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This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 2 Drawing Cubes and Rectangular Prisms provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 2 Answer Key Drawing Cubes and Rectangular Prisms

Draw on dot paper.

Question 1.
Draw a unit cube.

Answer:

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
Shown the volume of a unit cube = Side × Side × Side,
= 1 unit × 1 unit × 1 unit,
= 1 unit cubes.

Question 2.
Draw two different views of a rectangular prism made up of 2 unit cubes.

Answer:

Explanation:
Drawn two different views of a rectangular prism made up of 2 unit cubes,
A unit cube has all its sides of length 1 unit
and 2 unit cubes shows the volume of a 2 unit cubes = 2 X (Sides × Side × Side),
= 2 X (1 unit × 1 unit × 1 unit),
= 2 unit cubes.

Question 3.
Draw two different solids made up of 3 unit cubes each.

Answer:

Explanation:
Drawn two different views of a rectangular prism made up of 3 unit cubes,
A unit cube has all its sides of length 1 unit
and 3 unit cubes shows the volume of a 3 unit cubes = 3 X (Sides × Side × Side),
= 3 X (1 unit × 1 unit × 1 unit),
= 3 unit cubes.

Draw each cube or rectangular prism on the dot paper.

Example

Question 4.

Answer:

Explanation:
Drawn one cube on the dot paper,
As given cube has 4 units shown the volume of cube =
side X side X side = 4 units X 4 units X 4 units = 64 unit cubes.

Question 5.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 4 units X 4 units  X 1 unit =
16 unit cubes rectangular prism.

Question 6.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 4 units X 2 units  X 2 units =
16 unit cubes rectangular prism.

Draw each cube or rectangular prism on the dot paper.

Question 7.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 2 units X 2 units  X 2 units =
8 unit cubes rectangular prism.

Question 8.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 3 units X 1 unit  X 1 unit =
3 unit cubes rectangular prism.

Draw a cube with edges 4 times as long as the edges of this unit cube.

Question 9.

Answer:

Explanation:
Given 1 unit cube with volume 1 unit X 1 unit X 1 unit = 1 cubic unit and
Drawn a cube with edges 4 times as long as the given edge so the volume is
4 units X 4 units X 4 units = 64 cubic units.

Complete the drawing of each cube or rectangular prism.

Question 10.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 2 units.

Question 11.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 3 units.

Question 12.

Answer:

Explanation:
Completed the drawing of given rectangular prism as shown above
which has 2 units.

Question 13.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 3 units.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 5 Rounding and Estimating to finish your assignments.

Math in Focus Grade 5 Chapter 1 Practice 5 Answer Key Rounding and Estimating

Mark an ✗ to show where each number is located on the number line. Then round each number.

Example

656 rounded to the nearest ten is 660

Question 1.

9,709 rounded to the nearest hundred is ____
Answer: 9,700
Rounding is a way of simplifying numbers to make them easier to understand or work with. Rounding can be used when an exact number isn’t needed, and an approximate answer will do.
When rounding a number such as 9709 to the nearest hundred, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule B applies and 9709 rounded to the nearest hundred is: 9,700

9,709 rounded to the nearest hundred is 9,700.

Question 2.

31,600 rounded to the nearest thousand is ___
Answer: 32,000
Rounding off the numbers means shortening the length of the number from long digits by replacing it with the nearest value. Round of to the nearest 1000 means minimizing the given decimal number to its nearest 1000 value.
How to round off the numbers to the nearest 1000:
Based on the below steps, we can easily round the numbers to the nearest 1000.
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
Number 31,600 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 1.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply 3(i) conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
31,600 rounding of the nearest 1000 is equal to 32,000.

Round each number to the nearest thousand.

Question 3.
5,637 ____
Answer: 6000
Explanation:
Rounding off the numbers means shortening the length of the number from long digits by replacing it with the nearest value. Round of to the nearest 1000 means minimizing the given decimal number to its nearest 1000 value.
How to round off the numbers to the nearest 1000:
Based on the below steps, we can easily round the numbers to the nearest 1000.
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
Number 5,637 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 6.
Step 3: The hundred’s digit ‘6’ is >5, then we have to apply 3(ii) conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
5,637 rounding of the nearest 1000 is equal to 6000.

Question 4.
9,541 ____
Answer: 10,000
Explanation:
Number 9,541 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
9,541 rounding of the nearest 1000 is equal to 10,000.

Question 5.
1,399 ___
Answer: 1000
Explanation:
Number 1,399 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 1.
Step 2: Hundred’s digit of the number is 3.
Step 3: The hundred’s digit ‘3’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
1,399 rounding of the nearest 1000 is equal to 1000.

Question 6.
72,245 ____
Answer:  72000
Explanation:
Number 72,245 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 2.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
72,245 rounding of the nearest 1000 is equal to 72,000.

Question 7.
473,075 _________
Answer: 473,000
Explanation:
Number 473,075 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
473,075 rounding of the nearest 1000 is equal to 473,000.

Question 8.

69,547 ___
Answer: 70,000
Explanation:
Number 69,547 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
69,547 rounding of the nearest 1000 is equal to 70,000.

Question 9.
20,100 ____
Answer: 20,000
Explanation:
Number 20,100 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 0.
Step 2: Hundred’s digit of the number is 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
20,100 rounding of the nearest 1000 is equal to 20,000.

Question 10.
756,715 ____
Answer: 757000
Explanation:
Number 756,715 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
756,715 rounding of the nearest 1000 is equal to 757,000.

Answer each question. Use the number line to help you.

Example
Rounding to the nearest thousand, what is the least and the greatest number that rounds to 3,000?

Least number: 2,500
Greatest number: 3,499

Question 11.
Rounding to the nearest thousand, what is
a. the least number that rounds to 5,000?

_______
Answer: The least number of 5000 is 4,500.
Explanation:
Number 4,500 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
4,500 rounding of the nearest 1000 is equal to 5,000.
So, the least number to round up 5000 is 4,500.

b. the greatest number that rounds to 90,000?

Answer:90,499
Explanation:
Number 90,000 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 0.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
But here the greatest number is asked to round up the 90,000 that means the number we need to find out to get the 90,000 if we calculate the nearest values to that number.
If I take 90,499.
Step 1: The thousand’s place is 0.
Step 2: Hundred’s place is 4.
Step 3: The hundred’s digit ‘4’ is <5 then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Finally, if we calculate 90,499 with the nearest 1000 with the above rules then the number will be 90,000.

Round each number to the nearest thousand. Then estimate the sum.

Example
9,286 + 5.703
9,286 rounds to 9,000.
5,703 rounds to 6,000.
9,000 + 6,000 = 15,000

Question 12.
6,789 + 4,200
Answer:11000.
Explanation:
Number 6,789 and 4,200 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 4.
Step 2: Hundred’s digit of the number is 7 and 2.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’
6,789 rounding of the nearest 1000 is equal to 7000.
4,200 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 7000+4000=11000.

