Infinite Math Bar Model

MODEL-DRAWING to solve problems

-7=5
Take 7 away
7

Leaves 5

From the above model you can see that trhe unknown number in the box is equal to 7 + 5, which is 12. (Double check ? - 7 = 5)

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Finding an unknown number. Question 1b: Find the unknown number in the box ? - 18 = 9

Draw your own model on a piece of paper to answer this questions. Its great if you can calculate the answer mentally, without drawing the model. Then check the answer. 27 ?

9
- 18 =9

18

? ?

= 9 + 18

? 27 - 18 = 9

= 27

The number in the box is 27

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Now you should be able to find the unknown numbers without model drawing! ? - 13 =8 ? = 8 + 13 (So it is actually an addition sum!) = 21 21 - 13 = 8

can do these Practice 1 : Try the following exercise: (You can do these mentally)

1. 2. 3.

- 12 = 10 - 15 = 15 - 20 = 25

4. 5. 6.

- 30 = 60 - 65 = 100 - 73 = 127

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Question 2a Pam had some stamps. After she gave away 280 stamps to her brother, she had 754 stamps left. How many stamps did Pam have at first? The number sentence for this problem is : - 280 = 754 This model stands for the unknown numbers of stamps. ?

Gave away Solution to Q2a Number sentence

280

754

- 280 = 754 = 754 + 280 = 1034 - 280 = 754

?
1034

Pam had 1034 stamps at first. You can solve this problem without drawing this model, once you know how to write a number sentence for it! (saves your time)

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Question 2b
Mrs Brown went shopping . She spent 125 dollars on a dress. Thn she had 137 dollars left. How much money didi she have at first?

? dress

Spent RM125 Solution to Q2a Number sentence ?

RM 137 left

- 125 = 137 ? = 137 + 125 = 262 262 - 125 = 137

At first Mrs Brown had 262 dollars.

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Question creation: (Work on a piece of paper) Create your own question and solution. (You can use the guideline below.) Get someone (eg parents) to help check the answer. If you have done correctly, you have mastered the concept of solving this type of problem. Congratulation! Have fun creating problems for your friends to solve! Mary baked some tarts for her party. Her friends ate ______ of the tarts during the party. There were _____ tarts left over. How many tarts did Mary bake? Practice 2: 1) Mary had some money in her bank. Then she took out RM25 to buy a birthday present for her brother. After that she had RM35 left in her bank. How much money was there in her bank at first? ? Money left in bank RM 35 Number sentence : ? - 25 = 35 Cost of present RM 25

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2) Ben had some stamps in his album. Then he gave 175 stamps to his sister. Then he found that he had only 245 stamps left. How many stamps did he have at first?

? Stamps left in album 245 Number sentence : ? - 175 = 245 3) Mel wanted to pick her picture cards into a box. The box could hold only 396 cards. He still had 236 more cards left over. How many picture cards did he have altogether? 4) Many children visited the zoo on Sunday. The first 200 children were given a free balloon each.150 children were disappointed because they did not receive any balloons. How many children visited the zoo on Sunday? 5) Mr Brown bought a packet of sweet for a childrens party. The children ate 148 sweets. After the party, Mr Brown still had 52 sweets left. How many sweets were there in the packet? 6) After spending RM 35.50, Max had RM 20.50 left. How much money did Max have at first? Gave sister 175

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MODEL-DRAWING to solve problems

Finding an unknown number. Question 1a: 35- ? = 13 (What is the number in the box?) Study the following example.
35

35

35-

? =13 ?

35 13 = 35 13 = 22

The number in the box is 22.

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Finding an unknown number. Question 1b: Find the unknown number in the box. 99 ? = 43

Draw your own model on a piece of paper to answer this question. Then check the answer. 99

43 Take away ? 99 ? ? = 43 = 99 43 = 56 The number in the box is 56

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Now you should find the numbers without model drawing! Example : 85 ? = 38 ? = 85 38 = 47

Practice 1
Try the following exercise:

1. 1. 1.

97 - = 16 97 - = 16 97 - = 16

4. 5. 6.

- 30 = 60 - 65 = 100 - 73 = 127

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Question 2a: Jack went to a book store to buy a dictionary. He gave a cashier a RM 100 note. He got a back RM 22 change. How much did the dictionary cost?

Question 2a: On your paper or exercise book, write a number statement for the problem.

100

22

Change

Gave cashier

Unknown cost

Draw the model for the above number statement on your paper or book.

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Answer for Q2a 100

? Take away cost of dictionary

22

Number sentence

100 -

? ?

= 22 = 100 22

= 78 The dictionary cost RM 78 You can solve the problem without drawing the model, once you know how to write a number sentence for it! (saves your time) Question 2b:

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There were 520 students in Hillview Primary School in January. In June, some students left to join another school. Only 23 students remained in the school. How many students went to join other school? Hints for Q 2b: On your paper, write out the number statement. Use the guideline below. = How many remained?

Dont know how many left Draw a simple model on your paper to solve this problem or find the answer by working out the number sentence. Then check your answer on the next slide. Answer to Q 2b: 520

No. of students in Jan

? went to another school 520 ? ? = 213 = 520 213 = 307

213

307 students went to join the other school

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There were _____ balloons for a sale at a fair. By the end of the day _____ balloons were left. How many balloons were sold at the fair? Practice 2: Try to solve these problems. Draw a model to understand each problem. If you can understand each problem without drawing the model, just write a number sentence to solve it. 1. On Monday, a store had 2348 toy cars for sale. By Wednesday there were only 456 toy cars left. Ho many toy cars were sold? Kelly has RM27. Annie has RM 5.50 less than Kelly. a) How much money does Annie have? b) How much money do both of them have altogether? George and Ben bought a present for Ann. George paid RM 6.80 and Ben paid RM4.90. a) How much did the present cost? b) How much less did Ben pay? Mr. Donald has RM125. He needs RM12.90 more to buy a watch. How much does the watch cost? 2345 people visited the circus last Sunday. 986 were adults and the rest were children. a) How many more visitors were children? b) How many more children than adults visited the circus?

