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Math in Focus Grade 5 Chapter 2 Answer Key Whole Number and Multiplication and Division

Math Journal

Question 1.
Kelly has a 370-page sketch book. She wants to allocate an equal number of pages for making sketches to each month of the year. She uses division to find the number of pages she can possibly allocate to each month, and the number of pages she will have left over.
She works out the division like this:

Which part of the answer tells the number of pages that Kelly can possibly allocate to each month?
Which part tells the number of pages left over?
Answer:
Quotient
Remainder
Explanation:
Quotient part of the answer tells the number of pages that Kelly can possibly allocate to each month
Remainder part tells the number of pages left over

Question 2.
Mark was asked to simplify the numeric expression 6 + 4 × 2. He worked out the steps like this:
6 + 4 × 2 = 10 × 2
= 20
Is he correct? Explain why.
Answer:
No, he is not correct
Explanation:
the answer will be 8 · 6+2=8 · Order or operations. You must multiply or divide before adding or subtracting

Question 3.
Look at the following problem and the solution given by a student: Abel, Belle, and Cindy have $408 altogether. Belle has $7 more than Cindy and $5 more than Abel. How much does Abel have?

What was the mistake made? What should the correct answer be?
Answer:

Abel has 135
Explanation:
Abel has 135
408 – 9 = 399
399 divided by 3 = 133
133 + 2 = 135

Put On Your Thinking Cap!

Challenging Practice

Solve. Use any strategy.

Question 1.
A sticker costs 15¢, and a packet of 8 similar stickers costs $1. Clement buys 37 stickers. What is the least amount of money that Clement spends on the stickers?
Answer: $4 and  75¢
Explanation:
if buy Individual sticker:
37 x 15 = 555 =  $5 and 5¢
if buy packet of sticker:
37 ÷ 8 = 4 and remainder is 5
so, Clement needs to buy 4 packets and 5 stickers.
4 packets  cost is 4 x 1 = $4 and 5 stickers cost is 5 x 15 = 75
So total cost is = $4 75¢
least amount of money that Clement spends on the stickers is $4 and 75¢

Question 2.
40 members of a parents’ organization are making candles to raise money. 1 member drops out and the rest have to make 3 more candles each to make up. Each member makes the same number of candles. How many candles do they make altogether?
Answer: 4680
Explanation:
When possible, assign a variable to the value the problem wants you to find.  Here,

Solve. Use any Strategy.

Question 3.
Mr. Thomas puts up fence posts from one end of a field to the other, equal distances apart. There are 27 posts. The width of each post is 10 centimeters. The distance between two posts is 30 meters. Find the length of the fence.
Answer: 782 meters and 70 centimeters
Explanation:
There are 27 posts and puts up fence posts from one end of a field to the other, equal distances apart So total distances are 27 -1 = 26
The distance between two posts is 30 meters then total distance between posts is 26 x 30 = 780 meters
The width of each post is 10 centimeters and then total posts width is 27 x 10 =270 centimeters = 2 meters and 70 centimeters

Question 4.
Kirsten has 64 coins in her piggy bank. She has $9.25 in dimes and quarters. How many dimes and how many quarters does she have?
Answer: 45 dimes and 19 quarters
Explanation:
Let there be x dimes and 64-x quarters.
0.1x+0.25(64-x) = 9.25
0.1x+16-0.25x=9.25
-0.15x=-6.75
x= 45
64-x=64-45=19
so 45 dimes and 19 quarters

Put On Your Thinking

Problem Solving

Solve. Use any strategy.