Question 13.
7,264 + 7,153
Answer:14000
Explanation:
Number 7,264 and 7,153 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 7.
Step 2: Hundred’s digit of the number is 2 and 1.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
7,264 rounding of the nearest 1000 is equal to 7000.
7,153 rounding of the nearest 1000 is equal to 7000.
Now add the rounded figures: 7000+7000=14000.

Question 14.
4,885 + 6,075
Answer: 11000
Number 4,885 and 6,075 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 6.
Step 2: Hundred’s digit of the number is 8 and 0.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
4,885 rounding of the nearest 1000 is equal to 5000.
6,075 rounding of the nearest 1000 is equal to 6000.
Now add the rounded figures: 5000+6000=11000.

Question 15.
3,105 + 9,940
Answer: 13000
Number 3,105 and 9,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 3 and 9.
Step 2: Hundred’s digit of the number is 1 and 9.
Step 3: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
3,105 rounding of the nearest 1000 is equal to 3000.
9,940 rounding of the nearest 1000 is equal to 10000.
Now add the rounded figures: 3000+10000=13,000.

Question 16.
7,083 + 2,607
Answer:10,000
Number 3,105 and 9,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 2.
Step 2: Hundred’s digit of the number is 0 and 6.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,083 rounding of the nearest 1000 is equal to 7000.
2,607 rounding of the nearest 1000 is equal to 3000.
Now add the rounded figures: 7000+3000=10,000.

Round each number to the nearest thousand. Then estimate the difference

Example
8,156 – 6,109
8,156 rounds to 8,000.
6,109 rounds to 6,000.
8,000 – 6,00 = 2,000

Question 17.
4,924 – 4,127
Answer: 1000
Number 4,924 and 4,127 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 4.
Step 2: Hundred’s digit of the number is 9 and 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,924 rounding of the nearest 1000 is equal to 5000.
4,127 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 5000-4000=1,000.

Question 18.
7,105 – 3,940
Answer:3000
Number 7,105 and 3,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 3.
Step 2: Hundred’s digit of the number is 9 and 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,105 rounding of the nearest 1000 is equal to 7000.
3,940 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 7000-4000=3000.

Question 19.
4,885 – 1,075 ____
Answer:4000.
Number 4,885 and 1,075 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 1.
Step 2: Hundred’s digit of the number is 8 and 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,885 rounding of the nearest 1000 is equal to 5000.
1,075 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 5000-4000=1000.

Question 20.
3,522 – 2,815
Answer:1000
Step 1: Thousand’s digit of the number is 3 and 2.
Step 2: Hundred’s digit of the number is 5 and 8.
Step 3: The hundred’s digit ‘8 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
3,522 rounding of the nearest 1000 is equal to 4000.
2,815 rounding of the nearest 1000 is equal to 3000.
Now add the rounded figures: 4000-3000=1000.

Question 21.
6,480 – 1,397
Answer: 5000
Number 6,480 and 1,397 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 1.
Step 2: Hundred’s digit of the number is 4 and 3.
Step 3: The hundred’s digit ‘4 and 3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,480 rounding of the nearest 1000 is equal to 6000.
1,397 rounding of the nearest 1000 is equal to 1000.
Now add the rounded figures: 6000-1000=5000.

Use front-end estimation with adjustment to estimate each sum.

Example
1,963 + 3,290 + 7,837
1,000 + 3,000 + 7,000
= 11,000
900 + 200 – &00
= 1,900
To the nearest thousanci:
1,900 → 2,000
11,000 + 2,000 = 13,000

Question 22.
2,541 + 6,061 + 1,681
Answer: 11000
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 2,541, 6,061 and 1,681 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2, 6, and 1.
Step 2: Hundred’s digit of the number is 5, 0, and 6.
Step 3: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘5 and 6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,541 rounding of the nearest 1000 is equal to 3000.
6,061 rounding of the nearest 1000 is equal to 6000.
1,681 rounding of the nearest 1000 is equal to 2000
The front end estimations are 3000, 6000, 2000.
Now add all those estimations:3000+6000+2000=11000.

Question 23.
7,823 + 6,848 + 3,310
Answer:
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 7,823, 6,848 and 3,310 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7, 6, and 3.
Step 2: Hundred’s digit of the number is 8, 8, and 3.
Step 3: The hundred’s digit  ‘3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘8 and 8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,823 rounding of the nearest 1000 is equal to 8000.
6,848 rounding of the nearest 1000 is equal to 7000.
3,310 rounding of the nearest 1000 is equal to 3000
The front end estimations are 8000, 7000, 3000.
Now add all those estimations:8000+7000+3000=18000.

Question 24.
4,197 + 8,936 + 2,226
Answer:
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 4,197, 8,936 and 2,226 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4, 8, and 2.
Step 2: Hundred’s digit of the number is 1, 9, and 2.
Step 3: The hundred’s digit  ‘1 and 2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,197 rounding of the nearest 1000 is equal to 4000.
8,936 rounding of the nearest 1000 is equal to 9000.
2,226 rounding of the nearest 1000 is equal to 2000
The front end estimations are 4000, 9000, 2000.
Now add all those estimations:4000+9000+2000=15000.

Use front-end estimation with adjustment to estimate each difference.

Example .
2,943 – 1,272
2,000 – 1,000
= 1,000
900 – 200 = 700
To the nearest thousand:
700 → 1,000
1,000 + 1,000 = 2,000

Question 25.
6,770 – 3,081
Answer: 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 6,770 and 3,081 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 3.
Step 2: Hundred’s digit of the number is 7 and 0.
Step 3: The hundred’s digit ‘7 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,770 rounding of the nearest 1000 is equal to 7000.
3,081 rounding of the nearest 1000 is equal to 3000.
The front end estimations are 7000, 3000.
Now add all those estimations:7000-3000=4000.

Question 26.
8,764 – 3,589
Answer: 5000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 8,764and 3,589 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8 and 3.
Step 2: Hundred’s digit of the number is 7 and 5.
Step 3: The hundred’s digit ‘7 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
8,764 rounding of the nearest 1000 is equal to 9000.
3,589 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 9000, 4000.
Now subtract all those estimations:9000-4000=5000.

Question 27.
7,802 – 4,396
Answer: 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 7,802 and 4,396 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 4.
Step 2: Hundred’s digit of the number is 8 and 3.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
7,802 rounding of the nearest 1000 is equal to 8000.
4,396 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 8000, 4000.
Now subtract all those estimations:8000-4000=4000.

Use front-end estimation with adjustment to estimate each difference.

