Hillary

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.

Read More:

• COFORGE Pivot Calculator

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Cumulative Review Chapters 7 to 9 to score better marks in the exam.

Math in Focus Grade 2 Cumulative Review Chapters 7 to 9 Answer Key

Concepts and Skills

Fill in the blank.

Question 1.
Which is longer, 3 meters or 5 meters? ___ m
Measure the pencils.
Then fill in the blanks.

Answer: 5 meters is long.
A meter is a SI unit scientifically accepted as the base unit of distance and length. Along with other units like a kilometre or an inch, a meter is one of the fundamental units in SI. One meter equals the length of the path that a light travels in a vacuum for the time of 1/299,792,458 seconds. SI symbol for meter is m, and one meter is 100 centimetres or 1/1000^th (10^-3) of a kilometre.
5>3 so 5 metres is long.

Question 2.
Pencil A is ___ centimetres.
Answer: 300 centimetres.
Definition: Centimeter is considered a common unit of length used in SI. It is equivalent to 10 millimetres or 1/100^th (10^-2) of a meter. Years ago it was a basic unit in formerly used CGS (centimetre-gram-second) unit system, but in modern times the role of the basic unit of length is played by a meter. The symbol of centimetre is cm.
This is very easy to use a metre to centimetre converter. First of all, just type the meter (m) value in the text field of the conversion form to start converting m to cm, then select the decimals value and finally hit the convert button if auto calculation didn’t work. Centimetre value will be converted automatically as you type. The decimals value is the number of digits to be calculated or rounded of the result of meter to centimetre convert.
1 metre=100 centimetres.
Use the formula below to convert any value from meters to cm:
Centimetres=metres×100
To from meters to centimetres, you just need to multiply the value in meters by 100. (It is called the conversion factor)
Therefore, centimetres=3×100=300.

Question 3.
Pencil B is ___ centimetres.
Answer: 500 centimetres.
Explanation:
1 metre=100 centimetres.
Use the formula below to convert any value from meters to cm:
Centimetres=metres×100
To from meters to centimetres, you just need to multiply the value in meters by 100. (It is called the conversion factor)
Therefore, centimetres=5×100=500.

Question 4.
Which pencil is shorter? Pencil ______
Answer: Pencil A is shorter.

Because it is 300 cms which is lesser than pencil B.

Question 5.
How much shorter is it? ___ cm
Answer: 300 cms.
Pencil A is 300 cm shorter.

Draw. Then label.

Question 6.
Draw a line 7 centimetres long. Label it Line X.
__________
Answer:
– Construct a line L on a paper and mark A on it.
– Now place the metal point of the compass at the zero mark of the ruler.
– Make adjustments in the compass such that the pencil point is at the 7 cm mark on the ruler.
– Take compass on L such that its metal point is on A.
– Now mark a small mark as B on L which is corresponding to the pencil point of the compass.
– Here, AB is the required line segment of length 7 cm.
– The line is marked with X.

Question 7.
Draw a line 4- centimetres longer than Line X. Label it Line Y.
______________
Answer: 11 cm.
– Construct a line L on a paper and mark X on it.
– Now place the metal point of the compass at the zero mark of the ruler.
– Make adjustments in the compass such that the pencil point is at the 7 cm mark on the ruler and then mark 4 cms.
– Take compass on L such that its metal point is on X.
– Now mark a small mark as Y on L which is corresponding to the pencil point of the compass.
– Here, XY is the required line segment of length 11 cm.
– The line is marked with X and Y. And the total is 7+4=11 cm.

Fill in the blanks.

Question 8.

The books have a mass of ____ kilograms.
Answer: 3 kilograms.
Definition: kilogram (kg), the basic unit of mass in the metric system. A kilogram is very nearly equal (it was originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly. It is defined as being equal to the mass of the international prototype of the kilogram.
Explanation:
– It is showing the hand on 3.
– So it is 3 kgs.

Question 9.

The toy aeroplane has a mass of ___ grams.
Answer: 17 grams.
Explanation:
The weights are 10, 2, 5.
Add all the grams to get total mass. 10+2+5=17 grams.
Therefore, the toy aeroplane has a mass of 17 grams.

Fill in the blanks.

Question 10.
The chicken has a mass of ___ grams.
Answer: 550 grams.

– The gram is a unit of mass.
– One gram is one-thousandth the mass of one kilogram. The previous definition of the gram was the absolute weight of a 1-centimetre cube of pure water at 4 °C.
– The symbol for the gram is g.
– The gram is a small unit of mass. It is approximately the mass of one small paper clip.
Explanation:
– The hand is showing on after 500. And the small measurements can be written as 10,20, 20, 40, 50, 60, 70, 80, 90, and 100.
– The hand is showing on 50. So it is 550 grams.(500+50=550).

