Math in Focus

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 8 to 10 to score better marks in the exam.

Math in Focus Grade 5 Cumulative Review Chapters 8 to 10 Answer Key

Concepts and Skills

Mark ✗ to show where each decimal is located on the number line. (Lesson 8.1)

Question 1.
0.032

Answer:

Explanation:
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.
Then mark the given number on number line.
Question 2.
0.047
Answer:

Explanation:
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.
Then mark the given number on number line.

Complete. (Lesson 8.1)

Question 3.
3 tenths 5 hundredths = _________ thousandths
Answer:
0.350
3 tenths 5 hundredths = 0.305________ thousandths
Explanation:
Read the whole set of three decimal digits as a number, and say, “tenths”, “hundredths” and “thousandths.” 0.305 has 3 tenths, 0 hundredths, and 5 thousandths. While 0.305 is the sum of 3/10, 0/100, and 5/1000, it is also 305/1000

Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Question 4.
803 thousandths = ______ tenths _______ thousandths
Answer:
803 thousandths = 8 tenths 0 hundredths 3 thousandths
Explanation:
Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Question 5.
0.835 = 8 tenths 3 hundredths _____ thousandths
Answer:
0.835 = 8 tenths 3 hundredths 5 thousandths
Explanation:
Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Write the equivalent decimal. (Lesson 8.1)

Question 6.
8 ones and 214 thousandths = __________
Answer: 8.214
Explanation:
The first digit to the right of decimal point is in the tenths place.
The second digit to the right of decimal point is in the hundredths place.
The third digit to the right of decimal point is in the thousandths place.
So, 8 ones and 214 thousandths.

Question 7.
1,180 thousandths = __________
Answer: 1.180
Explanation:
If you divide 1180 by one thousand you get 1180 thousandths as a decimal which is 1.180.
1180 thousands = 1180/1000 = 1.180

Question 8.
7\(\frac{60}{1000}\) = __________
Answer: 7.06
Explanation:
7 x 1000 + 60 = 7000 + 60 = 7060
\(\frac{7060}{1000}\) = 7.06
7\(\frac{60}{1000}\) = 7.06

Question 9.
\(\frac{6050}{1000}\) = __________
Answer: 6.05
Explanation:
The easiest way to convert a fraction to a decimal is to divide the numerator by the denominator.
Or else count the number of zeros in denominator and place the decimal in the given number by moving from right.
\(\frac{6050}{1000}\) = 6.05

4.526 can be written in expanded form as 4 + 0.5 + 0.02 + 0.006. Write each decimal in expanded notation. (Lesson 8.1)

Question 10.
0.329 = ___ + ___ + ___
Answer:
0.329 = 0.3 + 0.02 + 0.009
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.

20.125 = ___ + ___ + ___ + ___
Answer:
20.125 =20 + 0 + 0.1 + .02 + 0.005
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.

Complete. (Lesson 8.1)

In 9.168,

Question 12.
the digit 6 is in the ___ place.
Answer:
Hundredths place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 6 is in the hundredths place in 9.168.

Question 13.
the value of the digit 8 is ___
Answer:
Thousands place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 8 is in the thousandths place in 9.168.

Question 14.
the digit 1 stands for _______
Answer:
Tenths place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 1 is in the tenths place in 9.168.

Compare. Write >, <, or =. (Lesson 8.2)

Question 15.
1.07 1.7
Answer: <

Explanation:
The value 1.07 is less than the other value 1.7, we use less than.
The symbol used to represent less than is “<”.
As there is no value for zero after decimal.

Question 16.
3.562 3.526
Answer: >

Explanation:
The value 3.562 is greater than the other value 3.526,
The symbol used to represent greater than is “>”.
The number after decimal is more in 562 than in 526.

Question 17.
15.4 15.40
Answer: =

Explanation:
The value 15.4 is equal to 15.40,
In decimal if zero is present in ones place there is no value.

Order the decimals. (Lesson 8.2)

Question 18.
2.08, 1.973, 6.1
Begin with the least:
_____________
Answer:
1.973 , 2.08, 6.1
Explanation:
Arranging the numbers from least to greatest is known as Ascending order.

Question 19.
1.567, 1.667, 1.376
Begin with the greatest:
________________
Answer:
1.667, 1.567, 1.376
Explanation:
Arranging the numbers from least to greatest is known as Descending order.

Fill in the blanks. (Lesson 8.2)

Question 20.
The mass of a strand of hair is 0.179 gram.
Round the mass to the nearest hundredth of a gram.
0.179 gram rounds to ___ gram.
Answer: 0.18
0.179 gram rounds to 0.18 gram.
Explanation:
For rounding decimal numbers to the nearest hundredth,
we need to know the decimal place values of the digits in the given number.
This refers to the digits given before the decimal point as well as the digits given after the decimal point.
It should be noted that when we round numbers to the nearest hundredth,
we always use the thousandths place to decide whether the hundredths place will round up or will remain the same.

Question 21.
The length of a rope is 2.589 yards.
Round the length to the nearest tenth of a yard.
2.589 yards rounds to ___ yards.
Answer: 2.6
2.589 yards rounds to 2.6 yards
Explanation:
For rounding decimal numbers to the nearest hundredth,
we need to know the decimal place values of the digits in the given number.
This refers to the digits given before the decimal point as well as the digits given after the decimal point.
It should be noted that when we round numbers to the nearest hundredth,
we always use the thousandths place to decide whether the hundredths place will round up or will remain the same.

Write each decimal as a mixed number in simplest form. (Lesson 8.3)

Question 22.
6.2 = ___
Answer:
6\(\frac{1}{5}\)
Explanation:
\(\frac{62}{10}\)
6\(\frac{2}{10}\)
6\(\frac{1}{5}\)

Question 23.
2.16 = _______
Answer:
2\(\frac{4}{25}\)
Explanation:
\(\frac{216}{100}\)
2\(\frac{16}{100}\)
2\(\frac{4}{25}\)

Multiply. (Lessons 9.7 and 9.2)

Question 24.
29.3 × 8 = _______
Answer: 234.4
Explanation:
To multiply decimals, first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.

Question 25.
12.08 × 5 = _______
Answer: 60.4
Explanation:
To multiply decimals, first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.