Example
7,594 – 2,831
7,000 – 2,000 = 5,000
800 – 500 = 300
To the nearest thouari:
300 → 0
5,000 – 0 = 5,000

Question 28.
5,780 – 3,962
Answer: 2000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 5,780 and 3,962 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5 and 3.
Step 2: Hundred’s digit of the number is 7 and 9.
Step 3: The hundred’s digit ‘7 and 9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
5,780 rounding of the nearest 1000 is equal to 6000.
3,962 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 6000, 4000.
Now subtract all those estimations:6000-4000=2000.

Question 29.
9,119 – 4,852
Answer; 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 9,119 and 4,852 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9 and 4.
Step 2: Hundred’s digit of the number is 1 and 8.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
9,119 rounding of the nearest 1000 is equal to 9000.
4,852 rounding of the nearest 1000 is equal to 5000.
The front end estimations are 9000, 5000.
Now subtract all those estimations:9000-5000=4000.

Question 30.
8,254 – 4,836
Answer: 3000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 8,254 and 4,836 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8 and 4.
Step 2: Hundred’s digit of the number is 2 and 8.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
8,254 rounding of the nearest 1000 is equal to 8000.
4,836 rounding of the nearest 1000 is equal to 5000.
The front end estimations are 8000, 5000.
Now subtract all those estimations:8000-5000=3000.

Estimate each product.

Example
4,512 × 2
4,512 rounds to 5,000.
5,000 × 2 = 10,000

Question 31
3,765 × 7
Answer: 8000
Number 3,765 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
3,765 rounding of the nearest 1000 is equal to 4000.
The estimation is 4000
Now multiply with the given number that is 7:
4000×2=8000

Question 32.
2,521 × 5
Answer: 15000
Explanation:
Number 2,521 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,521 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now multiply with the given number that is 5:
3000×5=15000.

Question 33.
5,108 × 6
Answer: 30,000
Explanation:
Number 5,108 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 1.
Step 3: The hundred’s digit  ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
5,108 rounding of the nearest 1000 is equal to 5000.
The estimation is 5000
Now multiply with the given number that is 6:
5000×6=30,000.

Question 34.
8,497 × 9
Answer: 72,000
Explanation:
Number 8,497 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8.
Step 2: Hundred’s digit of the number is 4.
Step 3: The hundred’s digit  ‘4’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
8,497 rounding of the nearest 1000 is equal to 8000.
The estimation is 8000
Now multiply with the given number that is 9:
8000×9=72,000.

Question 35.
6,060 × 3
Answer:
Explanation:
Number 6,060 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,060 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now multiply with the given number that is 3:
6000×3=18,000.

Estimate each quotient.

2,786 ÷ 5
2,500 ÷ 5
2,786 rounds to 3,000.
3,000 ÷ 5 = 600

Look for compatible numbers.

Which number is nearer to 2,786?

Question 36
6,509 ÷ 7
Answer: 1000
Explanation:

Why I choose 7000 to the nearest number I will explain below:
Number 6,509 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
6,509 rounding of the nearest 1000 is equal to 7000.
The estimation is 7000
Now divide with the given number that is 7:
7000÷7=1000.

Question 37.
5,512 ÷ 6
Answer: 1000

Explanation:
Why I choose 6000 to the nearest number I will explain below:
Number 5,512 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
5,512 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now divide with the given number that is 6:
6000÷6=1000.

Question 38.
2,785 ÷ 3
Answer: 1000
Explanation:

Number 2,785 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,785 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now divide with the given number that is 3:
3000÷3=1000.

Question 39.
6,287 ÷ 8
Answer: 750
Explanation:

Number 6,287 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 2.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,287 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now divide with the given number that is 8:
6000÷8=750.

Question 40.
2,963 ÷ 9
Answer: 333.33
Explanation:

Number 2,963 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 9.
Step 3: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,963 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now divide with the given number that is 9:
3000÷9=333.33.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 4 Answer Key Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals

Write each fraction as a decimal.

Example

\(\frac{3}{5}\) = \(\frac{3}{5}\)
= 0.6

Question 1.
\(\frac{13}{20}\) = ____
= _____
Answer:
\(\frac{13}{20}\) = \(\frac{13}{20}\)
= 0.65
Explanation:
Written the fraction as a decimal.

Question 2.
\(\frac{19}{25}\) = ____
= _____
Answer:
\(\frac{19}{25}\) =\(\frac{19}{25}\)
= 0.76
Explanation:
Written the fraction as a decimal.

Question 3.
\(\frac{47}{50}\) = ____
= _____
Answer:
\(\frac{47}{50}\) = \(\frac{47}{50}\)
= 0.94
Explanation:
Written the fraction as a decimal.

Express each division expression as a mixed number in simplest form and as a decimal.

Explanation:

Question 4.
7 ÷ 2
Answer:
7 ÷ 2 = \(\frac{6}{2}\) + \(\frac{1}{2}\)
= 3 + \(\frac{1}{2}\)
= 3 + 0.5
= 3.5

Explanation:
Converted division expression into mixed fraction and decimal

Question 5.
9 ÷ 4
Answer:
\(\frac{8}{4}\) + \(\frac{1}{4}\)
= 2 + \(\frac{1}{4}\)
= 2 + 0.25
= 2.25

Explanation:
Converted division expression into mixed fraction and decimal

Question 6.
21 ÷ 5
Answer:
\(\frac{20}{5}\) + \(\frac{1}{5}\)
= 4 + \(\frac{1}{5}\)
= 4 + 0.2
= 4.2

Explanation:
Converted division expression into mixed fraction and decimal

Question 7.
101 ÷ 25
Answer:
\(\frac{100}{25}\) + \(\frac{1}{25}\)
= 1 + \(\frac{1}{25}\)
= 4 + 0.04
= 4.04

Explanation:
Converted division expression into mixed fraction and decimal

Express each improper fraction as a decimal.

Example
\(\frac{3}{2}\) = \(\frac{2}{2}\) + \(\frac{1}{2}\)
= 1 + \(\frac{1}{2}\)
= 1 + 0.5
= 1.5
Explanation:
Converted each improper fraction into decimal

Question 8.
\(\frac{22}{5}\)
Answer:
\(\frac{20}{5}\) + \(\frac{2}{5}\)
= 4 + \(\frac{2}{5}\)
= 4 + 0.4
= 4.4
Explanation:
Converted each improper fraction into decimal

Question 9.
\(\frac{47}{20}\)
Answer:
\(\frac{40}{20}\) + \(\frac{7}{20}\)
= 2 + \(\frac{7}{20}\)
= 2 + 0.35
= 2.35
Explanation:
Converted each improper fraction into decimal

Question 10.
\(\frac{32}{25}\)
Answer:
\(\frac{25}{25}\) + \(\frac{7}{25}\)
= 1 + \(\frac{7}{25}\)
= 1 + 0.28
= 1.28
Explanation:
Converted each improper fraction into decimal

Solve. Show your work.

