A Two-Digit Divisor 21. Divide. Use the space on the left to write a multiplication table of the divisor. Lastly check.

2 × 37 = 74

a. 37 ) 4 1 0 7× 3 7

b. 58 ) 4 4 0 8× 5 8

c. 96 ) 9 7 9 2× 9 6

2. Divide. Use the space on the left to write a multiplication table of the divisor. Lastly check.

a. 48 ) 6 0 1 1

b. 92 ) 8 7 1 2

c. 55 ) 6 7 4 5

3. Angela is going to borrow money so she can purchase three beds for $156 each. She will pay back the loan in 12 equal payments, over one year. How much is one payment?

4. Mark paid 4/15 of his $3,600 salary in taxes.

a. How much did Mark pay in taxes? (Hint: First find 1/15 of his salary.)

b. How much does Mark have left after taxes?

5. If you need more practice, solve the problems below and fill in the cross-number puzzle. Use your notebook for long divisions.

Down

a. 3,762 ÷ 66

b. 19,750 ÷ 5

c. 9,960 ÷ 12

d. 27,339 ÷ 13

e. 9,384 ÷ 23

f. 9,135 ÷ 15

Across

a. 2,295 ÷ 45

b. 2,870 ÷ 82

c. 9,240 ÷ 11

d. 9,660 ÷ 35

e. 9,306 ÷ 22

f. 15,243 ÷ 3

b.

a. d. f.

f.

c.

e.

Check if you can solve these long divisions with a 3-digit divisor! These may have a remainder. Use your notebook.

a. 12,408 ÷ 118 b. 70,854 ÷ 235

Adding and Subtracting Large Numbers

1. Add.

2. Match.

Just like 25 marbles + 54 marbles = 79 marbles, so will 25 million + 54 million = 79 million.

Just keep in mind: a thousand thousands makes a million, and a thousand millions makes a billion.

800,000 + 200,000

Think of it as 800 thousand + 200 thousand. The answer is 1,000 thousand or 1,000,000.

Half a million

Think of it as half of a thousand thousands, or 500 thousands = 500,000.

34,999,000 + 1,000

This is 34 million 999 thousand + 1 thousand, making 34 million 1000 thousand or 35 million.

2 billion − 300 million

Think of it as 2,000 million − 300 million, which makes 1,700 million or 1,700,000,000.

a. 90,000 b. 99,000,000 c. 999,000

+ 1,000

+ 10,000

+ 100,000

+ 1,000,000

a.

1/2 million

a hundred hundreds

1/10 million

1/4 million

3/4 million

a thousand thousands

2/10 million

750,000

100,000

106

500,000

104

200,000

250,000

b.

1 million − 50,000

1 million − 500,000

108

1 billion − 500 million

1 billion − 50 million

1 million − 5,000

1 billion − 5 million

100,000,000

500,000

950,000,000

1/2 billion

950,000

995,000

995,000,000

3. Add or subtract. Simply write the numbers under each other, lining up the digits in the same places . Use the usual addition or subtraction algorithm, regrouping the same way as you have learned before.

4. Subtract and compare.

a. 329,145,000 + 2,809,125,093 b. 5,049 + 45,390,000 + 5,483,700

c. 45,700 + 90,567,000 + 2,560 + 2,300,560 d. 290,800 + 254,000,230 + 56,391 + 2,381

e. 480,560,000 − 23,980,000 f. 1,000,000 − 156,990

g. 22,300,000 − 4,431,190 h. 7,014,289,000 − 3,103,559,391

a. 1 million − 100 thousand =

1 million − 10 thousand =

1 million − 1 thousand =

b. 7 million − 500 thousand =

7 million − 50 thousand =

7 million − 5 thousand =

5. Continue counting for seven more numbers in each set:

6. Complete the addition path.

7. Solve for x.

a.

458,000,000

468,000,000

478,000,000

b.

79,650,000

79,800,000

79,950,000

c.

450,996,000

450,997,000

450,998,000

Each difference is

_______________

Each difference is

_______________

Each difference is

_______________

35,647,000 add 10,000 add a million

add 100

thousand

add 10 million add a thousand

a. x + 400,000 = 4,000,000

x = __________________

b. x − 350,000 = 2,000,000

x = __________________

c. 200,000 + x + 600,000 = 7,000,000

x = __________________

d. 2x = 3,000,000

x = __________________

Problem Solving with Bar Models 1

Solve. Draw a bar model. Write an expression (number sentence) for each calculation you do.