Question 26.
86.4 × 10 = _______
Answer: 864
Explanation:
Separate 10 as 1 ones and 0 tenths,
then multiply with ones first and later tens.
86.4 x 10 = (86.4 x 1) x 10
= 86.4 x 10
= 864
So, 86.4 x 10= 864
Question 27.
13.5 × 30 = ____
Answer: 405
Explanation:
Separate 30 as 3 ones and 1 tenths,
then multiply with ones first and later tens.
13.5 x 30 = (13.5 x 3) x 10
= 40.5 x 10
= 405
So, 13.5 x 30= 405

Question 28.
73.96 × 100 = ___
Answer:7,396
Explanation:
73.96 x 100 = (73.96 x10) x 10
=739.6 x 10
=7396
So, 73.96 x 100 = 7,396

Question 29.
6.2 × 700 = ___
Answer: 4,340
Explanation:
6.2 x 700 = (6.2 x70) x 10
= 434 x 10
=4340
So, 6.2 x 700 = 4,340

Question 30.
9.34 × 1,000 = ___
Answer: 9,340
Explanation:
9.34 x 1000 = (9.34 x 10) x 10 x 10
= 93.4 x 10 x 10
=934 x 10
= 9340
So, 9.34 x 1000 = 9,340

Question 31.
25.6 × 9,000 = ____
Answer: 230,400
Explanation:
25.6 x 1000 = (25.6 x 9) x 10 x 10
= 230.4 x 10 x 10
=2304 x 100
= 230400
So, 25.6 x 1000 = 230,400

Divide. (Lesson 9.3)

Question 32.
0.5 ÷ 5 = _______
Answer: 0.1
Explanation:
0.5 ÷ 5 = 5 tenths ÷ 5
= 1 tenths
= 0.1
So, 0.5 ÷ 5 = 0.1

Question 33.
0.63 ÷ 9 = ___
Answer: 0.07
Explanation:
0.63 ÷ 9 = 63 hundredths ÷ 9
=7 hundredths
= 0.07
So, 0.63 ÷ 9 = 0.07

Question 34.
36.8 ÷ 4 = ___
Answer: 9.2
Explanation:
Step 1
Divide the ones by 4.
36 ones ÷ 4 = 9 ones R 0 ones
Regroup the remainder into tenths.
0 ones = 0 tenths
Add the tenths.
0 tenths + 8 tenths = 8 tenths
Step 2
Divide the tenths by 4.
8 tenths ÷ 4 = 2 tenths
So, 36.8 ÷ 4 = 9.2

Question 35.
96.3 ÷ 5 = ___
Answer: 19.26
Explanation:
Step 1
Divide the ones by 5.
96 ones ÷ 5 = 19 ones R 2 ones
Regroup the remainder into tenths.
192 = 19 ones and 2 tenths
Step 2
Divide the tenths by 5.
10 tenths ÷ 5 = 2 tenths
So, 96.3 ÷ 5 = 19.26

Question 36.
3.36 ÷ 4 = ___
Answer: 0.84
Explanation:
Step 1
Divide the ones by 4.
3 ones ÷ 4 = 8 ones R 7 ones
Regroup the remainder into tenths.
0 ones = 0 tenths
Add the tenths.
0 tenths + 8 tenths = 8 tenths
Step 2
Divide the tenths by 4.
8 tenths ÷ 4 = 2 tenths
So, 3.36 ÷ 4 = 0.84

Question 37.
1.92 ÷ 8 = ___
Answer: 24
Explanation:
Step 1
Divide the ones by 8.
9 ones ÷ 8 = 1 ones R 1 ones
Regroup the remainder into tenths.
1 ones = 10 tenths
Add the tenths.
10 tenths + 9 tenths = 19 tenths
Step 2
Divide the tenths by 4.
19 tenths ÷ 8 = 4 tenths
So, 1.92 ÷ 8 = 24

Divide. Round the quotient to the nearest tenth and nearest hundredth. (Lesson 9.3)

Question 38.
19 ÷ 7 = ___ to the nearest tenth
19 ÷ 7 = ___ to the nearest hundredth
Answer:
19 ÷ 7 = 2.7 to the nearest tenth
19 ÷ 7 = 0.27 to the nearest hundredth
Explanation:
19 ÷ 7 = 2.7 to the nearest tenth

19 ÷ 7 = 0.27 to the nearest hundredth

19 ÷ 7 = 2.7_ to the nearest tenth
First, divide to two decimal places.
Then round the answer to the nearest tenth.
Explanation:
19 ÷ 7 = ___ to the nearest hundredth
First, divide to three decimal places.
Then round the answer to the nearest hundredth.

 

Divide. (Lesson 9.4)

Question 39.
3.8 ÷ 10 = ___
Answer: 0.38
Explanation:
3.8 ÷ 10 = (4.8 ÷ 1 ) ÷ 10
= 3.8 ÷ 10
= 0.38
So, 3.8 ÷ 10 = 0.38

Question 40.
19.6 ÷ 20 = ___
Answer: 0.98
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
19.6 ÷ 20 = (19.6 ÷ 2 ) ÷ 10
= 9.8 ÷ 10
= 0.98
So, 19.6 ÷ 10 = 0.98

Question 41.
4.5 ÷ 100 = ___
Answer: 0.045
Explanation:
4.5 ÷ 100 = (4.5 ÷ 10 ) ÷ 10
= 0.45 ÷ 10
= 0.045
So,  4.5 ÷ 100 = 0.045

Question 42.
375 ÷ 300 = ___
Answer: 1.25
Explanation:
375 ÷ 300 = (375 ÷ 30 ) ÷ 10
= 12.5 ÷ 10
= 1.25
So,  375 ÷ 300 = 1.25

Question 43.
5,030 ÷ 1,000 = ___
Answer: 5.03
Explanation:
5030 ÷ 1000 = (5030 ÷ 10 ) ÷ 10 ÷ 10
= 503 ÷ 10÷ 10
= 50.3÷ 10
=5.03
So, 5030 ÷ 1000 = 5.03

Question 44.
2,506 ÷ 7,000 = ___
Answer: 0.358
Explanation:
2506 ÷ 7000 = (2506 ÷ 70 ) ÷ 10 ÷ 10
= 35.8 ÷ 10÷ 10
= 3.58÷ 10
=0.358
So, 2506 ÷ 7000 = 0.358

Estimate each answer by rounding the numbers to an appropriate place. (Lesson 9.5)

Question 45.
91.2 + 25.9
Answer: 117.1
Estimate: 117
Explanation:
91.2 + 25.9
91.2 rounds to 91.
25.9 rounds to 26.
91 + 26 = 10
91.2 + 25.9 is about 117.

Question 46.
37.4 – 11.7
Answer: 25.7
Estimate: 25
Explanation:
37.4 – 11.7
37.4 rounds to 37.
11.7 rounds to 12.
37 – 12 = 25
37.4 – 11.7 is about 25.

Question 47.
21.63 × 5
Answer: 108.15
Estimate: 110
Explanation:
21.63 × 5
21.63 rounds to 22.
22 × 5 = 110
21.63 × 5 is about 110.

Question 48.
7.05 ÷ 8
Answer: 0.88
Estimate: 1
Explanation:
7.05 ÷ 8
7.05 is about 8.
8 ÷ 8 = 1
7.05 ÷ 8 is about 1.

Write each ratio in three ways. Complete the table. (Lesson 10.1)

Question 49.

Answer:

Explanation:
Ratios are smaller to fractions, and each fraction can be written as a fraction.
Divide the first number 23 by the second number 100.
Multiply by 100 to convert to a percentage.
Add the percent symbol (%) to the output.
To change a percent to a decimal we divide by 100.
This is the same as moving the decimal point two places to the left.

Question 50.

Answer:

Explanation:
Ratios are smaller to fractions, and each fraction can be written as a fraction.
Divide the first number 23 by the second number 100.
Multiply by 100 to convert to a percentage.
Add the percent symbol (%) to the output.
To change a percent to a decimal we divide by 100.
This is the same as moving the decimal point two places to the left.