Question 1.
Darcy, Jason, and Maria share $268. Jason has $20 more than Darcy and Maria has twice as much money as Jason. How much money do Darcy and Jason have altogether?
Answer: Darcy and Jason have altogether=$124
Explanation:
Let Darcy has money=x
Jason has $20 more than Darcy
Jason =20+x
Maria has twice as much money as Jason
Maria = 2(20+x)=40+2x
Darcy,Jason and Maria share $268
x+20+x+40+2x=268
4x+60=268
4x=208
x=52
So Darcy has money=$52
Jason has money=20+x=20+52=$72
Darcy and Jason have altogether=$(52+72)=$124

Question 2.
Juan and Rachel have the same number of marbles. Rachel gives away 10 marbles and Juan gives away 22 marbles. Rachel then has 3 times as many marbles as Juan. How many marbles did each of them have at first?
Answer: 28
Explanation:
Let X = the number of marbles that Juan or Rachel started with.
Rachel gives away 10 marbles–> X – 10 and Juan gives away 22–> X – 22
Than Rachel has 3 times as many marbles as Juan–> X-10 = 3(X-22)
X – 10 = 3X – 66
-56 =- 2X
X = 28

Solve. Use any strategy.

Question 3.
Gerry had a total of 30 pens and pencils. He decided to trade with his friends all his pens for pencils. If he traded every pen for 2 pencils, he would have 48 pencils in all. How many pens and how many pencils did he have before the trade?
Answer: 12 Pencils
Explanation:
Let p = pens
Pencils = 30-p
Total pencils after the exchange will be: 48 = 30-p + 2p
48 = 30 + p
18 = p (pens)
30-18 = 12 pencils
To check: 18×2 + 12 = 36+12 = 48

Math Journal

Multiply. Explain how you can check if your answer is reasonable.

184 × 97
Answer: 17848
200 × 100 = 20000 So 17848 is nearest number. It is reasonable.
Explanation:
184 × 97  = 17848

Math Journal

Jodi estimated these products.
a. 2,892 × 21 rounds to 3,000 × 20 = 60,000
b. 2,743 × 18 rounds to 3,000 × 20 = 60,000
She then worked out the actual answers. Even though the estimated answers were the same, Jodi found that the actual answers were very different from each other.
Answer:
2,892 × 21 =60732
2,743 × 18  =  49374

Question 1.
In which case is the estimate closer to the actual answer? Explain why.
Answer:
In case A
2,892 × 21 =60732
The Estimation is closer

Question 2.
If an estimate does not make your answer seem reasonable, what can you do to make sure you have done your work correctly?
Answer:
2,743 × 18  =  49374
We have to find the actual product
We have to round to Hundreds

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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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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.

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Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 2 Practice 6 Dividing by 2-Digit Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 2 Practice 6 Answer Key Dividing by 2-Digit Numbers

Divide.

Example
340 ÷ 20 = 34 ÷ 2
= 17

Question 1.
560 ÷ 80 = __7___
Answer:
7,

Explanation:
Given to find 560 ÷ 80 we get 560 ÷ 10 ÷ 8,
= 56 ÷ 8 = 7.

Question 2.
630 ÷ 60 = __10 R 3___
Answer:
10 R 3,

Explanation:
630 ÷ 60 = 63 ÷ 6 = 10 R 3,

Question 3.
590 ÷ 30 = __19 R 2___
Answer:
19 R 2,

Explanation:
590 ÷ 30 = 59 ÷ 3 = 19 R  2,

Question 4.
190 ÷ 90 = _2 R 1____
Answer:
2 R 1,

Explanation:
190 ÷ 90 = 19 ÷ 9 = 2 R 1,

Question 5.
360 ÷ 50 = __7 R 1___
Answer:
7 R 1,

Explanation:
360 ÷ 50 = 36 ÷ 5 = 7 R 1,

Divide.

Example
43 ÷ 12
12 rounds to 10.
4 × 10 = 40
The quotient is about 4.
4 × 12 = 48
The estimated quotient is too big. Try 3.

43 ÷ 12 = 3 R 7

Question 6.
98 ÷ 16 = _6 R 2_
Answer: 6 R 2
Explanation:
16 rounds to 20
5 x 20 = 100
The quotient is about 5
5 x 20 = 100
The estimated quotient is ok.

