TheMathBooklets: method and steps

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Sunday, 4 November 2018

F4-L10 Fractions Practice : Division and Word Problems

(Part 1) Revise (~15mins) Start Time :

1. Fraction Multiplication and Division

2. Solving 2-step word problems

Common Terms and Model

'Remainder/Remaining' Word Problems

(Part2) Practice (~50mins)

(I) Multiplication/Division (~15 mins) Working

1. 2 ÷ 1 2 . 2 x 1

3 3

3. 6 ÷ 4 4. 6 x 4

5 5

5. 12 ÷ 6 6. 12 x 6

7 7

7. 1 ÷ 3 8. 1 x 3

2 4 2 4

9. 5 ÷ 7 10. 5 ÷ 7

6 12 6 12

11. 2 ÷ 8. 12. 7 ÷ 14

5 15 18 15

13. 20 ÷ 6

(II) Word Problems/PSLE (~35 mins) Start Time:

14. Mariam has a piece of rope 10 m long.

She cuts them into equal pieces, each 7/6 m long, except for the last rope which

is less than 7/6 m long. What is the length of the last rope? (6/p2/18f)

15.         A string was 3m long. Zoe cut it into pieces of length 1/9 m long each. How many pieces did she get?

16.         The product of two numbers is 4/5. If one of the numbers is 5/6, what is the other number?

17.         4 cakes were shared among a group of children. Each child got 2/9 of a cake. How many children were there in the group?
18.         Zack spent 1/3 of his money on food. He then used 1/4 of the remainder to buy 3 breads. What fraction of his money did he spend on each bread?

19. Find the value of 1/6 ÷ 4/9. Give your answer in the simplest form. (16/p1/18s)

20*. Find the value of 4/5 ÷ 12. Give your answer as a fraction in the simplest form.

21. The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether? (7/p2/18s)

22. A fruit seller had 33 more watermelons than papayas. After he sold 1/3 of the watermelons and 4/5 of the papayas, he had 57 more watermelons than papayas. How many papayas did he have at first? (10/p2/18s)

Extra Practices

(1) 'Equal/Same' Word Problems (optional)

(2) General Word Problems (optional)

1. 35 ÷ 5

2. 45 ÷ 12

3. Ken bought 24kg of peanut. He sold 3/8 of it and packed the remaining peanut into smaller packets of 4/5 kg each.

a. How many packets of peanut are packed?

b. How much peanut was left unpacked?

4. Jane has a number of happy face stickers in three colours: yellow, orange and red. 2/7 of the stickers are yellow. The number of yellow stickers is twice the number of orange stickers. What fraction of the stickers are red?

5. A fruit seller had 33 more watermelons than papayas. After he sold 13 of the watermelons and 4/5 of the papayas, he had 57 more watermelons than papayas. How many papayas did he have at first?

6* A shop had a number of computers for sales. After selling 32 of them in the morning and 5/8 of the remainder in the afternoon, it was left with ¼ of the computers. How many computers were sold altogether?

7. The fraction 2/ _ lies between 1/8 and 1/9. Find the missing whole number in the box.

8. 3/5 of the children in the playgroup were boys. The instructor divided the boys equally such that each group of boys had 1/10 of the number of children in the playgroup. The instructor then divided the girls equally into groups such that each group of girls had 1/5 of the number of children in the playgroup.

(a) Find the number of groups of boys and girls

(b) If there were 16 girls in the class, how many boys were there in the group?

9. Every month, Peter spends 1/3 of his salary, save 3/8 of the remainder and shares the rest of his salary equally among his father, mother and sister.

a. What fraction of his salary does each of them receive?

b. If his salary is $5400, how much does he give his sister each month?
Answer Keys
1. 6
2. 2/3
3. 15
4. 4 4/5
5. 14
6. 10 2/7
7. 2/3
8. 3/8
9. 2 11/12
10. 1 3/7
11. 3/4
12. 5/12
13. 16 2/3
14. 4/7 m
15. 27
16. 24/25
17. 18
18. 1/18
19. 3/8
20. 1/15
21.
22. 120

MO1-L12 Money-Decimals Practice

MONEY: L1 (45-70mins) Date/Time: Tutor:

(Part 1) Revise (10-15mins) Start Time:

1. Add/Subtract money in decimal notation

https://themathbooklets.blogspot.sg/2016/10/speed-and-time.html

2. Common Terms in Word Problems

https://themathbooklets.blogspot.sg/2017/07/word-problems-vocabulary.html

(Part2) Practice (~50mins)

Tutor: Please observe and ensure that the student follows the method/step.