Express each fraction as a percent. (Lesson 10.2)

Question 51.
\(\frac{88}{200}\) =
Answer: 44%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 52.
\(\frac{204}{400}\) =
Answer: 51%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 53.
\(\frac{6}{20}\) =
Answer: 30%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 54.
\(\frac{7}{50}\) =
Answer: 14%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 55.
\(\frac{13}{20}\) =
Answer: 65%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 56.
\(\frac{16}{25}\) =
Answer: 64%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Problem Solving

Solve.

Question 57.
Hazel saves $5.75 each week.

a. How much does she save in 2 weeks?
Answer: $11.5
Estimate: 12
Explanation:
Hazel saves $5.75 each week.
Total amount she saves in two weeks
5.75 x 2 = 11.5
5.75 is rounded as 6
6 x 2 = 12
So, 5.75 x 2 is about 12.

b. She spends $23.83 on a book and $9.12 on a wallet. How much does she spend on the two items?
Answer: $32.95
Estimate: 33
Explanation:
Hazel spends $23.83 on a book and $9.12 on a wallet.
Total amount she spend on the two items
23.83 + 9.12
23.83 rounds as 24
9.12 rounds as 9
So, 24 + 9 = 33
23.83 + 9.12 = 32.95

Question 58.
Evelyn has 12.7 quarts of fruit punch in a cooler. She pours the fruit punch into glasses. She fills 5 glasses, each with a capacity of 0.36 quart. Then she fills 8 glasses, each with a capacity of 0.52 quart. How much fruit punch is left in the cooler?
Answer:
Explanation:
total fruit punch = 12.7 quarts
she fills 5 glasses with 0.36 quart
she fills 8 glasses with 0.52 quart
totalt fruit punch that she filled in glasses = 5 x 0.36 + 8 x 0.52
= 1.8 + 4.16 = 5.96 quarts
total fruit punch left in cooler = 12.7 – 5.96 = 6.74 quarts

Solve. Use models to help you.

Question 59.
The total weight of three tables is 16.9 pounds. The first table is twice as heavy as the second table. The weight of the third table is \(\frac{1}{3}\) the weight of the second table. What is the weight of the first table?
Answer:
weight of first table = 10.14 pounds
Explanation:
let weight of second table is x
weight of first table = 2 x weight of second table
weight of first table = 2x
weight of third table = \(\frac{1}{3}\) of weight of third table
weight of third table =  \(\frac{1}{3}\) x
So we get,
weight of first table = 2x
weight of second table = x
weight of third table =  \(\frac{1}{3}\) x
total weight = 16.9 pounds
first table + second table + third table = 16.9 pounds
2x + x + \(\frac{1}{3}\) x = 16.9
3x + \(\frac{1}{3}\) x = 16.9
\(\frac{3 x (3x) + x}{3}\) = 16.9
9x + x = 16.9 x 3
10x = 50.7
x = \(\frac{50.7}{10}\)
x = 5.07
weight of first table = 2x = 2 x 5.07
weight of first table = 10.14 pounds

Question 60.
There are 950 seats in a theater. 82% of the seats are occupied. How many seats are not occupied?
Answer:
151 seats
Explanation:
Total number of seats = 950
Occupied seats = 950 x \(\frac{82}{100}\)  = 799
Seats not occupied =  950 – 799 =  151 seats

Solve. Use models to help you.

Question 61.
Rahul spends 10% of his weekly allowance on Monday. On Wednesday, he spends \(\frac{1}{3}\) of the remainder. What percent of his allowance is left at the end of Wednesday?
Answer: 60%
Explanation:
x 100% –  x10% =x 90%
x 90% x \(\frac{1}{3}\)
x 30% he spent on Wednesday
total he spent 10% + 30% = 40%
percent of his allowance is left at the end of Wednesday is 60%

Question 62.
Ms. Jones buys a violin for $860. In addition, she has to pay 7% sales tax. How much does she pay in all?
Answer: $920.2
Estimate: $920
Explanation:
860 x \(\frac{7}{100}\) = 60.2 tax
she pay in all $860 + $60.2 = $920.2

Solve.

Question 63.
The regular price of a television set is $1,200. Albert buys the television set at a discount of 35%. How much does he pay for the television set?
Answer: $780
Explanation:
1200 x \(\frac{35}{100}\) = 420
1200 – 420 = 780
Albert pay for the television set $780

Question 64.
A school band gives a year-end concert. It is held in a 400-seat auditorium. Each concert ticket sells for $10, and 85% of the tickets are sold. How much money does the band earn from the sale of the tickets?
Answer: $3 400
Explanation:
total money to be collected by selling 400 tickets @$10
400 x 10 = 4000
4000 x 85%
4000 x \(\frac{85}{100}\) = 3400
$3400 much money does the band earn from the sale of the tickets.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 10 Practice 4 Real-World Problems: Percent to score better marks in the exam.

Math in Focus Grade 5 Chapter 10 Practice 4 Answer Key Real-World Problems: Percent

Solve. Show your work.

Question 1.
Jennifer bought a printer that cost $240. There was a 7% sales tax on the printer.

a. How much sales tax did Jennifer pay?

Answer: $16.8
Explanation:
240 x 7%
= (240  x 7)/100
=$16.8

b. How much did Jennifer pay for the printer with tax?
Answer: $256.8
Expanation:
Printer cost $240
Tax paid 7% = &16.8
Tota amount paid = $240 + $16.8 = $256.8

Question 2.
A company invests $8,000 in an account that pays 6% interest per year.

a. How much interest will the company earn at the end of 1 year?
Answer: $480
Explanation:
$8000 x 6%
= (8000 x 6)/100 = 480

b. How much money will the company have in the account at the end of 1 year?
Answer: $8480
Explanation:
invested amount = $8000
interest 6%
the company have in the account at the end of 1 year
$8000 + $480 = 8480

Solve. Show your work.

Question 3.
The regular price of a digital camera was $250. Tyrone bought the digital camera at a discount of 40%. How much did Tyrone pay for the digital camera?

Answer:
$150 Tyrone pay for the digital camera.
Explanation:
camera price is $250
40% of 250 is
(250 x 40)/100 = 25 x 4
= $100
Tyrone pay for the digital camera
$250 – $100 = $150

Question 4.
Len bought a new car for $22500. After o few years, he sold the car at a discount of 25%. What was the selling price of the car?
Answer: $16875
Explanation:
new car cost =  $22500
sold at a discount of 25%
25% of $22500
=(22500 x 25)/100
=225 x 25
= $5625
the selling price of the car is
$22500 – $5625 = $16875

Solve. Show your work.