Question 11.
The duck has a mass of ____ grams.
Answer: 710 grams.
– The gram is a unit of mass.
– One gram is one-thousandth the mass of one kilogram. The previous definition of the gram was the absolute weight of a 1-centimetre cube of pure water at 4 °C.
– The symbol for the gram is g.
– The gram is a small unit of mass. It is approximately the mass of one small paper clip.
Explanation:

– The hand is showing on after 700. And the small measurements can be written as 10,20, 20, 40, 50, 60, 70, 80, 90, and 100.
– The hand is showing on 10. So it is 710 grams. (700+10=710).

Question 12.
Which is lighter? ____
Answer: Chicken.
Explanation:
The mass of chicken is 550 grams and the mass of duck is 710 grams. By comparing both grams chicken is lighter than duck because the weight of duck is more than chicken.
550<710.

Question 13.
How much lighter is it? ___ g
Answer:160 grams lighter.
Explanation:
By comparing both duck is having higher mass and the chicken is 550 gms.
To know how much lighter the chicken we need to subtract duck mass and chicken mass. Assume it as X.
X= 710-550
X=160 grams.

Fill in the blank.

Question 14.

What is the mass of the bag of rice? __ kg
Answer:7 kgs.
Definition: kilogram (kg), the basic unit of mass in the metric system. A kilogram is very nearly equal (it was originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly. It is defined as being equal to the mass of the international prototype of the kilogram.
Explanation:
How do I choose the bag of rice that is 7 kgs? I will explain below:

– Observe the 2nd picture, In that the total weight of potatoes are given.
– The weight of potatoes are 3kg+5kg=8kg.
– In the first picture, two different masses are there. Those are rice and potatoes.
– We already know the potatoes weight that is 8 kgs and the remaining 7 kgs are rice.

Look at the pictures. Then fill in the blank.

Question 15.

Containers A and B are the same size. Which container has a greater volume of water? Container ____
Answer: container B

Observe the pictures carefully. Containers are equal but the water in them is different volumes. Container B is having more water than Container A. So I circles Container B.

Fill in the blanks.

Containers A, B, C, and D are the same size.

Question 16.
Which container has the most water? Container ____
Answer: Container B.
Definition of volume:
– Volume is the number of shares of security traded during a given period of time.
– Generally, securities with more daily volume are more liquid than those without, since they are more “active”.
– Volume is an important indicator in technical analysis because it is used to measure the relative significance of a market move.
– The higher the volume during a price move, the more significant the move and the lower the volume during a price move, the less significant the move.
– Formula: Volume of cylinder=π · r² · h

Observe the pictures carefully. Containers are equal but the water in them is different volumes. Container B is having more water than Container A, c, and D. So I circled the B container.
Question 17.
Container ___ contains the same amount as Container ____
Answer: C and D.
Container C and Container D have the same amount of water.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

Find the volume of water in each container.

Example

Question 18.

Volume of water = ___ or ____
Answer: 70 litres.
The volume of water is 70 litres or 70l.
Explanation:
– The volume of water is as good as the shape of the reservoir (container) it’s in. Often, the containers have a circular, rectangular or square cross-section.
– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h

– The volume of water is 70 l and each litre difference in between them is 10.

Question 19.

Volume of water = ___ or ____
Answer: 40 l
Explanation:
– The volume of water is as good as the shape of the reservoir (container) it’s in. Often, the containers have a circular, rectangular or square cross-section.
– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h

The volume of water is 40 litres or 40 l.

Question 20.

Volume of water = ___ or ____
Answer: 2 litres.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

From the given question, the volume of water is 2 litres.

Fill in the blanks.
Use your answers for Exercises 18 to 20.

Question 21.
Which container has the greatest volume of water?
Container ____
Answer: Container B.
Explanation:

– For a rectangular based container, we use the formula to calculate the volume of a rectangular prism also known as a cuboid.
– Formula: volume=l × b × h
By comparing containers B, C, and D. Container D have the highest volume of water and is a cuboid in shape.
The volume of water is 70 litres.

Question 22.
Which container has the least volume of water?
Container ____
Answer: Container D.
– If the water is in a cylindrical container, then the volume of that water is calculated using the formula to calculate the volume of the cylinder.
– If the water is only halfway high in the container, then you’ll need to use half the height of the cylinder in the formula.
Formula: Volume=π · r² · h

It has 2 litres of water which is least to compare all the containers.

Look at the pictures.
The containers are filled with water.
Which containers contain less than 1 liter of water each? Circle each answer.

Question 23.

Answer:

Explanation:
In the above picture, the last 3 cups will have less volume because 1 litre is divided into 3 parts. So the volume is less in those 3 cups.

Problem Solving

Solve.

Draw bar models to help you.

Question 24.
Mrs. Kim’s empty suitcase has a mass of 5 kilograms. After she packs some books into the suitcase, her suitcase has a mass of 21 kilograms. What is the mass of the books?
The mass of the books is ___ kilograms.
Answer: 16 kilograms.

The mass of empty suitcase=5 kgs
The mass of filled suitcase after packing books=21 kgs.
The mass of books=X
X=21-5
X=16 kgs.