98 ÷ 16 = 6 R 2.

Question 7.
65 ÷ 24 = _2 R 17__
Answer:
24 rounds to 20
3 x 20 = 60
The quotient is about 3
3 x 20 = 60

The estimated quotient is too small, therefore  65 ÷ 24 is 2 R 17.

Question 8.
94 ÷ 37 = _2 R 7__
Answer: 2 R 7
Explanation:

37 rounds to 40
2 x 40 = 80
The quotient is about 2
4 x 20 = 80
The estimated quotient is too small therefore 94 ÷ 37 = 2 R 7.

Divide.

Example

215 ÷ 51
215 rounds to 200.
4 × 50 = 200
The quotient is about 4.

215 ÷ 51 = 4 R 11

Question 9.
362 ÷ 60 = __10 R 2_
Answer: 10 R 2
Explanation:
362 ÷ 60
362 rounds to 360.
6 × 60 = 360
The quotient is about 10.

therefore, 362 ÷ 60 = _10 R 2.

Question 10.
178 ÷ 45 = _3 R 43__
Answer:
3 R 43,

Explanation:
178 ÷ 45,
178 rounds to 200.
45 rounds to 50
4 × 50 = 200
The quotient is about 4.

So 178 ÷ 45 = _3 R 43.

Question 11.
850 ÷ 88 = _9 R 58__
Answer:
9 R 58,

Explanation:
850 ÷ 88
850 rounds to 900.
88 rounds to 90
10 × 90 = 900
The quotient is about 9.

therefore 850 ÷ 88 = 9 R 58.

Question 12.
273 ÷ 59 = _4 R 37__
Answer:
4 R 37,

Explanation:
273 ÷ 59
273 rounds to 300.
59 rounds to 60
5 × 60 = 300
The quotient is about 4.

therefore 273 ÷ 59 =  4 R 37.

Divide.

Example
354 ÷ 14

354 ÷ 14 = 25 R 4

Question 13.
850 ÷ 17 = _50__
Answer:
50,

Explanation:

8 hundreds 5 tens = 85 tens
therefore 850 ÷ 17 = 50.

Question 14.
546 ÷ 25 = _21 R 21__
Answer:
21 R 21,

Explanation:

5 hundreds and 4 tens =  54 tens,
54 tens ÷ 25 = 2 tens R 4,
4 tens 6 ones = 46 ones,
46  ÷ 25 = 1 R 21,
therefore 546 ÷ 25 = 21 R 21.

Question 15.
700 ÷ 28 = _25__
Answer:
25,

Explanation:

7 hundreds and 0 tens =  70 tens
70 tens ÷ 28 = 2 tens R 14
14 tens 0 ones =140 ones
140  ÷ 28 = 5.
therefore 65 ÷ 24 = 2 R 17.

Question 16.
936 ÷ 43 = _21 R 33__
Answer:
21 R 33,

Explanation:

9 hundreds and 3 tens =  93 tens,
93 tens ÷ 43 = 2 tens R 7,
7 tens 6 ones =76 ones
So 76  ÷ 28 = 1 R 33.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 7 Practice 6 Real-World Problems: More Ratios to score better marks in the exam.

Math in Focus Grade 5 Chapter 7 Practice 6 Answer Key Real-World Problems: More Ratios

Solve. Show your work.

Question 1.
For a school fair, Lolita’s parents donated 4 bottles of orange juice, 10 bottles of fruit punch and 8 bottles of apple juice. Find the ratio of the number of bottles of orange juice to the number of bottles of fruit punch to the number of bottles of apple juice Lolita’s parents donated.
Answer: 2 : 5 : 4
Explanation:
Given,
Lolita’s parents donated 4 bottles of orange juice,
10 bottles of fruit punch,
8 bottles of apple juice,
By dividing 4 , 10 and 8 with 2 we get 2 : 5 : 4 to get into simplest form.