Start Time: End Time:

(I) Add/Subtract Money (~15 mins) Working

Do the followings:

1. $7.35 + $0.65

2. $47.65 + $6.80

3. $37.90 + $22.70

4. $9.70 + $7.90

5. Find the sum of $27.85 and $3.15

Do the followings:

6. $24.15 - $9.60

7. $15.40 - $8.65

8. $76.65 - $23.05

9. Find the difference between $25.00 and $16.25

(II) Word Problems/PSLE (~35 mins) Working

Start Time:

10. Mickey had an equal number of $2 notes and $5 notes.

He had $42 altogether. What was the total value of $5 notes Mickey had? (11/p2/18f)

11. Amy has 3 times as much savings as Billy. Charlie has $70 more savings than Billy. How much savings does Charlie have if their total savings is $815? (12/p2/18f)

12. Rajah paid $5 for a box of 20 pencils. What was the cost of each pencil?

For questions 13-14

Seven classes of pupils went to a concert. Each class paid $144 for the concert tickets.

13. How much was spent on concert tickets?

14. Each pupil paid $6 for the ticket. How many pupils went for the concert?

15. Bicycle for Rent:

First hour: $7.

Every additional ½ hour: $3

Irene rented a bicycle for 3 hours. How much did she pay?

16.

Mass Step Hong Kong New Zealand

First 20 g $0.65 $1.10

Every additional 10 g $0.25 $0.35

Fiona sent a letter weighting 32g to Hong Kong and a letter weighing 10g to New Zealand by airmail. How much did she pay altogether?

17. Cupcakes are sold at Han’s Bakery at the prices shown below.

Emma spent a total of $50 on 16 chocolate cupcakes and some strawberry cupcakes. How many strawberry cupcakes did Emma buy? (13/p1/18s)

(1) 6

(2) 9

(3) 10

(4) 18 ( )

18. Molly wanted to buy 7 identical dresses but found that she was short of $14.50. In the end, she bought 5 of the dresses and had $8.50 left. Find the cost of each dress. (2/p2/18s)

19. At a bakery, Jack paid $12.40 for a banana cake and 4 egg tarts. Sean paid $25.20 for a banana cake and 20 egg tarts. Raymond bought 5 banana cakes. How much did he pay?

Answer Keys
1. $8.00
2. $54.45
3. $60.60
4. $17.60
5. $31.00
6. $14.55
7. $6.75
8. $53.60
9. $8.75
10. $30
11. $219
12. 25 cents
13. $1008
14. $168
15. $12
16. $2.25
17. 2
18. $12.50
19. $41

D1-L13 Decimals Practice : Notation, Place Value, Compare and Order

DECIMAL NUMBERS – D1 Date/Time: Tutor:

(Part 1) Revise (20mins) Start Time:

1. Notation and Place Value, Comparing and Ordering of Decimals (up to 3 d.p)

2. Comparing and Ordering Decimals, Using Number Lines

3. Conversion of Decimals and Fractions

(Part2) Practice (45 mins) Start Time:

Express each decimal as a fraction or a mixed number in its simplest form

1. 0.4 =

2. 1.6 =

Express each fraction or mixed number as a decimal.

3. ¼ =

4. 3/8 =

Express each fraction or mixed number as a decimal.

5. 4 ½ =

6. 2 2/5 =

7. Which is the greatest?

3.5, 2.8, 3.04, 4.4

8. Which is the smallest?

64.049, 68.123, 65.408, 67.637

9. Arrange these numbers in decreasing order.

6.606, 6.66, 6.6, 6.066

Round each decimal to 2 decimal places.

10. 8.123

11. 2.367

12. 99.999

13. In the number pattern below, what is the missing number in the box? (6/p1/18f)
9.25, 9.55, 9.85, ? , 10.45

14. Express 0.15 as a fraction in the simplest form. (7/p1/18f)

(1) 3/10

(2) 3/15

(3) 3/20
(4) 3/25

15*. Round off 70.171 to the nearest tenth.

16.* Which digit in 68.57 is in the tenth place?

17*. In the number line below, what is the number indicated by the arrow?