Question 11.
A coil of rope 603 feet long is cut into 25 equal pieces. What is the length of each piece? Express your answer as a mixed number and as a decimal.
Answer:
24.12 in decimal
24\(\frac{3}{25}\) in mixed fraction.
Explanation:
A coil of rope 603 feet long is cut into 25 equal pieces.
603 ÷  25 = \(\frac{600}{25}\) + \(\frac{3}{25}\)
= 24 + \(\frac{3}{25}\)
= 24\(\frac{3}{25}\)
= 24 + 0.12
= 24 .12
24.12 is the length of each piece

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 5 Adding Mixed Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 5 Answer Key Adding Mixed Numbers

Add. Express each sum in simplest form.

Example

Question 1.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 2.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Add. Express each sum in simplest form

Question 3.
3\(\frac{2}{7}\) + 2\(\frac{5}{14}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 4.
5\(\frac{7}{12}\) + 3\(\frac{1}{4}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 5.
4\(\frac{1}{15}\) + 1\(\frac{3}{10}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 6.
12\(\frac{1}{9}\) + 9\(\frac{5}{6}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Add. Express each sum in simplest form.

Question 7.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 8.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 9.
2\(\frac{3}{4}\) + 3\(\frac{2}{5}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 10.
2\(\frac{5}{9}\) + 1\(\frac{5}{6}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 11.
7\(\frac{8}{9}\) + 9\(\frac{5}{12}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 12.
5\(\frac{7}{12}\) + 1\(\frac{3}{4}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Use benchmarks to estimate each sum.

Example

Question 13.
9\(\frac{6}{7}\) + 7\(\frac{5}{12}\)
Answer:
17\(\frac{1}{2}\)
Explanation:
\(\frac{6}{7}\) is near to the benchmark 1
\(\frac{5}{12}\) is near to the bench mark \(\frac{1}{2}\)
9 + 1 = 10
10 + 7 \(\frac{1}{2}\)
17\(\frac{1}{2}\)

Question 14.
4\(\frac{7}{12}\) + 10\(\frac{1}{9}\)
Answer:
14 \(\frac{1}{2}\)
Explanation:
\(\frac{7}{12}\) is near to the benchmark \(\frac{1}{2}\)
\(\frac{1}{12}\) is near to the bench mark 0
10 + 0 = 10
4\(\frac{1}{2}\) + 10
= 14 \(\frac{1}{2}\)

Go through the Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 3 and 4 to finish your assignments.

Math in Focus Grade 5 Cumulative Review Chapters 3 and 4 Answer Key

Concepts and Skills
Shade and label the model to show the sum of \(\frac{1}{3}\) and \(\frac{3}{5}\).
Then complete the addition sentence. (Lesson 3.1)

Question 1.

Answer:
\(\frac{1}{3}\) + \(\frac{3}{5}\) =
\(\frac{5}{15}\) + \(\frac{9}{15}\).=
\(\frac{14}{15}\)
Explanation:
Making unlike denominators to like denominators.

Explanation:
Making unlike denominators to like denominators.

Add. Express each sum in simplest form. (Lesson 3.1)

Question 2.
\(\frac{3}{4}\) + \(\frac{1}{12}\) =
Answer:
\(\frac{3}{4}\) + \(\frac{1}{12}\) =
\(\frac{9}{12}\) + \(\frac{1}{12}\) =
\(\frac{10}{12}\)
Explanation:
Making unlike denominators to like denominators.
And added the fractions

Question 3.
\(\frac{3}{5}\) + \(\frac{2}{7}\) =
Answer:
\(\frac{3}{5}\) + \(\frac{2}{7}\) =
\(\frac{21}{35}\) + \(\frac{10}{35}\) =
\(\frac{31}{35}\)
Explanation:
Making unlike denominators to like denominators.
and added the fractions

Estimate each sum by using the benchmarks, 0, \(\frac{1}{2}\) or 1. (Lesson 3.1)

Question 4.
\(\frac{8}{9}\) + \(\frac{2}{5}\) =
Answer:
= \(\frac{3}{2}\)
Explanation:
Estimating \(\frac{8}{9}\) as 1
and \(\frac{2}{5}\)  as \(\frac{1}{2}\)
1 + \(\frac{1}{2}\)
= \(\frac{3}{2}\)

Question 5.
\(\frac{1}{8}\) + \(\frac{6}{7}\) + \(\frac{1}{6}\) =
Answer:
\(\frac{1}{8}\) + \(\frac{6}{7}\) + \(\frac{1}{6}\) =
Estimated answer = 1
Explanation:
Estimating the bench marks
\(\frac{1}{8}\) = 0
\(\frac{6}{7}\) = 1
\(\frac{1}{6}\) = 0
0 + 1  + 0 = 1

Shade and label the model to show the difference between \(\frac{4}{5}\) and \(\frac{2}{3}\). Then complete the subtraction sentence. (Lesson 3.2)

Question 6.

Answer:

Explanation:
Simplified the fractions.

Subtract. Express each difference in simplest form. (Lesson 3.2)

Question 7.
\(\frac{3}{4}\) – \(\frac{1}{12}\) = \(\frac{2}{3}\)
Answer:
\(\frac{3}{4}\) – \(\frac{1}{12}\) = \(\frac{2}{3}\)
Explanation:

Question 8.
\(\frac{3}{5}\) – \(\frac{3}{9}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{3}{9}\) = \(\frac{4}{15}\)
Explanation:

Estimate each difference by using the benchmarks, 0, \(\frac{1}{2}\) or 1. (Lesson 3.2)

Question 9.
\(\frac{4}{5}\) – \(\frac{3}{8}\)
Answer:
\(\frac{4}{5}\) – \(\frac{3}{8}\) = \(\frac{1}{2}\)
Explanation:
Estimating the fractions to bench marks
\(\frac{4}{5}\) = 1
\(\frac{3}{8}\) = \(\frac{1}{2}\)
1 – \(\frac{1}{2}\)  = \(\frac{1}{2}\)

Question 10.
\(\frac{7}{12}\) – \(\frac{5}{9}\)
Answer:
\(\frac{7}{12}\) – \(\frac{5}{9}\) = 1
Explanation:
Estimating the fractions to bench marks
\(\frac{7}{12}\)  = \(\frac{1}{2}\)
\(\frac{5}{9}\) = \(\frac{1}{2}\)
\(\frac{1}{2}\)  + \(\frac{1}{2}\)  = 1

Write each fraction as a division expression. (Lesson 3.3)

Question 11.

Answer:

Explanation:
\(\frac{4}{9}\)
Fraction into expression.

Question 12.

Answer:

Explanation:
\(\frac{8}{11}\)
Fraction into expression.

Write each division expression as a fraction. (Lesson 3.3)

Question 13.
\(\frac{5}{6}\) = ___ ÷ ___
Answer:
5 ÷ 6
\(\frac{5}{6}\) = 5 ÷ 6
Explanation:
converting division expression as a fraction.