Question 2.
A company gave a total of $900 to three charities. Charity A received $200, Charity B received $400 and Charity C received the remaining amount. What is the ratio of the amount Charity A received to the amount Charity B received to the amount Charity C received?
Answer: 2 : 4 : 3
Explanation:
Given,
A company gave a $900 to three charities,
Charity A received $200,
Charity B received $400,
Charity C received the remaining amount,
By subtracting Charity A’s and Charity B’s amount from the total amount,
900 – 600 = 300
The ratio of amount Charity A received to the amount Charity B received to the amount Charity C is 200 : 400 : 300 to get into the simplest form we get 2 : 4 : 3

Solve. Show your work

Question 3.
Ruth cuts a piece of string into three parts. Their lengths are in the ratio 2:3:5. The longest part is 35 centimeters long. How long is the shortest part?
Answer: The shortest part is 14 cm
Explanation:
Given,
The lengths are in the ratio of 2 : 3 : 5,
The longest part is 35 centimeters long,
By multiplying all the three parts with 7 we get the ratio as 14 : 21 : 35,
Therefore, it states that the longest part is 35 cm and shortest part is 14 cm.

Question 4.
The ages of three brothers, Dave, Randy, and Martin, are in the ratio 1 : 2 : 3. Dave is 7 years old. Find the total age of all three brothers.
Answer: The total age of all three brothers is 42 years
Explanation:
Given,
Dave, Randy and Martin are in the ratio of 1 : 2 : 3,
Dave is 7 years old,
By multiplying all the three ratios with 7 we get the ratio as 7 : 14 : 21,
By adding 7 with 14 we get 21,
By adding 21 with 21 we get 42 as total.

Solve. Show your work.

Question 5.
The number of movies that Lisa, Mia, and Nina have seen are in the ratio 6 : 4 : 7. Nina has seen 21 movies this year.
a. How many movies has Lisa seen?
Answer: Lisa has seen 18 movies
Explanation:
Given,
The numbers of movies that Lisa, Mia and Nina have seen are in the ratio of 6 : 4 : 7,
Nina has seen 21 movies,
By multiplying 6, 4 and 7 with 3 we get 18, 12 and 21.

b. What is the total number of movies that the three girls have seen?
Answer: The total number of movies that three girls have seen is 51
Explanation:
Given,
Lisa watched 18 movies,
Mia watched 12 movies,
Nina watched 21 movies,
By adding 18, 12 and 21 we get 51,
So the total number of movies three girls watched is 51.

Question 6.
Amin, Barb, and Curt collected seashells in the ratio of 10 : 12 : 7. Curt collected 98 seashells. How many seashells did they collect together?
Answer: They collected 406 shells together
Explanation:
Given,
Amin, Barb and Curt collected seashells in the ratio of 10 : 12 : 7,
Curt collected 98 seashells,
By multiplying 10, 12 and 7 with 14 we get 140 : 168 : 98,
By adding 140, 168 and 98 we get 406.

Solve. Show your work

Question 7.
By the end of a year, Kieran’s savings is \(\frac{9}{2}\) of Simon’s savings.

a. What is the ratio of Kieran’s savings to Simon’s savings to their total savings?
Answer: 9 : 2 : 11
Explanation:
Given,
The ratio of Kieran’s savings to Simon’s savings to their total savings is 9 : 2 : 11

b. How many times the total amount of money saved is Kieran’s savings?
Answer: 9 : 11
Explanation:
Given,
Kieran’s savings is 9,
Total amount of money is 11,
The ratio of Kieran’s savings to the total amount of money is 9 : 11

c. How many times the total amount of money saved is Simon’s savings?
Answer: 2 : 11
Explanation:
Given,
Simon’s savings is 2,
Total amount of money is 11,
The ratio of Simon’s savings to the total amount of money is 2 : 11

d. Simon saves $28 less than Kieran. How much do both of them save altogether?
Answer: They saved 44 altogether
Explanation:
Given,
Simon saves $28 less than Kieran,
Kieran and Simon’s savings are in the ratio of 9 : 2,
By multiplying 9 with 4 we get 36, 2 with 4 we get 8,
Kieran has $36 and Simon has $8,
By adding 36 with 8 we get 44.