Question 5.
The price for dinner in a restaurant was $80. The customer paid on additional 7% meals tax and left o $15 tip.

a. How much meals tax did the customer pay?
Answer: $5.6
Explanation:
Dinner cost = $80
Tax = 7%
80 x 7% =
(80 x 7)/100 = $5.6

b. How much did the customer spend altogether in the restaurant?
Answer: $100.6
Explanation:
Dinner cost = $80
Tip = $15
meal tax =$5.6
the customer spend altogether in the restaurant
=$80 + $15 + $5.6 = $100.6

Question 6.
The regular price of a pair of hockey skates was $250. Ron bought the skates at a discount of 8%. However, he had to pay 5% sales tax on the skates after the discount.

a. What was the selling price of the skates?
Answer: $230
Explanation:
hockey skates cost= $250
8% of $250=
(250 x 8)/100 = $20
the selling price of the skates is
$250 – $20 = $230

b. How much did Ron pay for the skates in total?
Answer: $241.5
Explanation:
5% sales tax on the skates after the discount
5% of $230
(230 x 5)/100 = 11.5
Ron pay for the skates in total
$230 + $11.5 = $241.5

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 1 Angles on a Line provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 12 Practice 1 Answer Key Angles on a Line

In each figure, \(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.

Question 1.

m∠DBC = ____
m∠DBA = ____
m∠DBC + m∠DBA = ___ + _____
= _____
Answer:
m∠DBC = 60°
m∠DBA = 120°
m∠DBC + m∠DBA = 60° + 120°= 180°
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠DBC = 60°
Then subtract m∠DBC = 60° from 180°,
We get m∠DBA = 120°

Question 2.

m∠x = ____
m∠y = ____
m∠x + m∠y = ___ + ___
= _____
Answer:
m∠x = 70°
m∠y = 110°
m∠x + m∠y = 70° + 110° =  180°
Explanation:

To measure the unknown angles, first take a protractor and measure m∠x = 70°
Then measure m∠y = 110°
Add both the angles m∠x + m∠y = 70° + 110° =  180°

 

\(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.

Question 3.

m∠p = ____
m∠q = ____
m∠r = ____
m∠p + m∠q + m∠r = ___ + ___ + ___
= ____
Answer:
m∠p = 20°
m∠q = 100°
m∠r =  60°
m∠p + m∠q + m∠r = 20° + 100° + 60°= 180°
Explanation:

To measure the unknown angles, first take a protractor and measure m∠p = 20°
Then measure m∠q = 100°
Then measure m∠r = 60°
Add all the angles m∠p + m∠q + m∠r = 20° + 100° + 60° =  180°

Name the angles on each line.

Question 4.
\(\overleftrightarrow{X Z}\) is a line.

Answer:
m∠XYW = 40°
m∠WYZ = 140°
m∠XYW + m∠WYZ = 40°+ 140° = 180°
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠XYW = 40°, an angle less than 90° is acute angle.
Then take a protractor and measure m∠WYZ = 140°, an angle more than 90° is obtuse angle.
Add both the angles m∠XYW + m∠WYZ = 40°+ 140° = 180°

Question 5.
\(\overleftrightarrow{P R}\) is a line.

Answer:
m∠PQS = m∠a = 40° Acute Angle
m∠TQS = m∠b = 90° Right Angle
m∠TQR = m∠c = 50° Acute Angle
m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠PQS = m∠a = 40° Acute Angle, an angle less than 90° is acute angle.
Then take a protractor and measure m∠TQS = m∠b = 90° Right Angle.
Then take a protractor and measure m∠TQR = m∠c = 50° Acute Angle
Add all the angles m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle.

Name each set of angles on a line.

Question 6.
\(\overleftrightarrow{A C}\) is a line.

Answer:
m∠p = 50°
m∠q = 120°
m∠r =  60°
m∠s =  60°
m∠t =  70°
∠p + ∠q + ∠r + ∠s + ∠t = 50° + 120° + 60°+ 60°+ 70° = 360°
Explanation:

m∠p and m∠q are Vertical angles where the two angles cross each other.
m∠r , m∠t and m∠s are acute angle, where the angle is less than 90°

Question 7.
\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) are line.

Answer:
∠p = 60°
∠q = 100°
∠r =  20°
∠s =  160°
∠t =  20°
∠p + ∠q + ∠r + ∠s + ∠t = 60° + 100° + 20°+ 160°+ 20° = 360°
Explanation:

∠p, ∠r and ∠t are acute angles, where the angle is less than 90°
∠q and ∠s are obtuse angles, where the angles is more than 90°

Find the unknown angle measures.

Question 8.
\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠DBC.

Answer:

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given m∠DBC + 125° = 180°
m∠DBC – 180° = 125° = 55°

Question 9.
\(\overleftrightarrow{E G}\) is a line. Find the measure of ∠HFE.

Answer:

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠FIG = 42° = 180°
∠HFI = 90°
∠EFH = 180° – (42° + 90°)
= 180° – 132° = 48°

Find the unknown angle measures.

Question 10.
\(\overleftrightarrow{O Q}\) is a line. Find the measure of ∠SPT.

Answer:
m∠SPT =180° – (15°+70°+39°) =  56°

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠POR = 15°
∠RPS = 70°
∠TPQ = 39°
m∠SPT = 180° – (∠POR +∠RPS +∠TPQ )
m∠SPT =180°- (15°+70°+39°) =  56°

Question 11.
\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠EBF.

Answer:
m∠EBF =180° – (41° + 27° + 90°) = 180° – 158° = 22°

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠DBA = 41°
∠DBE = 27°
∠FBC = 90°
m∠EBF = 180° – (∠DBA +∠DBE +∠FBC )
m∠EBF =180°- (41°+27°+90°) =  22°

Question 12.
\(\overleftrightarrow{J K}\) is a line. Find the measure of ∠y and ∠z.

Answer:

Explanation:
Angles formed by two rays lie in the plane that contains the rays.
Angles are also formed by the intersection of two planes.
Given:
∠JOI = 80°
∠JOG = 36°
∠GOH= 72°
m∠y = 180° – (∠JOG+∠GOH)
m∠y =180°- (36°+72°)
=180°- 108°
= 72°
m∠z =180°- ∠JOI
= 180° – 80°
= 100°

Question 13.
\(\overleftrightarrow{E F}\) and \(\overleftrightarrow{G H}\) are line. Find the measure of ∠a and ∠b.

Answer:

Explanation:
Angles formed by two rays lie in the plane that contains the rays are called vertex of the angle.
Angles are also formed by the intersection of two planes.
Given:
∠GOF = 160°
∠FOH = 20°
∠HOJ= 50°
∠JOI = 90°
m∠a =180°- ∠GOF
= 180° – 160°
= 20°
m∠b= 180° – (∠HOJ+∠FOH+∠JOI )
=180°- (50°+20°+90°)
=180°- 160°
= 20°

 

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Angles provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 12 Answer Key Angles

Math Journal

Check the box for each correct statement. Then explain your answer.

Question 1.
\(\overleftrightarrow{X Y}\) is a line.

Answer:

Explanation:
The XY is a line and the angle on a straight line is 180°, known as straight angle.
Angle POQ is 90° as per the given information in the diagram.
180° – 90° = 90°
Angle ∠XOP and ∠YOQ are equal angle = 45°

Question 2.
\(\over left right arrow{A B}\) and \(\over left right arrow{C D}\) meet at O.