A fractional part of a whole

Problem. Jackie earns $1,840 monthly and Jessie earns 3/4 as much. How much does Jessie earn?

Solution. In the model, Jackie’s salary is divided into four equal parts (blocks). To find 3/4 of it, first find 1/4 of it, which is one block in the model.

$1,840 ÷ 4 = $460

Then multiply that result by three: 3 × $460 = $1,380.So, Jessie earns $1,380.

1. A camera that cost $125 was discounted by 1/5 of its price. What is the new price?

______ ÷ ______ = ______

________________________

2. A pizza that weighs 680 g is divided into five equal pieces. How much do two pieces weigh?

______ ÷ ______ = ______

______ × ______ = ______

3. A bottle of water costs 2/3 as much as a bottle of juice that costs $1.50. How much do two bottles of water and two bottles of juice cost?

Solve. Draw a bar model. Write an expression (number sentence) for each calculation you do.

A Fractional Part More

Problem. The school year in country A is 180 days long. In country B it is 1/6 part longer than that. How long is the school year in country B?

Solution. First, we divide the 180-day school year into 6 parts, to find how much one “block” is in the model:

180 ÷ 6 = 30. So, one block is 30 days.

Then we add one-sixth more to the whole bar model, and that is how long the school year is in country B.

180 + 30 = 210

So, the school year in country B is 210 days long.

4. The price of a train ride is $12. It went up by 1/6. What is the new price?

______ ÷ ______ = ______

______ + ______ = ______

5. A cafeteria lunch used to cost $4.50 but the price was increased by 1/5. What is the price now?

6. A one-way bus ride from Helen’s home to town costs $1. The bus company will raise the price by 1/10 in June.

a. How much will a one-way ride cost in June?

b. How much more will a two-way ride (home to town to home) cost Helen in June than in May?

7. A T-shirt cost $10.50, but now it is discounted by 2/5 of its price. Annie buys ten shirts with the discounted price. What is the total cost?

8. Duckville has 3,687 inhabitants, which is 3/5 of the number of inhabitants in Eagleby. How many people in total live in Eagleby and Duckville?

9. A package of 10 small envelopes costs $2.50, and a package of 10 large ones costs 2/5 more. Find the total cost of buying 50 envelopes of each kind.

1. Write the fractions as decimals, to three decimal digits.

Fractions and division

and a division problem 1 ÷ 8. This gives us a means of writing fractions as decimals!

Remember? The fraction line is also a division symbol. So 18

can mean both one-eighth (a fraction)

We simply divide 8 by 9, but writing 8 as 8.0000—with lots of decimal zeros.Look at the division on the right. We need to find four decimal digits for thequotient before we can round it to three decimal digits:

Example 1. Write 89

as a decimal, to three decimal digits.

89

= 8 ÷ 9 ≈ 0.889.

0 .8 8 8 89 )8 .0 0 0 0

7 2 8 0- 7 2 8 0

- 7 28 0

- 7 28

a.58

= b.67

=

2. Calculate. You will need to add decimal zeros to the dividend.

c.16

= d.720

=

a. 250 ÷ 6 to two decimal digits b. 37.5 ÷ 11 to three decimal digits

4. Three friends shared equally the cost of a taxi fare, $35.40, and the cost of a meal, $128.95. How much did each person pay?

5. Write a word problem that matches each calculation below. You don't have to calculate anything.

a. ($50 − $26) ÷ 3 = $8

b. 25 × $1.40 ÷ 2 = $17.50

3. a. Fill in the explanation as to how to solve the problem.

Three packs of transistors and seven packs of capacitors cost a total of $8.70. One capacitor pack costs $0.60. Find the cost of one transistor pack.

First ________________ the cost of seven capacitor packs

from ________. Then divide that result by _______.

b. Write a single expression to match the explanation above.

c. Solve the problem.

SELF EVALUATION

UNITARY METHOD

1. A shopkeeper sells 8 chairs for Rs. 33,728. Another shopkeeper

sells 5 chairs for Rs. 19,740 of same brand. From whom should I buy

the chairs to get the profit?

2. A daily worker makes 42 tables in 6 hours.

a. If there are 9 such workers in the factory, then how many tables

will be produced every hour?

b. How many hours he need to make 112 tables?

c. How many tables will be make in 19 hours?