Solve. Show your work.

Question 8.
Lita, Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4 : 1. If Rose typed 48 words, how many words did Lita type?
Answer: Lita types 384 words
Explanation:
Given,
Lita typed 2 times as fast as Kala which is 8,
Kala and Rose typed in the ratio of 4 : 1,
By multiplying 8, 4 and 1 with 48 we get 384 : 192 : 48,
Therefore, Lita typed 384 words in a typing competition

Solve. Show your work

Question 9.
Young’s Dairy Bar produces yogurt in three flavors: vanilla, strawberry, and banana. The amount of vanilla yogurt they produce in a day is 2 times the amount of banana yogurt. The amount of banana yogurt they produce in a day is 3 times the amount of strawberry yogurt.
a. What is the ratio of the amount of vanilla yogurt to the amount of banana yogurt to the amount of strawbery yogurt it produces in a day?
Answer: The ratio of the amount of vanilla yogurt to the amount of banana yogurt to the amount of strawberry yogurt is 6 : 3 : 1
Explanation:
Given,
The amount of vanilla yogurt they produce is 2 times the amount of banana yogurt,
The amount of banana yogurt they produce is 3 times the amount of strawberry amount.

b. How many times the total amount of yogurt produced is the amount of vanilla yogurt produced?
Answer:3 / 5 times
Explanation:
Given,
The total amount of yogurt produced is by adding 6, 3 and 1 we gt 10,
The amount of vanilla yogurt produced is 6
The ratio of total amount of yogurt produced is the amount of vanilla yogurt produced is 6 / 10,
By dividing 6 / 10 with 2 we get 3 / 5.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 8 Decimals to score better marks in the exam.

Math in Focus Grade 5 Chapter 8 Answer Key Decimals

Math Journal

Question 1.
Explain why 1.8, 1.80, and 1.800 have the same value.
Answer: 1.8, 1.80, and 1.800 have the same value as all the three values have 0 at their decimal value after 8.
since the value after the decimal point if it’s less than 5 then the value will be the same and there won’t be much change

Question 2.
Howard does not know how to find the values of A and B on the number line. Write the steps Howard should use to find these values.

Answer:
Howard should use the tenth and hundredth value counting and then rounding value  method to identify the value
that is to find A Howard should start counting numbers from2.1 and go on as 2.11,2.12,2.13,2.14,2.15,2.16 at 2.16 the value is hundredth value is more than 5 so the value will be 2.2
and at the point A value will be 2.13
Same to find value of B it will be 2.21

Put on Your Thinking cap!

Challenging Practice

Solve.

Question 1.
You are given two numbers, 3.987 and 70.140.

a. Round each number to the nearest tenth.
Answer:
The nearest tenth for 3.987 is 4.0
The nearest tenth for 70.140 is 70.1
Explanation:
For 3.987,  the nearest tenth place value is 9 and to round the number which is nearest to the tenth we have to look at the next place value which is the hundredth so 8 is more than 5 we have to go onto the next highest tenth value  will be 4.o
For 70.140,  the nearest tenth place value is 1 and to round the number which is nearest to the tenth we have to look at the next place value which is the hundredth so since 4 is less than 5 the round of value will be 70.1

b. Round each number to the nearest hundredth.
Answer:
Explanation:
The nearest hundredth for 3.987 is 3.99
The nearest hundredth for 70.140 is 70.14
For 3.987, to get to the nearest hundredth we go to the thousandth position and the value is more than  5 we have to go onto the next highest hundredth value which will be 3.99
For 70.140,  the nearest hundredth place value is 4 and to round the number which is nearest to the hundredth we have to look at the next place value which is the thousandth so since 0 is less than 5 the round of value will be 70.14