Answer:

Explanation:
\(\over left right arrow{A B}\) is a line and \(\over left right arrow{C D}\) is a line are crossed at O, the opposite angles are same.
So, m∠e = m∠h and
m∠f + m∠g = m∠j   are true statements.

Put On Your Thinking Cap!

Challenging Practice

Find the unknown angle measures. Explain.

Question 1.
\(\over left right arrow{G J}\) is a line. ∠LHK is a right angle. Find the measure of ∠LHJ.

Answer: 65°
Explanation:
Given information
GJ is a straight line, ∠LHK = 90°
∠JHK = 180° – ∠JHK
= 180° – 155° = 25°
∠JHK = ∠LHK – ∠JHK
= 90° – 25° = 65°

Question 2.
\(\over left right arrow{M N}\) and \(\over left right arrow{X Y}\) meet at O and m ∠a = m ∠b. Find the measure of ∠c.

Answer: 135°
Explanation:
\(\over left right arrow{X Y}\) is a line and \(\over left right arrow{M N}\) is a line are crossed at O, the opposite angles are same.
given information m∠a = m∠b and ∠XOP = 90
as XOY is a straight line, the angle is 180°
90° + m∠a + m∠b = 180°
∠c = 180° -∠XOM= 180 – 45° = 135°

Question 3.
\(\over left right arrow{A C}\) is a line. ∠ABE and ∠DBF are right angles. Find the measure of ∠FBC.

Answer: 26°
Explanation:
∠ABE and ∠DBF = 90°
∠EBF = ∠DBF – ∠DBE
=  90° – 26° = 64°
∠ABD = ∠ABE – ∠DBE
= 90° – 26° = 64°
∠FBC = 180 – (∠ABE + ∠EBF)
= 180° – (90° + 64°)
=180° – 154° = 26°

Question 4.
\(\over left right arrow{A B}\) and \(\over left right arrow{W X}\) meet at O. ∠YOX are right angles. Find the measures of ∠AOX and ∠COY.

Answer:
∠AOX  = 124°
∠COY  =  56°
Explanation:
90° – 56° = 34°
90° – 34° = 56°
∠COY = ∠COB – ∠BOY
= 90° – 34° = 56°
∠AOX = ∠WOX – ∠AOW
=180°- 56° = 124°

Put on Your Thinking cap!

Problem Solving

Solve.

Question 1.
\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.
Check the box for each correct statement.

Answer:
\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.

Explanation:
\(\over left right arrow{J K}\) is a line and \(\over left right arrow{L M}\) is a line are crossed at O, the opposite angles are same.
so, m∠r + m∠s = m∠p + m∠q is the wrong statement.

Question 2.
\(\over left right arrow{A B}\), \(\over left right arrow{C D}\), and \(\over left right arrow{E F}\) meet at O. Find the sum of the measures of ∠AOC, ∠FOD, and ∠BOE.
m∠AOC + m∠FOD + m∠BOE = _____

Answer: 180°
Explanation:
m∠AOC = 45°

m∠FOD = 45°

m∠BOE = 90°

m∠AOC + m∠FOD + m∠BOE = 180°

Question 3.
ABCD is a square. \(\over right arrow{B E}\) is a ray. Find the measure of ∠x.

Answer: 135°
Explanation:
As BE is a straight line and the angle is 180° at point D
and a square is ABCD is with 90° angle formed at point D
the ange ∠EDC is 135° angle ∠CDB is 45° and ∠ADB is also 45°
now the
∠x =  ∠EDB – ∠ADB
=  180° – 45°  =  135°

Question 4.
How many degrees does the hour hand of a clock turn between 3 P.M. and 7:30 P.M.?
Answer: 135°
Explanation:

Hour hand at 3PM is at 3 and 7:30 as shown in the clock diagram
Total angle is 360°, keep it in mind
and 360° divide in 12 parts
each part is of 30°
from hours hand 3 to 7 :30 its 135°

Question 5.
\(\over left right arrow{A B}\) is a line. The measures of ∠a and ∠b are whole numbers.

If the measure of ∠b is twice that of ∠a, find the measures of ∠a and ∠b.
Answer:
∠a = 60°
∠b = 120°

Explanation:
Here the hint is angle ∠b is twice that of ∠a, and The AB is a line and the angle on a straight line is 180, known as straight angle
∠b + ∠a = 180°
2∠a + ∠a = 180°
3∠a = 180°
∠a = 180°/3 = 60°
∠a = 60°
∠a = 60°
∠b = 2x∠a = 120°

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 17 Practice 2 Right Angles provides detailed solutions for the textbook questions.

Math in Focus Grade 3 Chapter 17 Practice 2 Answer Key Right Angles

Look at these angles. Use a piece of folded paper
to help you answer the questions.

Question 1.
Which angle is less than a right angle?
Angle ________________
Answer:

Angle  C, D and E are angles less then a right angle.
Explanation:
Angle less than a right angles are Acute angles.

Question 2.
Which angle is greater than a right angle?
Angle ________________
Answer:

Angle A is greater then a right angle.
Explanation:
Angle greater than a right angles are Obtuse angles.

Question 3.
Which angles are the same size as right angles?
Angles _________________
Answer:

Angle A and F are the same as right angles.
Explanation:
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Mark all the right angles in each figure.

Question 4.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 5.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 6.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 7.

Answer:

Explanation:
The above figure has,
One right angle triangles , the angle is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 8.

Answer:

Explanation:
The above figure has,
Two right angle are there, which are marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 9.

Answer:

Explanation:
The given figure has,
Two right angle are there, which are marked in blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Surface Area and Volume provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Answer Key Surface Area and Volume

Math Journal

This rectangular container is \(\frac{2}{5}\)-filled with water.
How much more water is needed to increase the height of the water level to 3 centimeters?

Show two methods of solving this problem. Which method do you prefer? Why?
Answer:
Given rectangular tank has volume 8 cm X 10 cm X 5 cm = 400 cm³,
Method 1:
Knowing the volume of tank and water filled in it
as the rectangular container is \(\frac{2}{5}\)-filled with water.
\(\frac{2}{5}\) X 400 cm³ = 160 cm³, filled with water.
as 1 cubic centimeter is equal to 1 milliliters,

Put on Your Thinking Cap!

Challenging Practice

Question 1.
A rectangular tank is half-filled with water.
Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.
How much water will be in the tank when it is \(\frac{3}{5}\) full?
Answer:
3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full,

Explanation:
Given a rectangular tank is half-filled with water.
Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.
Let x cubic centimeters of water so \(\frac{1}{2}\)x + \(\frac{3}{5}\)x = 650 cm³ + x,
\(\frac{5x + 6x}{10}\) = 650 cm³ + x,
\(\frac{11x}{10}\) = 650 cm³ + x,
11 x = 10 X (650 cm³ + x),
11 x =  6500 cm³ + 10 x,
11x – 10 x = 6,500 cm³,
x = 6,500 cm³,
So, water will be in the tank when it is \(\frac{3}{5}\) full is
\(\frac{3}{5}\) x 6,500 cm³ = \(\frac{3 X 6,500}{5}\) cm³,
\(\frac{19,500}{5}\) cm³ = 3,900 cm³,
therefore 3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full.