Copyright: Math in English Page 7

Multiply and use the boxes

x 3

7 5 43

,

,

x 5

7 6 36

,

,

x 4

3 6 05

,

,

x 7

1 4 88

,

,

x 6

1 4 35

,

,

x 3

0 0 47

,

,

x 9

3 0 42

,

,

x 3

5 4 45

,

,

x 9

3 9 81

,

,

x 8

3 2 18

,

,

x 7

1 5 93

,

,

x 5

8 7 04

,

,

x 6

0 0 82

,

,

x 3

8 2 07

,

,

Multiplying 4 digits by 1 digit

Round the following numbers off to the nearest hundred

980

460

3,202

750

1,214

65

44

2,229

102

876

4,251

299

750

230

6,879

249

1,549

23

79

5,766

333

245

9,949

309

749

830

3,098

14

5,102

192

257

4,099

125

Complete the table

Round of the nearest:

Ten Hundred ThousandNumber

345

1,245

99

9,987

4,560

749

3,456

301

9

999

5,761

4,098

3,987

51

4,049

Find the factors of the following numbers:

18

25

16 45

20 64

15 12

28 10

35 40

42 32

39 24

45 100

63 22

21 50

Find the first common multiple of:

2 and 3 1 and 8

3 and 4 2 and 6

2 and 5 8 and 6

3 and 5 8 and 2 7 and 9

3 and 6 8 and 7 5 and 1

1 and 6 8 and 5 9 and 5

3 and 7 4 and 6 9 and 6

4 and 5 5 and 7 1 and 3

3 and 9 9 and 4 8 and 6

2 and 9 6 and 5 6 and 7

8 and 3 8 and 9 2 and 8

9 and 1 7 and 2 1 and 2

SELF EVALUATION

CIRCLES

1. Draw and name the following :

a. ray –

b. line segment –

c. parallel lines-

d. non-collinear points-

2. Calculate the reflex angle for the angles :

a. 23

b. 150

3.Find the supplement of 39.7

II. Construct the following:

1. Using compass and ruler, construct 30

2. Construct a circle of radius 4.5cm using compass

SELF EVALUATION

DIVISIBILITY

1. 6 is a factor of 12066 and 49320. Is 6 a factor of 49320 + 12066 and 49320 - 12066?

5. Is 9 a factor of the following?

(i) 394683

(ii) 1872546

(iii) 5172354

2. Fill in the smallest digit to make the number divisible by:

(i) by 5 : 7164__, 32197__

(ii) by 3 : 1__43, 47__05, __316

(iii) by 6 : __428, 9__52, 721__

(iv) by 4 : 2462__, 91__ __, 670__

v) by 8 : 1232__, 59__16, 4642__

3. Which of the two nearest numbers to 19506 are divisible by 9?

SELF EVALUATION

FRACTIONS AND DECIMALS

II. Do the sums:

1. 1

+ 2

+ 3

2. 7

- 3

3.

x

x

4. Simplify: 9.6+2.85-3.965+4.70

5. Multiply: 12.12 x 1.2 x 0.1

IV. Do the following sums:

1. A car covers 40.5 km in one hour. How much distance will it cover in

18 hours?

2. The product of two fractions is 24. If one fraction is 4

. Find the

other.

SELF EVALUATION LARGE NUMBERS

I. Using divisibility rules, check the divisibility of the following numbers: Numbers 2 3 9 15 25 2895 8000 9010 33,045 96,184 436564 20994 II. Do the following: 1. Write the divisibility rules for 11. 2. Write the divisibility rules for 4and 8. 3. Test the divisibility of the given numbers. i. 3987715 by 6. ii. 6346128 by 7 iii. 3657840 by 10

SELF EVALUATION

PERCENTAGE I. Do the following sums:

1. Find: 9% of 305 m.

2. What percent is 85litre of 13litre.

3. Find the average of first seven multiples of 9. Is the average a multiple of 9.

II. Solve the following:

1. In a blood donation camp, 2500 people donated blood. 75% of the donors were

college students and the rest were office employees. How many college students

donated blood?

2. In a cricket tournament , Dhoni and Kohli scored the following runs in the

various matches:

Match I II III IV V VI VII

Dhoni 35 58 82 73 91 15 27

Kohli 45 82 39 72 29 99 54

Find the average runs scored by each player. Whose performance is better?

Self evaluation

Profit and loss,bills

a. solve

1. The furniture shop dealer bought a cupboard for Rs. 7800 and he sold it at a

loss of Rs. 300. Find the loss per cent he incurred.