Question 14.
\(\frac{7}{12}\) = ___ ÷ ___
Answer:
7 ÷ 12
\(\frac{7}{12}\) = 7 ÷ 12
Explanation:
converting division expression as a fraction.

Complete. (Lesson 3.3)

Question 15.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Question 16.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Divide. Express each quotient as a mixed number in simplest form. (Lesson 3.3)

Question 17.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Question 18.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Express each fraction as a decimal. (Lesson 3.4)

Question 19.
\(\frac{4}{5}\) = ____
= _________
Answer:
\(\frac{4}{5}\) = 0.8
Explanation:

Question 20.
\(\frac{17}{20}\) = ____
= _________
Answer:

Explanation:
\(\frac{17}{20}\) = 0.85

Express each division expression as a mixed number and as a decimal. (Lessons 3.3 and 3.4)

Explanation:

Question 21.
13 ÷ 4 = 3\(\frac{1}{4}\)
Answer:

Explanation:
13 ÷ 4 = 3.25

Question 22.
23 ÷ 5
Answer:

Explanation:
23 ÷ 5 = 5.6

Add. Express each sum in simplest form. (Lesson 3.5)

Question 23.
2\(\frac{2}{7}\) + 3\(\frac{1}{2}\)
Answer:

2\(\frac{2}{7}\) + 3\(\frac{1}{2}\) = 5\(\frac{11}{14}\)

Question 24.
1\(\frac{1}{2}\) + 1\(\frac{5}{9}\)
Answer:

Explanation:
1\(\frac{1}{2}\) + 1\(\frac{5}{9}\) = 3\(\frac{1}{18}\)

Estimate each sum by using the nearest whole number or half. (Lesson 3.5)

Question 25.
1\(\frac{5}{8}\) + 1\(\frac{1}{5}\)
Answer:

Explanation:
1\(\frac{5}{8}\) + 1\(\frac{1}{5}\) = 3\(\frac{1}{18}\) = 3 + 0 = 3
Converting the fraction into a whole number.

Question 26.
2\(\frac{1}{6}\) + 3\(\frac{4}{5}\)
Answer:

Explanation:
2\(\frac{1}{6}\) + 3\(\frac{4}{5}\) = 5\(\frac{29}{30}\)
Converting the fraction into a whole number.
5 + 1 = 6

Subtract. Express each difference in simplest form. (Lesson 3.6)

Question 27.
5\(\frac{8}{9}\) – 3\(\frac{5}{6}\)
Answer:

Explanation:
5\(\frac{8}{9}\) – 3\(\frac{5}{6}\) = 2\(\frac{1}{18}\)
2 + 0 = 2

Question 28.
4\(\frac{2}{7}\) – 2\(\frac{7}{8}\)
Answer:

Explanation:
4\(\frac{2}{7}\) – 2\(\frac{7}{8}\) = 1\(\frac{23}{56}\)
= 1 + \(\frac{1}{2}\)
= \(\frac{3}{2}\)

Estimate difference by using the nearest whole number or half. (Lesson 3.6)

Question 29.
2\(\frac{1}{10}\) – 1\(\frac{4}{7}\)
Answer:

Explanation:
2\(\frac{1}{10}\) – 1\(\frac{4}{7}\) = \(\frac{37}{70}\) = \(\frac{1}{2}\)
Converting the fraction into a half

Question 30.
3\(\frac{3}{8}\) – 1\(\frac{7}{12}\)
Answer:

Explanation:
3\(\frac{3}{8}\) – 1\(\frac{7}{12}\) = 1\(\frac{19}{24}\)
= 1 + 1 = 2

Find the product in simplest form. (Lesson 4.1)

Question 31.
\(\frac{6}{7}\) × \(\frac{5}{8}\) =
Answer:

Explanation:
\(\frac{6}{7}\) × \(\frac{5}{8}\) = \(\frac{15}{28}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 32.
\(\frac{4}{5}\) × \(\frac{10}{12}\) =
Answer:

Explanation:
\(\frac{4}{5}\) × \(\frac{10}{12}\) = \(\frac{2}{3}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 33.
\(\frac{2}{5}\) of \(\frac{10}{11}\) =
Answer:

Explanation:
\(\frac{2}{5}\) of \(\frac{10}{11}\) =\(\frac{4}{11}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 34.
\(\frac{8}{9}\) of \(\frac{5}{12}\) =
Answer:

Explanation:
\(\frac{8}{9}\) of \(\frac{5}{12}\)  = \(\frac{10}{27}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product in simplest form. (Lesson 4.3)

Question 35.
\(\frac{2}{5}\) × \(\frac{15}{7}\) =
Answer:

Explanation:
\(\frac{2}{5}\) × \(\frac{15}{7}\) = \(\frac{6}{7}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 36.
\(\frac{9}{5}\) × \(\frac{5}{12}\) =
Answer:

Explanation:
\(\frac{9}{5}\) × \(\frac{5}{12}\) = \(\frac{3}{4}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.3)

Question 37.
\(\frac{4}{3}\) × \(\frac{7}{6}\) =
Answer:

Explanation:
\(\frac{4}{3}\) × \(\frac{7}{6}\) = \(\frac{14}{9}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 38.
\(\frac{8}{3}\) × \(\frac{9}{12}\) =
Answer:

Explanation:
\(\frac{8}{3}\) × \(\frac{9}{12}\)= 2
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 39.
\(\frac{7}{8}\) × \(\frac{6}{5}\) =
Answer:

Explanation:
\(\frac{7}{8}\) × \(\frac{6}{5}\) = \(\frac{21}{20}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 40.
\(\frac{25}{4}\) × \(\frac{10}{8}\) =
Answer:

Explanation:
\(\frac{25}{4}\) × \(\frac{10}{8}\) = \(\frac{125}{16}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.4)

Question 41.
2\(\frac{1}{4}\) × 16 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 16
And done the simplest form to make into a whole number

Question 42.
27 × 1\(\frac{2}{9}\) =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 27
And done the simplest form to make into a whole number

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.4)

Question 43.
5\(\frac{3}{6}\) × 42 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 42
And done the simplest form to make into a whole number

Question 44.
2\(\frac{5}{6}\) × 15 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 15
And done the simplest form to make into a whole number

Divide. Express each quotient in simplest form. (Lesson 4.6)

Question 45.
3 ÷ \(\frac{1}{9}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 46.
6 ÷ \(\frac{1}{8}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 47.
5 ÷ \(\frac{1}{5}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 48.
2 ÷ \(\frac{1}{10}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 49.
\(\frac{7}{8}\) ÷ 5 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 50.
\(\frac{5}{8}\) ÷ 4 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 51.
\(\frac{4}{7}\) ÷ 12 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 52.
\(\frac{2}{9}\) ÷ 6 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Problem Solving

Solve. Show your work.