Question 2.
A cube has a surface area of 21 6 square centimeters.
A second cube has edges that are 3 times as long.
How much greater is the surface area of the second cube than the first cube?
Answer:
1,728 cm² greater is the surface area of the second cube than the first cube,

Explanation:
Given a cube has a surface area of 216 square centimeters as
surface area of cube is 6 X a²= 216 cm²,
a² = 36 cm² = 6 cm X 6 cm,
edge a    = 6 cm,
A second cube has edges that are 3 times long as
6 cm X 3 = 18 cm, Surface area of second cube is 6 x (18)² =
6 X 18 cm X 18 cm = 1,944 cm², Now compairing much greater is the
surface area of the second cube than the first cube is 1,944 cm² – 216 cm² = 1,728 cm².

Put on Your Thinking Cap!

Problem Solving

A prism has a square base whose edges each measure 5 centimeters.
The ratio of its height to its width is 4 : 1.
Find the volume of the rectangular prism in cubic centimeters.

Answer:
Given a prism has a square base whose edge each measure 5 centimeters.
height = 4 cm
width = 1 cm
Volume of the rectangular prism = 2l × 2w × 2h
V = 2 × 5 × 2 × 1 × 2 × 4
V = 80 cubic centimeters

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 4 Understanding and Measuring Volume provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 4 Answer Key Understanding and Measuring Volume

These solids are formed by stacking unit cubes in the corner of a room.
Find the volume of each solid.

Question 1.

Volume = _________ cubic units
Answer:
Volume of give cube has 27 cubic units,

Explanation:
As we know volume of  solid is l X w X h,
so given cube  has 3 unit X 3 unit X 3 unit = 27 cubic units.

Question 2.

Volume = _________ cubic units
Answer:
Volume of give cube has 32 cubic units,

Explanation:
As we know the volume of solid is l X w X h,
so the given cube has 4 units X 4 units X 2 units = 32 cubic units.

Question 3.

Volume = _________ cubic units
Answer:
Volume of given cube has  16 cubic units,

Explanation:
As we know the volume of  solid is l X w X h,
Given cube contains 2 fewer small unit cubes so first we
calculate the total surface and subtract missing cubic units,
Total surface area has 3 units X 2 units X 3 units = 18 cubic units.
the surface area of small unit cubes is 1 unit X 1 unit X 2 units = 2 cubic units,
therefore the volume of the given cube is 18 cubic units – 2 cubic units = 16 cubic units.

Question 4.

Volume = _________ cubic units
Answer:
Volume of 9 cubic units,

Explanation:
Given solid cube has 9 unit cubes with 1 unit X 1 unit X 1 unit each,
So the volume of given cube is 9 X (1 unit X 1 unit X 1 unit)  = 9 cubic units.

These solids are formed by stacking 1-centimeter cubes in the corner of a room.
Find the volume of each solid.

Question 5.

Volume = ______ cm³
Answer:
Volume 11 cm³,

Explanation:
Given solid cube has 11 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 11 X (1 cm X 1 cm X 1 cm)  = 11 cm³.

Question 6.

Volume = _________ cm³
Answer:
Volume 8 cm³,

Explanation:
Given solid cube has 8 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 8 X (1 cm X 1 cm X 1 cm)  = 8 cm³.

Question 7.

Volume = _________ cm³
Answer:
Volume 10 cm³,

Explanation:
Given solid cube has 10 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 10 X (1 cm X 1 cm X 1 cm)  = 10 cm³.

Question 8.

Volume = ______ cm³
Answer:
Volume 12 cm³,

Explanation:
Given solid cube has 12 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 12 X (1 cm X 1 cm X 1 cm)  = 12 cm³.

Question 9.

Volume = _________ cm³
Answer:
Volume 7 cm³,

Explanation:
Given solid cube has 7 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 7 X (1 cm X 1 cm X 1 cm)  = 7 cm³.

Question 10.

Volume = _________ cm³
Answer:
Volume 11 cm³,

Explanation:
Given solid cube has 11 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 11 X (1 cm X 1 cm X 1 cm)  = 11 cm³.

These solids are built using 1-centimeter cubes. Find the volume of each solid.
Then compare their volumes and fill in the blanks.

Question 11.

Solid _________ has a greater volume than solid _________.
Answer:

Solid B has a greater volume than solid A,

Explanation:
Given solid cube A has 5 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 5 X (1 cm X 1 cm X 1 cm)  = 5 cm³,
and given solid cube B has 8 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 8 X (1 cm X 1 cm X 1 cm)  = 8 cm³.
Solid B has a greater volume than solid A.

These solids are built using 1-meter cubes. Find the volume of each solid.
Then compare their volumes and fill in the blanks.

Question 12.

Solid _________ has less volume than solid _________.
Answer:

Solid 8 m³ has less volume that solid 11 m³,

Explanation:
Given solid cube C has 8 units m’s with 1 m X 1 m X 1 m each,
So the volume of given cubes is 8 X (1 m X 1 m X 1 m)  = 8 m³,
and given solid cube D has 11 units m’s with 1 m X 1 m X 1 m each,
So the volume of given cubes is 11 X (1 m X 1 m X 1 m)  = 11 m³.
Solid 8 m³ has less volume that solid 11 m³.

These solids are built using 1-inch cubes.
Find the volume of each solid.
Then compare their volumes and f411 in the blanks.

Question 13.

Length = __________ in.
Width = __________ in.
Height = _________ in.
Volume = _________ in.³

Length = __________ in.
Width = __________ in.
Height = _________ in.
Volume = _________ in.³
Solid _________ has less volume than solid _________.
Answer:
Solid E has less volume than solid F,

Explanation:
Given the solid cube of E which has a length of 2 in, width 2 in and height 3 in,
so the volume of cube E is 12 in.³,
Given solid cube of F which has a length of 4 in, width of 2 in, and height of 2 in,
so volume of cube F is 16 in.³.
Solid E has less volume than solid F.

These solids are built using 1-foot cubes. Find the volumes of each solid.
Then compare their volumes and fill in the blanks.

Question 14.

Length = _____2_____ ft.
Width = ______2____ ft.
Height = _____2____ ft.
Volume = _____8____ ft.³

Length = ____4______ ft.
Width = _____4_____ ft.
Height = _____4____ ft.
Volume = _____64____ ft.³
Solid _________ has a greater volume than solid _________.
Answer:
Solid H has greater volume than solid G,

Explanation:
Given the solid cube of  G which has a length 2 ft, width 2 ft, and height 2 ft,
so volume of cube G is 8 ft.³,
Given the solid cube of H which has a length 4 ft, width 4 ft and height 4 ft,
so volume of cube H is 64 in.³.
Solid H has a greater volume than solid G.

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 1 Building Solids Using Unit Cubes provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 1 Answer Key Building Solids Using Unit Cubes

Find the number of unit cubes used to build each solid.

Question 1.

__________ unit cubes
Answer:
5 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 5 unit cubes,
So, the volume of a 5 unit cubes = 5 X (Side × Side × Side),
= 5 X (1 unit × 1 unit × 1 unit),
= 5 X (unit cubes).