(1) 9.88

(2) 10.05

(3) 10.15

(4) 10.42 ( )

18. In 356.174, what does the digit 7 stand for? (1/p1/18s)

(1) 7 thousandths

(2) 7 hundredths

(3) 7 tenths

(4) 7 tens ( )

19. Which one of the following numbers is the largest? (4/p1/18s)

(1) 0.8

(2) 0.72

(3) 0.098

(4) 0.605 ( )

20. Simon’s height is 1.85 m. Round off his height to the nearest tenth. (19/p1/18s)

Answer Keys

1. 2/5
2. 1 2/5
3. 0.25
4. 0.375
5. 4.5
6. 2.4
7. 4.4
8. 64.049
9. 6.66, 6.606, 6.6, 6.066
10. 8.12
11. 3.37
12. 1.00
13. 3
14. 3
15. 7.02
16. 5
17. 102
18. 2
19. 1
20. 1.9m

D3-L15 Decimals Practice : Multiplication and Division

DECIMAL NUMBERS – D4 (~70 min) Date/Time: Tutor:

(Part 1) Revise(15-20mins) Start Time:

1. Multiplication and Division of Decimals (by 1 digit whole number, up to 2.d.p.)

(Part2) Practice (30-40mins)

Complete the Multiplication Tables (~5mins)

3x2=	4x2=	5x2=	6x2=	7x2=	8x2=	9x2=	12x2=
3x3=	4x3=	5x3=	6x3=	7x3=	8x3=	9x3=	12x3=
3x4=	4x4=	5x4=	6x4=	7x4=	8x4=	9x4=	12x4=
3x5=	4x5=	5x5=	6x5=	7x5=	8x5=	9x5=	12x5=
3x6=	4x6=	5x6=	6x6=	7x6=	8x6=	9x6=	12x6=
3x7=	4x7=	5x7=	6x7=	7x7=	8x7=	9x7=	12x7=
3x8	4x8	5x8	6x8	7x8	8x8	9x8	12x8
3x9=	4x9=	5x9=	6x9=	7x9=	8x9=	9x9=	12x9=

(I) Decimals (~20 mins) Start Time:

Give your answer correct to 1 decimal place.

1. 2.84 x 9

2. 7 x 30.12

3. 26.15 x 8

4. 0.75 ÷3

5. 47.36 ÷ 8

6. 28.16÷4

7. Find the value of 10.4 x 30

8. Divide 1.7 by 7 correct to 2 decimal places.

9. Estimate (a) 4.3 ¸6. Then find the actual value correct to 1 decimal place.

End Time: Mark: /10

(II) PSLE/Word Problems (~25 mins) Start Time:

10. A running track is 0.4 km long. James jogs 6 laps. What is the total distance that James jogs?

11. Linda bought 3 oranges and a mango for $4.05. The mango cost $1.50. How much did each pineapple cost?

12. Ken had $20. He bought 8 cans of drinks at 0.75 each. How much money did Ken have left?

For questions 13-14

3 groups of students collected $198 for their outing. This amount included $30 from their teacher.

13. How much did the group collected?

14. How much did each groups of students paid?

15. Sally has $204.80. She has 4 times as much money as Eric. How much more money does Sally have than David?

16*. Find the value of 0.46 x 70

17. Peter wanted to buy 6 books of the same price but found that he was short of $10.50. In the end, he bought 4 of the books and had $6 left. Find the cost of each book.

18. Mindy sold 4 times as many headphone as mobile phone and collected a total of $8400. Each mobile phone costs $325 more than an headphone. The amount collected for all the headphones sold was $3480 more than the amount collected for all the mobile phones sold. How many mobile phones did Mindy sell?

End Time: Total Mark:

Extra Practice

1. Multiply. Give your answer correct to 1 decimal place.

(a) 2.84 x 4

(e) 3 x 6.05

2. Divide.

(b) 6.79 ÷7

(d) 27.36 ÷9

(e) 20.04 ÷4

3. Ronald bought two cakes for $2.40 and one packet of drink for $0.90. He then bought another 5 cakes and 3 packets of drinks for his friends. How much did he pay altogether?

4. Mindy was given $3 pocket money every day of the week. She spent $2.60 per day from Monday to Friday and saved the rest. She saved all her pocket money on Saturday and Sunday. Starting on a Monday, how many days did it take her to save $50?

Answer Keys

1. 25.56

2. 210.84

3. 20.92

4. 0.25

5. 5.92

6. 7.04

7. 312

8. 0.24

9. ~0.7, 0.72

10. 2.4 km

11. $0.85

12. $2

13. $168

14. $56

15. $153.60

16. 3.22

17. $13.25

18. 3