Question 53.
Ron used \(\frac{3}{5}\) pound of flour to bake bread and \(\frac{2}{7}\) pound of flour to bake scones. How many more pounds of flour did he use to bake bread than scones?
Answer: \(\frac{11}{35}\) more pounds of flour he used to bake bread than scones
Explanation:
Subtract them…
But to subtract fractions you need a common denominator (the smallest thing that 5 and 7 both go into)
Remember when making equivalent fractions with your common denominator (which is 7×5 = 35) make sure you multiply the top by whatever you multiplied the bottom by.

Question 54.
Tina uses 4\(\frac{5}{12}\) yards of wire for her science project. Kelvin uses 1\(\frac{2}{3}\) yards of wire for his project. How many yards of wire do they use altogether?
Answer: 6\(\frac{1}{12}\) yards of wire used altogether
Explanation:

Solve. Show your work

Question 55.
Rosa poured 1\(\frac{3}{4}\) quarts of grape juice into a container. She added 3\(\frac{1}{3}\) quarts of apple juice. She then poured 2\(\frac{2}{3}\) quarts of the mixed juice into a pitcher. How many quarts of mixed juice were left in the container?
Answer: 2\(\frac{5}{12}\)
Explanation:
1\(\frac{3}{4}\) =1\(\frac{9}{12}\)
3\(\frac{1}{3}\) = 3\(\frac{4}{12}\)

1\(\frac{9}{12}\)+ 3\(\frac{4}{12}\) = 4\(\frac{13}{12}\) = 5\(\frac{1}{12}\)

4\(\frac{13}{12}\) – 2\(\frac{8}{12}\) = 2\(\frac{5}{12}\)

Question 56.
A race was \(\frac{11}{12}\) mile long. Hamish ran \(\frac{4}{5}\) of the distance.

a. Without multiplying, explain how you know that the answer must be less than \(\frac{11}{12}\).
Answer:
With the help of bench mark. Both the values are lesser than 1. So he ran less than \(\frac{11}{12}\).

b. How far did he run?
Answer: \(\frac{7}{60}\)
Explanation:

Solve. Show your work.

Question 57.
Ashley uses \(\frac{1}{4}\) package of raisins for o fruit cake. She then uses \(\frac{1}{9}\) of the remainder for muffins. What fraction of the package of raisins does she have left?
Answer: \(\frac{23}{36}\) of the package of raisins she have left
Explanation:

Question 58.
Mrs. Vernon used 4\(\frac{3}{8}\) pounds of meat in each of her 12 pots of soup. How many pounds of meat did she use for the 12 pots of soup?
Answer: 52\(\frac{1}{2}\) pounds of meat she used.
Explanation:

Solve. Show your work.

Question 59.
A custodian pours \(\frac{1}{8}\) gallon of cleaning solution into each pail of water that she uses.

a. How many pails of water and cleaning solution can the custodian make using 16 gallons of cleaning solution?
Answer:

b. Find the volume of solution in two of these pails.
Answer:

 

 

 

Question 60.
A carnival sold 135 bottles of juice in one day. They sold \(\frac{1}{3}\) of the bottles in the first hour and \(\frac{2}{5}\) of the bottles in the second hour. How many bottles of juice did they sell altogether in these two hours?
Answer: 99 bottles sold altogether in these two hours
Explanation:

Solve. Show your work.

Question 61.
Ms. Li spent $840 on a vacation. She spent \(\frac{2}{3}\) of the amount on a plane ticket and \(\frac{1}{2}\) of the remaining amount on food. How much did she spend on the ticket and food altogether?
Answer: So she spent $560+$140 = $ 700  on the ticket and food altogether
Explanation:
Ms. Li spent $840 on a vacation. She spent \(\frac{2}{3}\) of the amount on a plane ticket. So she spent $560 for plane ticket.

She spent \(\frac{1}{2}\) of the remaining amount on food.
Remaining amount is $280.
So she spent $ 140 on food

So she spent $560+$140 = $ 700  on the ticket and food altogether

Question 62.
Sam traveled \(\frac{3}{4}\) of a journey by bus. He jogged \(\frac{1}{2}\) the remaining distance and walked the rest of the way. If he walked 800 feet, what was the total distance he traveled?
Answer: 6400 feet he traveled
Explanation:
Total Distance = x
Sam traveled \(\frac{3}{4}\) of a journey by bus. So it is \(\frac{3}{4}\) x
So remaining distance is x – \(\frac{3}{4}\) x =\(\frac{1}{4}\) x
He jogged \(\frac{1}{2}\) the remaining distance. So he jogged \(\frac{1}{8}\) x

walked the rest of the way . So remining is x – \(\frac{3}{4}\) x + \(\frac{1}{8}\) x  =800

Solve. Show your work.

Question 63.
Matthew used \(\frac{1}{5}\) of a box of flour for cooking and \(\frac{3}{4}\) of the remainder to make bread. The rest of the flour was packed equally into 5 containers. What fraction of the total amount of flour was in each container? r
Answer: \(\frac{1}{100}\) fraction of the total amount of flour was in each container
Explanation:
Matthew used \(\frac{1}{5}\) of a box of flour for cooking. So remaining flour is

\(\frac{3}{4}\) of the remainder to make bread

The rest of the flour was packed equally into 5 containers

Question 64.
A bus driver filled up \(\frac{7}{8}\) of her fuel tank for a trip. She used \(\frac{6}{7}\) of the fuel by the end of the trip. The capacity of her tank is 70 gallons. How much fuel did she use for the trip? Express your answer as a decimal.
Answer: 52.5gallons of fuel she used for the trip
Explanation:
The capacity of her tank is 70 gallons.
A bus driver filled up \(\frac{7}{8}\) of her fuel tank for a trip

So she filled 61.25 gallons of fuel in tank.
She used \(\frac{6}{7}\) of the fuel by the end of the trip.

Question 65.
Sergio walked to and from school on \(\frac{3}{5}\) of the days in one month. He got a ride to school on \(\frac{7}{8}\) of the remaining days. On the one remaining school day that month, he stayed home with a cold. How many school days were there that month?
Answer: 20 days
Explanation:
Total Days = x
Sergio walked to and from school on \(\frac{3}{5}\) of the days in one month = \(\frac{3}{5}\)x
So remaining days = x – \(\frac{3}{5}\)x = \(\frac{2}{5}\)x
He got a ride to school on \(\frac{7}{8}\) of the remaining days. = \(\frac{7}{20}\)x .Since

On the one remaining school day that month, he stayed home with a cold.
So

x =20

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 7 Subtraction with Regrouping in Hundreds, Tens, and Ones to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 7 Answer Key Subtraction with Regrouping in Hundreds, Tens, and Ones

Regroup.
Then subtract.