Question 2.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X (1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 3.

__________ unit cubes
Answer:
8 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 8 unit cubes,
So, the volume of a 8 unit cubes = 8 X (Side × Side × Side),
= 8 X ( 1 unit × 1 unit × 1 unit),
= 8 unit cubes.

Question 4.

__________ unit cubes
Answer:
6 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 6 unit cubes,
So, the volume of a 6 unit cubes = 6 X (Side × Side × Side),
=6 X (1 unit × 1 unit × 1 unit),
= 6 unit cubes.

Question 5.

__________ unit cubes
Answer:
8 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 8 unit cubes,
So, the volume of a 8 unit cubes = 8 X (Side × Side × Side),
= 8 X (1 unit × 1 unit × 1 unit),
= 8 unit cubes.

Question 6.

__________ unit cubes
Answer:
9 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 9 unit cubes,
So, the volume of a 9 unit cubes = 9 X (Side × Side × Side),
= 9 X (1 unit × 1 unit × 1 unit),
= 9 unit cubes.

Find the number of unit cubes used to build each solid.

Question 7.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X ( 1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 8.

__________ unit cubes
Answer:
9 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 9 unit cubes,
So, the volume of a 9 unit cubes = 9 X (Side × Side × Side),
= 9 X (1 unit × 1 unit × 1 unit),
= 9 unit cubes.

Question 9.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X (1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 10.

__________ unit cubes
Answer:
10 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 10 unit cubes,
So, the volume of a 10 unit cubes = 10 X (Side × Side × Side),
= 10 X (1 unit × 1 unit × 1 unit),
= 10 unit cubes.

Question 11.

__________ unit cubes
Answer:
15 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 15 unit cubes,
So, the volume of a 15 unit cubes = 15 X (Side × Side × Side),
= 15 X (1 unit × 1 unit × 1 unit),
= 15 unit cubes.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 1 Adding Unlike Fractions to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 1 Answer Key Adding Unlike Fractions

Find two equivalent fractions for each fraction.

Example

Question 1.
\(\frac{3}{4}\) = ___ = ____
Answer:

Question 2.
\(\frac{2}{5}\) = ___ = ____
Answer:

Question 3.
\(\frac{5}{6}\) = ___ = ____
Answer:

Question 4.
\(\frac{1}{7}\) = ___ = ____
Answer:

Express each fraction in simplest form.

Question 5.
\(\frac{6}{8}\) = ___
Answer:

Question 6.
\(\frac{8}{20}\) = ___
Answer:

Question 7.
\(\frac{10}{15}\) = ___
Answer:

Question 8.
\(\frac{9}{21}\) = ___
Answer:

Rewrite each pair of unlike fractions as like fractions.

Example

Question 9.
\(\frac{1}{4}\) = ___ \(\frac{5}{12}\) = ___
Answer:

Question 10.
\(\frac{1}{10}\) = ___ \(\frac{2}{5}\) = ___
Answer:

Question 11.
\(\frac{5}{9}\) = ___ \(\frac{2}{3}\) = ___
Answer:

Question 12.
\(\frac{3}{8}\) = ___ \(\frac{9}{16}\) = ___
Answer:

Write equivalent fractions for each fraction. Then find the least common denominator of the fractions.

Example
\(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{3}{6}\)
\(\frac{2}{3}\) = \(\frac{4}{6}\)
The least common denominator is 6.

Question 13.
\(\frac{2}{3}\) =
\(\frac{3}{4}\) =
The least common denominator is ____
Answer:

Question 14.
\(\frac{1}{4}\) =
\(\frac{5}{6}\) =
The least common denominator is ____
Answer:

Question 15.
\(\frac{5}{6}\) = ____
\(\frac{3}{8}\) = ____
The least common denominator is ____
Answer:

Shade and label each model to show the tractions. Then complete the addition sentence.

Example

Question 16.
\(\frac{1}{5}\), \(\frac{1}{2}\)

Answer:

Look at the model. Write two addition sentences.

Question 17.
\(\frac{1}{6}\), \(\frac{1}{4}\)

\(\frac{1}{6}\) + \(\frac{1}{4}\) = ___ + ___
= ____
Answer:

Question 18.
\(\frac{1}{5}\), \(\frac{2}{3}\)

\(\frac{1}{5}\) + \(\frac{2}{3}\) = ____ + ___
= ____
Answer:

Question 19.
Addition sentence 1:

Answer:

Question 20.
Addition sentence 2 (fractions in simplest form):
____ + ____ = ____
Answer:

Add. Express each sum in simplest form.

Question 21.
\(\frac{1}{3}\) + \(\frac{1}{9}\) =
Answer:

Question 22.
\(\frac{5}{8}\) + \(\frac{2}{4}\) =

Question 23.
\(\frac{1}{2}\) + \(\frac{6}{7}\) =
Answer:

Question 24.
\(\frac{4}{8}\) + \(\frac{1}{5}\) =
Answer:

Use benchmarks to estimate each sum.

Example

Question 25.
\(\frac{2}{3}\) + \(\frac{2}{9}\)
Answer:

Question 26.
\(\frac{7}{9}\) + \(\frac{1}{7}\) + \(\frac{3}{5}\)
Answer:

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 3 Place Value to finish your assignments.

Math in Focus Grade 5 Chapter 1 Practice 3 Answer Key Place Value

Complete. Use the place-value chart.

In 345,201:

Question 1.
a. the digit 3 stands for ___________
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 3 stands for a hundred thousand.

b. the value of the digit 3 is _____
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of the digit is 300,000.

Question 2.
a. the digit 4 stands for ___.
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 4 stands for ten thousand.

b. the value of the digit 4 is ______
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of digit 4 is 40,000.

Question 3.
a. the digit 5 stands for ___.
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 5 stands for thousands.

b. the value of the digit 5 is ______
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of digit 5 is 5000.

Write the value of each digit in the correct box.

Question 4.

Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Complete.

In 346,812:

Question 5.
the digit 3 stands for ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 3 stands for a hundred thousand.

Question 6.
the digit 6 stands for ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 6 stands for thousand.

Write the value of the digit 2 in each number.

Question 7.
329,051 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 20,000 because it represents the ten thousand places.

Question 8.
903,521 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 20 because it represents the tens place.

Question 9.
712,635 ___
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 2000 because it represents the thousands place.

Question 10.
258,169 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 200,000 because it represents the hundred thousand place.

Complete.

Question 11.
In 320,1 87, the digit ___ is in the thousands place.
Answer: 0
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit present in the thousands place is 0.

Question 12.
In 835,129, the digit 8 is in the ____ place.
Answer: Hundred thousand place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of 8 in the given number is a hundred thousand and its digit value is 800,000.

Question 13.
In 348,792, the digit 4 is in the ____ place.
Answer: Ten thousand place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 4 in the given number is ten thousands place and its digit value is 40,000.

Complete to express each number in expanded form.