4. Swathi went to a restaurant and bought 9 dosas at Rs.48 each, 8 rice cakes at

Rs. 34 each, 5 chapattis at Rs. 25 each and 4 ice-creams at Rs. 50 each. Prepare a

bill on behalf of the shopkeeper. The restaurant’s name is “GOOD DAY” and the

bill number is 1976.

5. Mr.Durai bought a washing machine for Rs. 9,999 . He spent Rs. 3,568

on repairing. On selling the washing machine he made a profit of

Rs.2,643. Find the selling price of the washing machine.

SELF EVALUATION

RATIO AND PROPORTION

A.SOLVE:

1. 44 kg 200g rice has to be divided into 2 bags in the ratio 9 :

6 . How much will each bag weigh?

2. Swathi prepares 976 rice cakes in 8 hours. How much time

will she take to prepare 488 rice cakes ?

SELF EVALUATION

REPRESENTATION OF DATA

1. Express the following decimal into percentage.

21.95 =

2.. What percent is 80 cm 0f 10 cm?

3.Find:

90% of RS . 2700

II. Do the following sums:

1. Out of 140 teachers in a school, 40% are males. Find the

number of female teachers in the school.

2.The favorite sports of students of class V are given in the

table below:

SPORT CRICKET

FOOTBALL

HOCKEY

BADMINTON

NO.OF STUDENTS

14 6 4 12

Represent this data using a pictograph taking scale 1ball= 2

students

SELF EVALUATION

ADD AND SUBTRACTION

I. Do the following sum:

1.Mrs. Khanna has Rs.9,48,238 in her bank account. She

withdrew Rs. 4,37,200 from her account. How much money is left

with her.

2.Find the difference between greatest 7- digit number and

smallest 7- digit number.

3.Geetha bought a bed for Rs. 32,428 and a dining table for

Rs.22,946 and a television set for Rs. 14,567. How much money

did she pay to the shopkeeper?

4.In Maths olympiad, 2,48,736 students passed in the

examination and 1,20,008 students failed in the examination.

Find the total number of students who appeared in the

examination.

SELF EVALUATION

(Multiplication and Division)

I. Answer the following: ( 5×1=5)

1.When a number is multiplied by zero, then the product is______________.

2.983×400=_____________.

3.79× (259×20) = (79×259) ×_____=_____ (79×20).

4. To divide a number by 10,000, we simply remove the last four digits to get

the__________.

5. When zero is divided by any number, then the quotient is always_____________.

II.Choose the best answer: ( 5×1=5)

1. To multiply a number by 100, we multiply the number by 1 and add_________zeros to the

right of the product.

a. Two b .three c. one d. eight.

2. 5 can be written as__________

a. 7 ½ b.3 ½ c. 10½ d. none of these.

3.8012985 ÷10000 =_______________.

a.Q=8 R=12985 b. Q=80 R=12985 c. Q=801 R=2985 d.Q=0 R=0

4.0÷99999=___________.

a.99999 b.1 c. 0 d. not possible.

5. The product of two numbers does not change with a change in the order of the numbers.

This is called as _________________ property of multiplication.

a. associative b. commutative c. distributive d. multiplicative.

WORKSHEET

CIRCLES

I. Fill in the blanks:

1. The longest chord of the circle is _________________.

2. The length of the circumference of a circle is called its _________________.

3. Circumference = _________x Diameter.

4.___________________ lines meet at a point.

5. A part of a line which extends indefinitely in one direction is called a

_____________

II. Answer the following :

1. Find the diameter of the circle whose radius is 16 cm.

2. Find the circumference and radius of the circle whose diameter is 5 cm.

WORKSHEET

FRACTIONS AND DECIMALS

I. Fill in the blanks: (3x1=3)

1. If the numerator is greater than or equal to denominator is called __________________.

2.

-

=

3. Write the equivalent fraction.

=

II. Choose the best answer: (4x1=4)

1. 0.07X100= __________

a.7 b. 0.7 c. 7 d. 70

2. Difference of 9.6 and 5.60=____________.

a. 4 b. 4.4 c. 4.01 d4.3

3. Pick out the mixed fraction for the given improper fraction- 15/6

a.1

b. 2

c. 1

d. 1

4.98 divided by 10= ___________

a.98 b.9.8 c. 0.098 d.0.89

II. Do the sums: - ( 4x2=8)

1. 1

+ 2

2.

x

3. Simplify: 9.6+2.85-3.965+4.45

4. Convert the given fraction into decimal:

IV. Do the following sums: (2x2.5=5)

1. Praveen bought vegetables weighing 12.552 kg. If he bought 3.55 kg onions, 4.75 kg tomatoes and the

rest potatoes, find the weight of the potatoes.