Question 1.
241 – 173 = ?
241 – 173
= 2 hundreds 4 tens 1 one – 1 hundred 7 tens 3 ones
= 2 hundreds ________ tens 11 ones – 1 hundred 7 tens 3 ones
= _________ hundred 13 tens 11 ones – 1 hundred 7 tens 3 ones
= _________ hundreds _________ tens _________ ones
241 – 173 = ____
Use addition to check your answer.

Answer:
241-173 = 68,
173+68 = 241.

Explanation:
Given that 241 – 173 which is 68. So to check the answer we will perform addition, which is 173+68 = 241.
241 – 173
= 2 hundreds 4 tens 1 one – 1 hundred 7 tens 3 ones
= 2 hundreds 3 tens 11 ones – 1 hundred 7 tens 3 ones
= 1 hundred 13 tens 11 ones – 1 hundred 7 tens 3 ones
= 0 hundreds 6 tens 8 ones.

Question 2.

Answer:
478 – 199 = 279,
279+199 = 478.

Explanation:
Given that 478 – 199 which is 279. So to check the answer we will perform addition, which is
279+199 = 478.

Question 3.

Answer:
555-457 = 98,
457+98 = 555.

Explanation:
Given that 555 – 457 which is 98. So to check the answer we will perform addition, which is
457+98 = 555.

Question 4.
924 – 886 = ___

Answer:
924-886 = 38,
38+886 = 924.

Explanation:
Given that 924-886 which is 38. So to check the answer we will perform addition, which is
38+886 = 924.

Question 5.
818 – 669 = ___

Answer:
818-669 = 149,
149+669 = 818.

Explanation:
Given that 818-669 which is 149. So to check the answer we will perform addition, which is
149+669 = 818.

Help Daryl ride past these rocks to reach the shore. Subtract and write the correct answer on each rock.

Question 6.

Answer:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 2 Practice 5 Addition with Regrouping in Tens to finish your assignments.

Math in Focus Grade 2 Chapter 2 Practice 5 Answer Key Addition with Regrouping in Tens

Add and regroup the tens.

Question 1.
534 + 283 = ?
Add the ones.
4 ones + 3 ones = ones
Add and regroup the tens.
3 tens + 8 tens = ___ tens

= ___ hundred ___ ten
Add the hundreds.
1 hundred + 5 hundreds + 2 hundreds = ___ hundreds
534 + 283 = ____
Answer:
534 + 283 = 817
Explanation:
4 ones + 3 ones = 7 ones
Add and regroup the tens.
3 tens + 8 tens = 11 tens
= 1 hundred 1 ten
Add the hundreds.
1 hundred + 5 hundreds + 2 hundreds = 8 hundreds

Question 2.

Answer:

Explanation:
2  ones + 5 ones = 7 ones
Add and regroup the tens.
6 tens + 7 tens = 13 tens
= 1 hundred 3 ten
Add the hundreds.
1 hundred + 4 hundreds + 1 hundreds = 6 hundreds

Question 3.

Answer:

Explanation:
8 ones + 1 ones = 9 ones
Add and regroup the tens.
4  tens + 6 tens = 10 tens
= 1 hundred 0 ten
Add the hundreds.
1 hundred + 6 hundreds + 1 hundreds = 8 hundreds

Question 4.
295 + 633 = ___

Answer:

Explanation:
5 ones + 3 ones = 8 ones
Add and regroup the tens.
9 tens + 3  tens = 12 tens
= 1 hundred 2 ten
Add the hundreds.
1 hundred + 2 hundreds + 6 hundreds = 9 hundreds

Question 5.
462 + 456 = ___

Answer:

Explanation:
2 ones + 6 ones = 8 ones
Add and regroup the tens.
6 tens + 5 tens = 11 tens
= 1 hundred 1 ten
Add the hundreds.
1 hundred + 4 hundreds + 4 hundreds = 9 hundreds

Add.

Question 6.

Answer:

Kim lost her robots.
Her robots have the same answer.
To help her find her robots, color the robots with the same answer.
Explanation:
no matches were found
for Kim’s lost robots.

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 7 Practice 4 Comparing Lengths in Centimeters to score better marks in the exam.

Math in Focus Grade 2 Chapter 7 Practice 4 Answer Key Comparing Lengths in Centimeters

Look at each drawing. Then fill in the blanks.

Question 1.
Which is longer? Drawing ___

Answer: Drawing A is longer than Drawing B

Question 2.

Drawing ___ is the shortest.
Drawing ___ is the longest.
Explain your answers.
Answer: Drawing B is the shortest.
Drawing C is the longest.

Find each length.

Question 3.

The straw is about ___ centimeters long.
Answer: The straw is about 8 centimeters long.

Question 4.

The wallet is about ____ centimeters long.
Answer: The wallet is about 6 centimeters long.

Question 5.

The key is about __ centimeters long.

Answer: The key is about 2 centimeters long.

Find each length.

Question 6.

The pen is about _________ centimeters long.
Answer: The pen is about 12 centimeters long

These rulers are smaller than in real life.

Question 7.

The bracelet is about _________ centimeters wide.
Answer: The bracelet is about 5 centimeters wide.

Use your answers for Exercises 3 to 6. Fill in the blanks with longer or shorter.

Question 8.
The pen is _________ than the straw.
Answer: The pen is longer than the straw.

Question 9.
The key is _________ than the pen.
Answer: The key is shorter than the pen.

Question 10.
The wallet ¡s _________ than the straw.
Answer: The wallet is shorter than the straw.

Use your answers for Exercises 3 to 7. Fill in the blanks.

Question 11.
The straw is ___ centimeters longer than the key.
Answer:
The straw is 4 centimeters longer than the key
Explanation:
Given,
Straw is 8 cm,
Key is 4 cm,
By subtracting 4 from 8 we get 4,
Therefore, the straw is 4 centimeters longer than the key.

Question 12.
The straw is ___ centimeters shorter than the pen.
Answer: The straw is 4 centimeters shorter than the pen.
Explanation:
Given,
Straw is 8 cm,
Pen is 12 cm,
By subtracting 8 from 12 we get 4,
Therefore, the straw is 4 centimeters shorter than the Pen

Question 13.
The pen is ____ centimeters longer than the key.
Answer: The pen is 10 centimeters longer than the key.
Explanation:
Given,
Pen is 12 cm,
Key is 2 cm,
By subtracting 2 from 12 we get 10,
Therefore, the Pen is 10 centimeters longer than the key

Question 14.
The bracelet is ___ centimeter shorter than the wallet.
Answer: The bracelet is 1 centimeter shorter than the wallet.
Explanation:
Given,
Bracelet is 5 cm,
Wallet is 6 cm,
By subtracting 5 from 6 we get 1,
Therefore, the bracelet is 1 centimeter shorter than the wallet

Question 15.
The longest object is the _____
Answer: The longest object is the pen with 12 cm long.

Question 16.
The shortest object is the ____
Answer: The shortest object is the key with 2 cm.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 5 Practice 5 Real-World Problems: Algebra to finish your assignments.