Question 14.
153,420 = 100,000 + ___ + 3,000 + 400 + 20
Answer:
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
How to write numbers in expanded form:
Go through the below steps to write the numbers in expanded form:
Step 1: Get the standard form of the number.
Step 2: Identify the place value of the given number using the place value chart.
Step 3: Multiply the given digit by its place value and represent the number in the form of (digit × place value).
Step 4: Finally, represent all the numbers as the sum of (digit × place value) form, which is the expanded form of the number.
Now write the expanded form for the given number by using the above steps:
Step 1: The standard form of the number is 153,420.
Step 2: The place value of the given number is:
1 – Hundred thousand
5 – Ten thousand
3 – Thousands
4 – Hundreds
2 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 1×100,000, 5×10,000, 3×1000, 4×100, 2×10, 0×1
Step 4: Expanded form is 100,000+50,000+3000+400+20+0
Finally, the expanded form of the number 100,000+50,000+3000+400+20+0.

Question 15.
760,300 = ____ + 60,000 + 300
Answer: 700,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 760,300.
Step 2: The place value of the given number is:
7 – Hundred thousand
6 – Ten thousand
0 – Thousands
3 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×100,000, 6×10,000, 0×1000, 3×100, 0×10, 0×1
Step 4: Expanded form is 700,000+60,000+0+300+0+0
Finally, the expanded form of the number 700,000+60,000+300.

Question 16.
700,000 + 8,000 + 500 + 4 = ____
Answer: 708,504
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 760,300.
Step 2: The place value of the given number is:
7 – Hundred thousand
0 – Ten thousand
8 – Thousands
5 – Hundreds
0 – Tens
4 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×100,000, 0×10,000, 8×1000, 5×100, 0×10, 4×1
Step 4: Expanded form is 700,000+0+8000+500+0+4
Finally, the expanded form of the number 700,000+8000+500+4.
The number is 708,504.

Question 17.
200,000 + 2,000 + 10 = ____
Answer:
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 202,010.
Step 2: The place value of the given number is:
2 – Hundred thousand
0 – Ten thousand
2 – Thousands
0 – Hundreds
1 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 2×100,000, 0×10,000, 2×1000, 0×100, 1×10, 0×1
Step 4: Expanded form is 200,000+0+2000+0+10+0
Finally, the expanded form of the number 200,000+2000+10
The number is 202,010.

Complete. Use the place-value chart.

In 1,508,369.
Question 18.
a. the digit 1 stands for ____
Answer:
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The place value of the 1 in the given number 1,508,369 is millions.

b. the value of the digit 1 is ____
Answer: 1,000,000.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use

The value of digit of 1 in the given number 1,508,369 is 1,000,000.

Complete

Question 19.
a. the digit 8 stands for _____
Answer: Thousands place.
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The place value of 8 in the given number 1,508,369 is thousand place.

b. the value of the digit 8 is ________________
Answer: 8000
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 8 in the given number 1,508,369 is 8000.

Question 20.
the digit 0 is in the ___ place.
Answer:
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The digit 0 in the given number 1,508,369 is ten thousands place.

Write the value of each digit in the correct box.

Question 21.

Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Complete

Question 22.
In 5,420,000, the digit 5 is in the ____ place.
Answer: Millions place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 5 in the given number 5,420,000 is millions place.

Question 23.
In 1,077,215, the digit in the hundred thousand place is ____
Answer: 0
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

In the given number 1,077,215, the hundred thousand place is 0.

Question 24.
In 9,400,210, the digit 9 stands for _____
Answer: Millions place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 9 in the given number 9,400,210 is millions place.

Complete to express each number in expanded form.

Question 25.
4,130,000 = ___ + 100,000 + 30,000
Answer: 4,000,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 4,130,000.
Step 2: The place value of the given number is:
4 – Millions
1 – Hundred thousand
3 – Ten thousand
0 – Thousands
0 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 4×1,000,000,  1×100,000, 3×10,000, 0×1000, 0×100, 0×10, 0×1)
Step 4: Expanded form is 4,000,0000+100,000+30,000+0+0+0+0
Finally, the expanded form of the number 4,000,0000+100,000+30,000
The number is 4,130,000.

Question 26.
6,123,750 = 6,000,000 + 100,000 + 20,000 + 3,000 + 700 + ____
Answer: 50
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 6,123,570.
Step 2: The place value of the given number is:
6 – Millions
1 – Hundred thousand
2 – Ten thousand
3 – Thousands
5 – Hundreds
7 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 6×1,000,000,  1×100,000, 2×10,000, 3×1000, 7×100, 5×10, 0×1)
Step 4: Expanded form is 6,000,0000+100,000+20,000+3,000+700+50+0
Finally, the expanded form of the number 6,000,0000+100,000+20,000+3,000+700+50
The number is 6,123,750.

Question 27.
7,550,100 = 7,000,000 + ___ + 50,000 + 100
Answer: 500,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 7,550,100.
Step 2: The place value of the given number is:
7 – Millions
5 – Hundred thousand
5 – Ten thousand
0 – Thousands
1 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×1,000,000,  5×100,000, 5×10,000, 0×1000, 1×100, 0×10, 0×1)
Step 4: Expanded form is 7,000,0000+500,000+50,000+0+100+0+0
Finally, the expanded form of the number 7,000,0000+500,000+50,000+100.
The number is 7,550,100.

Question 28.
5,000,000 + 200,000 + 7,000 + 70 = ____
Answer: 5,207,070.
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 5,207,070.
Step 2: The place value of the given number is:
5 – Millions
2 – Hundred thousand
0 – Ten thousand
7 – Thousands
0 – Hundreds
7 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 5×1,000,000,  2×100,000, 0×10,000, 7×1000, 0×100, 7×10, 0×1)
Step 4: Expanded form is 5,000,0000+200,000+0+7,000+0+70+0
Finally, the expanded form of the number 5,000,000+200,000+7,000+70
The number is 5,207,070.

Question 29.
3,000,000 + 20,000 + 9,000 + 100 + 5 = ____
Answer: 3,029,105.
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 3,029,105.
Step 2: The place value of the given number is:
3 – Millions
0 – Hundred thousand
2 – Ten thousand
9 – Thousands
1 – Hundreds
0 – Tens
5 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 3×1,000,000,  0×100,000, 2×10,000, 9×1000, 1×100, 0×10, 5×1)
Step 4: Expanded form is 3,000,0000+0+20,000+9,000+100+0+5
Finally, the expanded form of the number 3,000,000+20,000+9,000+100+5
The number is 3,029,105.

Read the clues to find the number.

It is a 7-digit number.
The value of the digit 7 is 700.
The greatest digit is in the millions place.
The digit 1 is next to the digit in the millions place. The value of the digit 8 is 8 tens.
The value of the digit 3 is 3 ones.
The digit 5 is in the thousands place.
The digit 6 stands for 60,000.

Question 30.
The number is ____
Answer: 8,165,783
The greatest digit in the given clue is the number 8. So I kept 8 in the millions place.
The hundred thousand place is the digit 1. In the clue already given that 1 is next to the millions place.
The ten thousand place is the digit 6.
The thousands place is the digit 5.
The hundreds place is the digit 7.
The tens place is the digit 8.
The units place is the digit 3.