2. The cost of 4

sugar is Rs. 153. What is the cost of 1 kg of sugar?

WORKSHEET LARGE NUMBERS

I. Answer the following: 1. What are the 3- digit numbers which is less than 130 is divisible by 6? 2. A number is divisible by 12 if it is divisible by both _______ and________. 3. Use the divisibility tests to determine whether each of the following numbers is divisible by 3 and 9. a. 1002- b. 14238- 4. Apply divisibility rule and write a number that is divisible by 25. 5. We can find out whether the given number is divisible by another, without actual division, using ___________________________.

WORKSHEET

MULTIPLICATION AND DIVISION

I. Do the following sums:

1. Multiply:

a.896542×999 (using distributive property).

b. 1968×426.

2. Divide and check the answer.(any one)

a.16985÷121

b.48935÷256.

II. Solve the following:

1. A table costs $ 1750. What will be the cost of 40 tables?

2. 52098 apples are to be packed in 16 boxes. How many apples will be

there in each box? How many apples will be left over?

WORKSHEET

REPRESENTATION OF DATA

I. Fill in the blanks:

1. A percentage is a fraction with denominator __________

2. The symbol for percentage is__________.

3. When we represent the data using pictures, it is called

_____________.

4. Bar graph is otherwise called ______________ .

II. Answer the following:

1. Express the following percentage as fraction.

54%

WORKSHEET

UNITARY METHOD

I. Solve the following word problems using UNITARY

METHOD:

1. The cost of 19 pair of ear rings is Rs. 3952. What is the cost

of one pair of ear rings?

2. Mr. Tilak earns Rs. 91,000 in 7 months.

a. How much will he earn in one month?

b. In how many months will he earn Rs. 1, 43,000?

WORKSHEET

PROFIT AND LOSS , BILLS

1. Find the profit or loss:

2. Mrs.Ram bought a saree for Rs. 5,600. She spent Rs. 900 for stone work in the

saree. She later sold it for Rs.9,432. Did she make a profit or loss and by how

much?

ITEMS COST PRICE (in Rs)

SELLING PRICE( in Rs)

PROFIT (in Rs)

LOSS (in Rs)

SOAP 95 109 TOWEL

247 38

SHIRT 567 90 PANT 987 68 TROUSER

123 95

OIL 451 56

Search answers from your brain

Search

Worksheet on divisibility rules will help us to practice different types of questions on test of

divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to find

whether the given number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

1. Which of the following numbers are divisible by 2, 5 and 10?

(i) 149

(ii) 19400

(iii) 720345

(iv) 125370

(v) 3000000

2. Check whether the numbers are divisibility by 4:

(i) 23408

(ii) 100246

(iii) 34972

(iv) 150126

(v) 58724

(vi) 19000

(vii) 43938

(viii) 846336

3. In each of the following numbers without doing actual division, determine whether the first number is divisible by the second number:

(i) 3409122; 6

(ii) 17218; 6

(iii) 11309634; 8

(iv) 515712; 8

(v) 3501804; 4

WORKSHEET

ADD AND SUBTRACTION

I. Answer the following:

1.32,435 + 28,962 + 63,108 = 28,962 + 32,345 + ____________.

2. The number which is subtracted is called as ________________.

3. 10000+1000+100+10+1=___________.

II. Fill in the boxes:

1. Add:

7 8 4

9 0 6 2

____________

9 2 8

____________

2.Sub:

8 7

0 1 9 2

______ ____

9 1 2 6

_____________

III. Match the following:

1. 19,478-100 92,625.

2. 32,401+ 0 1107

3. (928+327)-438 4,888.

4.4,388+500 19,378.

5. 92,625-0 817.

6. 999+99+9 32,401.

WORKSHEET

RATIO AND ITS PROPORTION

1. In a sports day, 108 students participated in

silambam, 96 students participated in yoga and

24 students participated in atheletics. Find the

following ratios in its lowest form:

a. silambam students to atheletics.

b. yoga students to atheletics.

WORKSHEET

PERCENTAGE AND AVERAGE

I. Convert the following:

Fractions decimals percentage

0.1

50%

0.3

20%

II. Fill in the blanks:

1. 92% is written _______.

2. 20 % of 2 kg is _____.

3. An improper fraction as a percentage is always _______________ than 100.

4. Average =

5. Average of all the factors of 18 _____________.