c. Find the difference between your rounded answers for 3.987.
Answer: 0.01
The nearest tenth for 3.987 is 4.0
The nearest hundredth  for 3.987 is 3.99
By removing 3.99 from 4.0 we get 0.01
4.0 – 3.99 = 0.01
so, The difference will be 0.01

d. Find the difference between your rounded answers for 70.140.
Answer:0.04
The nearest tenth for 70.140 is 70.1
The nearest hundredth  for 70.140 is 70.14
By removing 70.1 from 70.14 we get 0.04
70.14 – 70.1 = 0.04
so, The difference will be 0.04

e. Are your answers in Exercises a and b the same? Explain why or why not.
Answer: No, the answers are not same as the exercises a is done to find the round value of tenth and the exercise b is done to find the round value of hundredth.

Complete.

Question 2.

Answer:
4.129=4+0.1+0.029

Question 3.

Answer:
2.075=2+0.070+0.005

Question 4.

Answer:

Put on Your Thinking Cap!

Problem Solving

Solve. Show your work.

Question 1.
Kimberly has 3.25 kilograms of flour in a container. She adds 45 grams of flour to the container. How many kilograms of flour does she have now?
Answer: 3.295 Kilograms
Kimberly has 3.25 kilograms of flour in a container.
Kimberly has 3.25 kilograms of flour in a container.
Convert grams into kilograms
To convert grams divide 45 with 1000
As 1 gram is equal to 0.001 kilogram
45 grams = \(\frac{45}{1000}\)
= 0.045  Kilograms
Now by adding 3.25 and 0.045 we get 3.295 kilogram
3.25 + 0.045 = 3.295 kg

Question 2.
The weight of four objects are 3\(\frac{1}{5}\) pounds, 3\(\frac{39}{1000}\) pounds, 3\(\frac{99}{100}\) Pounds and 3\(\frac{52}{10}\) Pounds. Arrange the weights in order from least to greatest.
Answer: 3\(\frac{39}{1000}\) pounds, 3\(\frac{99}{100}\) Pounds, 3\(\frac{1}{5}\) pounds, 3\(\frac{52}{10}\) Pounds

The oder given is 3\(\frac{1}{5}\) pounds , 3\(\frac{39}{1000}\) pounds , 3\(\frac{99}{100}\) Pounds , 3\(\frac{52}{10}\) Pounds

Explanation:
We have 3\(\frac{52}{10}\) Pounds as the highest
When compared 3\(\frac{1}{5}\) pounds with 3\(\frac{99}{100}\) Pounds, 3\(\frac{1}{5}\) pounds is the highest value
And When compared 3\(\frac{99}{100}\) Pounds with 3\(\frac{39}{1000}\) pounds is the highest value
therefor weights in order from least to greatest is

3\(\frac{39}{1000}\) pounds, 3\(\frac{99}{100}\) Pounds, 3\(\frac{1}{5}\) pounds, 3\(\frac{52}{10}\) Pounds

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 11 Practice 2 Comparing Amounts of Money to score better marks in the exam.

Math in Focus Grade 2 Chapter 11 Practice 2 Answer Key Comparing Amounts of Money

Compare the amounts.

Complete the tables and fill in the blanks.

Example

Question 1.

Answer:

$70.40 = 70 dollars and 40 cents
$70.35 = 70 dollars and 35 cents
$70.40 > $70.35
$70.35 < $70.40

Question 2.

Are all of these amounts the same? _______
$_________ is the greatest amount.
$_________ is the least amount.
Answer:

$16.70 = 16 dollars and 70 cents.
$16.15 = 16 dollars and 15 cents.
$16.45 = 16 dollars and 45 cents.
All the amounts are not same
$16.70 is the greatest amount.
$16.15 is the least amount.

Question 3.

