opposite of multiplication, find a multiple of 5 that is close to 8.

5 × 10 = 50

5 × 20 = 100

85 is closer to 100 than to 50.

So, 85 ÷ 5 rounds to 100 ÷ 5.

100 ÷ 5 = 20

85 ÷ 5 is about 20.

17 is close to 20.

Answer 17 is reasonable.

Question 17.

78 ÷ 2

Answer:

78 ÷ 2 = 39

The answer is 39

since division is the opposite of multiplication, find a multiple of 2 that is close to 78.

2 × 20 = 40

2 ×30 = 60

2 × 40 = 80

78 is closer to 80

so, 78 ÷ 2 rounds to 80 ÷ 2

80 ÷ 2 = 40

78 ÷ 2 is about to 40.

39 is close to 40

Answer 39 is reasonable.

Question 18.

68 ÷ 4

Answer:

**Solve. Decide whether to find an estimate or an exact answer.**

Example

Danny and his 3 friends buy baseball tickets for $26 each. About how much money do they need altogether?

Because the question asks ‘about how much money they need, you can estimate.

4 × $30 = $120

They need about $120.

Question 21.

Jonathan, Shia, and Casey bought 35 toy figures. Each of the boys decides to make a team of 11 figures. Do they have enough toy figures?

Answer: yes

Explanation:

The number of toys figures they bought=35

The number of figures they want to decide to make a team=11

Now the above-given question was asked do they have enough toy figures=?

If we go for the estimation process:

35 is close to 40

11 is close to 10

If we divide both the numbers then we get the estimated answer which is close to the original answer.

The original answer:

35/11=3.18

Now do the estimation process:

40/10=4

3.18 is close to the 4.

So, the answer is reasonable.

Question 22.

A turtle hatchery collected 457 turtle eggs in a week. The next week, it collected 656 eggs. About how many eggs did the hatchery collect in the two weeks?

Answer:

The number of turtle eggs a title hatchery collected in a week=457

The number of turtles eggs a title hatchery collected in a next week=656

The number of turtle eggs he collected in two weeks=X

X=457+656

X=1113

Therefore, he collected 1113 eggs in two weeks.

Question 23.

The table shows the number of beads in Stella’s collection.

Stella needs 400 yellow beads, and 700 green beads to make a necklace. Does she have enough beads for the necklace?

Answer: yes, she could have enough beads.

The number of yellow beads Stella needs=400

The number of green beads Stella needs=700

In the above-given figure, the number of colours of beads is given.

But in the question, green beads are more than yellow beads. Moreover, the question asked was yellow and green beads are given. So according to that, we calculate the beads.

In the above-given figure:

Yellow beads=417

Green beads=609

The total number of beads=1026

In the question given:

Yellow beads=400

Green beads=700

The total number of beads=1100

So, definitely she can make necklace with the given number of beads.

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