Math in Focus Grade 5 Chapter 5 Practice 5 Answer Key Real-World Problems: Algebra

Solve. Show your work.

Question 1.
Raul has 5 boxes of golf balls. Each box contains y golf balls. His father gives him another 8 golf balls.

a. Find the total number of golf balls Raul has in terms of y.
Answer:
Number of boxes of golf balls Raul has = 5
As each box contains ‘y’ balls, total number of balls Raul has = 5y
Number of balls given by Raul’s father = 8
So, total number of golf balls does Raul has = 5y+8

b. If y = 4, how many golf balls does Raul have altogether?
Answer:
Total number of golf balls Raul has = 5y+8
If y=4, then total number of golf balls Raul has = (5×4)+8 = 20+8 = 28
So, Raul altogether has 28 balls.

Question 2.
Glenda bought z containers of laundry detergent at $9 each. She gave the cashier $50.

a. Find the change Glenda received in terms of z.
Answer:
Total number of laundry detergent containers bought = z
Cost of all containers bought = (9×z) $
Cash given to cashier = 50 $
Change received by Glenda = [50 – (9×z)] $

b. If z = 3, how much change did Glenda receive?
Answer:
If z=3. then total change received = [50-(9×3)] $ = [50-27]$ = 23$

Question 3.
Garrett is w years old. His mother is 4 times his age. His father is 3 years older than his mother.

a. How old is Garrett’s father in terms of w?
Answer:
Age of Garrett = w years
Age of Garrett’s mother = (4×w) years
Age of Garrett’s father = [(4×w)+3] years

b. If w = 9, how old is Garrett’s father?
Answer:
Age of Garrett’s father = [(4×w)+3] years
If w=9, then age of Garrett’s father = [(4×9)+3] = 39 years

Question 4.
An office manager bought 16 boxes of pens, each containing m pens. Workers took 10 pens from the supply room.

a. How many pens were left? Give your answer in terms of m.
Answer;
Total number of boxes of pens bought = 16
Number of pens each box contains = m
So, total number of pens bought = 16×m
Number of pens workers took from supply room = 10
So. then number of pens left = total number of pens – pens taken by workers
=(16×m)-10

b. If m = 5, how many pens were left in the supply room?
Answer:
Total number of pens left in supply room = (16×m)-10
If m=5, then total number of pens left = (16×5)-10 = 80-10= 70

Solve. Show your work.

Question 5.
Sarah has a box containing x ribbons and 4 extra ribbons. Jill has 1 2 ribbons.

a. Express the number of ribbons that Sarah has in terms of x.
Answer:
Number of ribbons Sarah has in box = x
Number of extra ribbons Sarah has = 4
So, total number of ribbons Sarah has= x+4

b. For what value of x will Sarah and Jill have the same number of ribbons?
Answer:
Number of ribbons Sarah has = x+4
Number of ribbons Jill has = 12
If we need to have same number of ribbons for Sarah and Jill, then
x+4 =8
x=8-4 = 4
So, for the value of x as 4, Sarah and Jill have the same number of ribbons

Question 6.
Henry made (2y + 4) paper cranes. Elise made (3y – 9) paper cranes.

a. If y = 6, who would have made more paper cranes?
Answer:
If y=6,
Paper cranes made by Henry = (2y+4) = [(2×6)+4] = 12+4 = 16
Paper cranes made by Elise= (3y-9) = [(3×6)-9] = 18-9 = 9

b. For what value of y will they have made the same number of paper cranes?
Answer:
Number of paper cranes Henry has = 2y+4
Number of paper cranes Elise has = 3y-9
If we need to have same number of paper cranes for Henry and Elise, then
3y-9 = 2y+4
3y-2y = 4+9
y=13
So, for the value of y as 13, Henry and Elise will have the same number of paper cranes

Solve. Show Your Work

Question 7.
Mary has y yards of fabric. She used 2 yards to sew a skirt. She used the remaining fabric to make 5 jackets.

a. Find the amount of material that was used to make each jacket in terms of y.
Answer:
Total number of yards of fabric = y
Total yards used to sew a skirt = 2
So, total number of yards left = y-2
Number of jackets made with remaining fabric = 5
So, amount of material that was used to make each jacket  = (y-2)/5

b. If she has 17 yards of fabric, how much material was used for each jacket?
Answer:
If y=17, then material used for each jacket = (y-2)/5 = (17-2)/5 = 15/5 = 3

Question 8.
A magazine costs half as much as a book. The book costs p dollars. A pen costs $2 more than the magazine.
a. How much does the pen cost in terms of p?
Answer:
Cost of book = p$
A magazine costs half as much as a book which implies a book is twice the cost of a magazine.
So, cost of magazine = 2p $
A pen costs $2 more than the magazine.
So, cost of pen = 2p$ + 2$ = (2p+2) $

b. If the book costs $5, how much does the pen cost?
Answer:
If book costs $5,
cost of pen = (2p+2) $ = [(2×5)+2] $ = (10+2) $ = 12$

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 6 Practice 3 Finding the Area of a Triangle to score better marks in the exam.

Math in Focus Grade 5 Chapter 6 Practice 3 Answer Key Finding the Area of a Triangle

Example

Question 1.

Area of a triangle = _____
= ________
Answer:
Height = 26 m
Base = 17m
Area of the triangle = 1/2 × b × h
= 1/2 × 17 × 26
= 221 m²

Question 2.

Area of a triangle = _____
= ________
Answer:
From the above figure Base of the triangle is 72 cm. Height of the triangle is 54 cm.
Area of the triangle = 1/2 × b × h
= 1/2 × 72 × 54
= 1,944 cm²

Question 3.

Area of triangle = ____
= _______
Answer:
From the above figure Base of the triangle is 38 ft. Height of the triangle is 45 ft.
Area of the triangle = 1/2 × b × h
= 1/2 × 38 × 45
= 855 ft²

Find the area of each shaded triangle.

Example

Question 4.

Area = ____
= ______
Answer:
From the above figure Base of the triangle is 12 in. Height of the triangle is 4 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 12 × 4
= 24 in²

Question 5.

Area = _____
= ______
Answer:
From the above figure Base of the triangle is 28 in. Height of the triangle is 18 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 28 × 18
= 252 in²

Question 6.

Area = _____
= ______
Answer:
From the above figure Base of the triangle is 5 cm. Height of the triangle is 5 cm.
Area of the triangle = 1/2 × b × h
= 1/2 × 5 × 5
= 25/2 cm²

Question 7.

Area = ____
= ______
Answer:
From the above figure Base of the triangle is 7 in. Height of the triangle is 4 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 4
= 14 in²

Question 8.

Area = _____
= _______
Answer:
From the above figure Base of the triangle is 14 in. Height of the triangle is 15 in.
Area of the triangle = 1/2 × b × h
= 1/2 ×14 × 15
= 105 in²