Which is the greatest amount? _________
Which is the least amount? _________
Answer:

$45.30 = 45 dollars and 30 cents.
$42.95 = 42 dollars and 95 cents.
$45.75 = 45 dollars and 75 cents.
$45.75 is the greatest amount.
$42.95 is the smallest amount.

Write the amount in each set.
Then check (✓) the set that has the greater value.

Example

Question 4.

Answer:

5 dollars + 5 dollars + 1 dime + 1 dime = 10 dollars + 2 dime
1 dime = 0.1dollar
so 10.1 dollar
10 dollars + 10 dollars + 5 dollars + 1 dollar + 1 dollar + 1 dollar = 28 dollars

Question 5.

Answer:

5 dollars + 1 dollar + quarter dollar + quarter doller + quarter dollar + 1 dime + 5 cents + 5 cents
Quarter dollar = 25 cents.
6 dollars 85 cents 1 dime.
1 dime = 10cents
85 cents 1 dime = 95 cents
so
$ 6.95
10 dollars + 10 dollars + 5 dollars + 1 dollar + 1 dollar + 1 doller + 5 cents + 5 cents + 5 cents = 28 dollars 15 cents
$28.15

Circle the amount that is less.

Question 6.
$3.85 $4.10
Answer:

$3.85 amount is less.

Question 7.
$62.40 $62.25
Answer:

$62.25 amount is less.

Circle the amount that is more.

Question 8.
$28.90 $27.95
Answer:

$28.90 amount is more.

Question 9.
$71.09 $790
Answer:

$71.09 amount is more.

Compare the amounts.

Answer:
$37.05 greater than $27.90 greater than $27.45.

Question 10.
Which customer paid the most? Customer _______
Answer:
Customer C paid the most.

Question 11.
Which customer paid the least? Customer _______
Answer:
Customer A paid the least.

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 10 Practice 1 Meaning of Sum to score better marks in the exam.

Math in Focus Grade 2 Chapter 10 Practice 1 Answer Key Meaning of Sum

Find the sum of the numbers.

96 and 73

The sum of 96 and 73 is 169

Question 1.
700 and 200

The sum of ___ and ___ is ____.
Answer:

The sum of 700 and 200 is 900

Question 2.
215 and 507

The sum of ___ and ___ is ____.
Answer:

The sum of 215 and 507 is 722

Solve.

Use bar models to help you.

Question 3.
Al spent $27 on a shirt and $120 on books. Find the sum of money Al spent.
___ + ___ = _____
The sum of money Al spent is $ _____.
Answer:

Explanation:
Given:
Al has spent $ 27 on a shirt
And $ 120 on a Book
The total amount he spent was
$27 + $120 = $147
The sum of money Al spent is $ 147.

Question 4.
Harry is 12 years old. His sister is 9 years younger. Find the sum of their ages.
____ + ___ = ____
The sum of their ages is ____ years.
Answer:

Explanation:
Given:
harry is 12 years old
and he has a sister who is 9 years old
the total sum of the there age will be as follows
12 + 9 = 21
The sum of their ages is 21 years.

Question 5.
Greg has collected 32 green jumping beans. His mother gives him 15 red jumping beans more. Find the sum of jumping beans Greg has now.
___ + ____ = ____
The sum of jumping beans Greg has now is ____
Answer:

Explanation:
Greg has 32 green colored jumping beans
Later on his mother had given more 15 jumping beans which were in red color
Now, The total jumping beans now Greg has is
32 + 15 = 47
The sum of jumping beans Greg has now is 47

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 10 Practice 2 Mental Addition to score better marks in the exam.

Math in Focus Grade 2 Chapter 10 Practice 2 Answer Key Mental Addition

Climb each step by adding mentally.

Question 1.

Answer:

Find the missing numbers.
Add mentally.

Example

Question 2.
75 + 6 = ?