Question 25.
Seth has a ball of string. He uses 35 centimetres of string to decorate his scrapbook. He uses another 78 centimetres of string to decorate a gift.
a. How much string does he use in all?

b. If he had 200 centimetres of string at first how much string does he have now?

a. He uses ___ centimetres of string in all.

b. He has ___ centimetres of string now.
Answer:
a. He uses 113 centimetres of string in all.
Explanation:

The number of cms he used string to decorate book=35
The number of cms he used string to decorate gift=78
The total string he used for decorating book and gift=X
Add both the cms to get the total cms of string.
X=35+78
X=113 cms.
b. He has 87 centimetres of string now.
Explanation:
The total string =113 cms
If he had 200 cms at first, now the string cms are how much?. Assume it as X.
Subtract supposed cms-actual cms. Then we get the answer.
X=200-113
X=87 cms.

Question 26.
Tania’s hand puppet has a mass of 440 grams. It is 120 grams heavier than Hector’s hand puppet. What is the total mass of the two hand puppets?
The total mass of the two hand puppets is ___ grams.
Answer: 1000 grams.
Explanation:

The mass of Hector’s hand puppet=440
The mass of Tania’s hand puppet which is 120 grams more than Hector’s hand puppet=440+120=560
The total mass of two hand puppets is 560+440=1000 grams.

Question 27.
A tank contains 65 litres of oil Another 15 litres of oil are added. Later, 40 litres are poured out. What is the volume of oil in the tank in the end?
The volume of oil in the tank, in the end, is ___ litres.
Answer: 40 litres.
Explanation:

The number of litres of oil tank have=65
The number of litres added extra into the tank=15
The total number of litres of oil tank have after adding extra 15 litres=65+15=80
The number of litres poured out=40
The volume of the tank after pouring the 40 litres of oil=X
X=80-40
X=40 litres.

Question 28.
Sarah sells 27 liters of milk in the morning. She sells another 8 liters of milk in the afternoon. Ray sells 4-8 liters of milk.
a. Who sells more milk?

b. How much more?

a. ______ sells more milk.

b. sells ______ more litres of milk.
Explanation:
a. Sarah sells more milk.

The number of litres she sells in the morning=27
The number of litres she sells in the afternoon=8
The total number of litres Sarah sells=27+8=35.
The number of litres Ray sells=4-8
By comparing both of them Sarah is selling 35 litres of milk which is more than Ray.
b. sells 27 more litres of milk.
Explanation:
The total number of litres Sarah sells=35
The maximum number of litres Ray sells is totally=8.
We need to calculate the number of more litres more Sarah is selling than Ray.
Subtract the total number of litres sold by Sarah – sold by Rey
=35-8
=27.
therefore, Sarah sells 27 litres more than Rey.

Try Once:

• COLPAL Pivot Calculator

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Properties of Triangles and Four-sided Figures provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Answer Key Properties of Triangles and Four-sided Figures

Put On Your Thinking Cap!

Challenging Practice

This figure is a rhombus and ∠ADO = ∠CDO. Find the measure of ∠DOC.

Answer:
∠DOC = 90°
Explanation:
The diagonals of a rhombus bisect each other at right angles (90°)
∠DOC = 90°

Put on Your Thinking cap!

Problem Solving

Question 1.
ABCD is a trapezoid in which \(\overline{A D}\) || \(\overline{B C}\). Find the measure of ∠CED.

Answer:

Explanation:
With the help of protractor we find the Measure of ∠CED.
∠CED. = 70°

Question 2.
ABCD is a parallelogram and CDEF is a rhombus. Find the measure of ∠ADE.

Answer:

Explanation:
By using the protractor we can find the Angle of ADE
∠ADE. = 137°

Math Journal

Question 1.
A teacher asked her students to sketch and label the angles of a triangle. These are the angle measures that three students chose to draw.
Wayne: 120°, 80°, 10° Ashley: 70°, 28°, 72° Frank: 51 °, 37°, 92°
Will each student be able to draw his or her triangle? Explain your answer.
Wayne: _______
Ashley: ________
Frank: ______
Answer:
Wayne: 120°, 80°, 10° = 210°
Ashley: 70°, 28°, 72° = 170°
Frank: 51 °, 37°, 92° =  180°
Explanation:
The sum of all the angles of an triangle is equal to 180 degrees
Only Frank can draw the triangle.

Question 2.
What are two ways to identify an isosceles triangle?
Answer:
Isosceles. An isosceles triangle can be drawn in many different ways. It can be drawn to have two equal sides and two equal angles or with two acute angles and one obtuse angle.

Question 3.
Jordan is measuring the angles of a triangle. He finds out that m∠A = m∠B = 60°. Without measuring ∠C, he says that triangle ABC is an equilateral triangle. Is he correct? Explain why.

Explanation:
Yes.
The sum of all the angles of an equilateral triangle is equal to 180 degrees. As all the angles are equal to 60 degrees, the sum is equal to 60°+ 60°+ 60° =180 degrees
m∠C = 60°