75 + ___ = ____
____ – ___ = ____
So, 75 + 6 = ___
Answer:

Explanation:
75 + 10 = 85
85 – 4 = 81
So, 75 + 6 = 81

Question 3.
69 + 5 = ___
Answer:

Explanation:
69 + 10 = 79
79 – 5 = 74
So, 69 + 5 = 74

Question 4.
48 + 4 = ___
Answer:

Explanation:
48 + 10 = 58
58 – 6 = 52
So, 48 + 4 = 52

Question 5.
29 + 9 = ___
Answer:

Explanation:
29 + 10 = 39
39 – 1 = 38
So, 29 + 9 = 38

Question 6.
65 + 8 = ___
Answer:

Explanation:
65 + 10 = 75
75 – 2 = 73
So, 65 + 8 = 73

Find the missing numbers. Add mentally.

Example
123 + 5 = ?

Question 7.
632 + 7 = ___
Answer:

Explanation:
2 + 7 = 9
630 + 9 = 639
so, 632 + 7 = 639

Question 8.
712 + 3 = ___
Answer:

Explanation:
2 + 3 = 5
710 + 5 = 715
so, 712 + 3 = 715

Question 9.
534 + 5 = ___
Answer:

Explanation:
4 + 5 = 9
530 + 9 = 539
so, 534 + 5 = 539

Question 10.
375 + 6 = ___
Answer:

Explanation:
5 + 6 = 11
370 + 11 = 381
so, 375 + 6 = 381

Question 11.
275 + 8 = ___
Answer:

Explanation:
5 + 8 = 13
270 + 13 = 283
so, 275 + 8 = 283

Question 12.
629 + 9 = ___
Answer:

Explanation:
9 + 9 = 18
620 + 18 = 638
so, 629 + 9 = 638

Find the missing numbers.
Add mentally.

Example
246 + 20 = ?

Question 13.
348 + 50 = ___
Answer:

Explanation:
40 + 50 = 90
308 + 90 = 398
so, 348 + 50 = 398

Question 14.
741 + 30 = ___
Answer:

Explanation:
40 + 30 = 70
701 + 70 = 771
so, 741 + 30 = 771

Question 15.
653 + 10 = ___
Answer:

Explanation:
50 + 10 = 60
603 + 60 = 663
so, 653 + 10 = 663

Example
352 + 70 = ?

Question 16.
427 + 80 = ___
Answer:

Explanation:
427  + 100 = 527
527 – 20 = 507
so, 427 + 80 = 507

Question 17.
535 + 90 = ___
Answer:

Explanation:
535  + 100 = 635
635 – 10 = 625
so, 535 + 90 = 625

Question 18.
164 + 60 = ___
Answer:

Explanation:
164  + 100 = 265
264 – 40 = 224
so, 164 + 60 = 224

Find the missing numbers.
Add mentally.

Example
315 + 200 = ?

Question 19.
765 + 100 = ?

Explanation:
___ + 100 = ___
____ + ____ = ____
So, 765 + 100 = ___
Answer:

Explanation:
700 + 100 = 800
65 + 800 = 865
So, 765 + 100 = 865

Add mentally.

Question 20.
452 + 500 = ___
Answer:

Explanation:
400 + 500 = 900
52 + 900 = 952
So, 452 + 500 = 952

Question 21.
264 + 300 = ___
Answer:

Explanation:
200 + 300 = 500
64 + 500 = 564
So, 264 + 300 = 564

Question 22.
412 + 300 = ___
Answer:

Explanation:
400 + 300 = 700
12 + 700 = 712
So, 412 + 300 = 712

Question 23.
178 + 300 = ____
Answer:

Explanation:
100 + 300 = 400
78 + 400 = 478
So, 178 + 300 = 478

Question 24.
708 + 200 = ___
Answer:

Explanation:
700 + 200 = 900
8 + 900 = 908
So, 708 + 200 = 908

Question 25.
320 + 600 = ___
Answer:

Explanation:
300 + 600 = 900
20 + 900 = 920
So, 320 + 600 = 920