2.

3.

4. 5.

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Model Drawing to solve problems

A quick recap: (Counting by 2s) 2,4,6,8,10,12,14,16,18,20,22,24 (Counting by 3s) 3,6,9,12,15,18,21,24,27,30,33,36 (Counting by 4s) - 4,8,12,16,20 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, 23,24,25,26,27,28 (Counting by 5s) 5,10,15,20,25,30,35,40,45,50,55,60

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, 23,24,25 (Counting by 10s) 10,20,30,40,50,60,70,80,90,100, 110,120 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, 23,24,25,26,27,28,29,30 You need to understand and memorize these multiplication tables.

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Sample problem: There are 5 rows of chairs. Each row has 4 chairs. How many chairs are there altogether? Method 1: model drawing R1

R2

8 5 rows 4 chairs = 20 chairs There are 20 chairs altogether

R3

12

R4

16

R5

20

Method 2: Quick drawing

Method 3:Mental Calculation

cccc cccc cccc cccc cccc

5 4 = 20 chairs There are 20 chairs altogether I know multiplication tables! 5 4 = 20

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Problem 1a: Work out this problem in your exercise book or paper. You can use any method, as long as you get the correct answer. Davids pocket money is RM3 a day. How much money does he receive in a week? RM 3 RM 3 RM 3 RM 3 RM 3 RM 3 RM 3

7 3 = 21 He gets 21 dollars a week. There are 7 days in a week.

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Question 1b: Work out this problem in your exercise book or paper. Can you calculate the answer mentally? There are 10 similar of beads. Each box has 5 red beads and 4 blue beads. How many beads are there altogether?

5+4=9 There are 9 beads in each box. 10 9 = 90 There are 90 beads altogether.

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Q 2a: After buying 6 melons at RM8 each, Jane had RM 12 left. How much money did Jane have at the beginning? Solution to Q 2a:

6 8 = 48

RM 12

Janes money at the beginning. 6 8 = 48 Jane spent RM 48 on 6 melons 48 + 12 = 60 She had RM60 at the beginning

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Question 2b: After buying 3 tins of milk and 7 boxes of chocolates, Mrs Brown had RM9 left. How much did she have at first? RM 10 each Milk RM 5 each Chocolate

Milk (3 RM 10)

Chocolates (7RM 5)

RM 9

3 tins of milk 3 RM 10 = RM 30 7 boxes of chocolates 7 RM 5 = RM 35 She spent RM 30 + RM 35 = RM 65 RM 65 + RM 9 = RM74 Mrs Brown had RM 74 at first.

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Practice 1: 1. 2.

Try solving this problems yourself.

3.

4.

A toy car cost RM 8. Bob bought 4 toy cars and a bag for RM42. Find the cost of the bag. A teacher bought some sweets for her class of 20 students. After giving 5 sweets each, she had 10 sweets left. How many sweets did she buy? A baker bought 4 trays of eggs. Each tray had 12 eggs. He used some eggs to bake 3 cakes. Then he had 18 eggs left. How many eggs did he use? Mary read 12 pages of a story book per day. She finished reading the book in 5 days. How many pages are there in the book?

ANSWER TO PRACTICE 1: Q1: A toy car cost RM 8. Bob bought 4 toy cars and a bag for RM42. Find the cost of the bag. RM 42 Bag ? 4 toy cars Bags 4 toy cars 4 RM 8 4 RM 8 = RM 32 RM 42 - RM 32 = RM 10

The bag cost RM 10

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ANSWER TO PRACTICE 1: Q2: A teacher bought some sweets for her class of 20 students. After giving 5 sweets each, she had 10 sweets left. How many sweets did she buy? Total number of sweets 10 ? Sweets for 20 students Number of sweets She bought 110 sweets ANSWER TO PRACTICE 1: Q3: A baker bought 4 trays of eggs. Each tray had 12 eggs. He used some eggs to bake 3 cakes. Then he had 18 eggs left. How many eggs did he use? 4 trays of eggs 12 12 12 12 4 12 = 48 20 5 4 RM 8 20 5= 100 100 + 10 = 110

The baker bought 48 eggs. 48 eggs ? Used for cakes 18 left 48 18 = 30

He used 30 eggs. Page | 22

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ANSWER TO PRACTICE 1: Q4: Mary read 12 pages of a story book per day. She finished reading the book in 5 days. How many pages are there in the book? Whole book 12 12 12 12 12 12 5 12 = 60

Pages read per day Pages read in 5 days

There are 60 pages in the storybook. After buying ____ books at RM ____ each, Alice had RM ____ left. How much money did Alice have at first?

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Mental sums (1): Try the mental sums. Look at the model drawing.

- 20 = 42 ?

? more than 42 is 64 64 more

Take away 20 42 42 ?

56 -

= 30 56

45 is

? less than 100 100 ? less

Take away ? 30 20

42

Mental sums (1): Answers 1. 3. 62 20 = 42 22 more than 42 is 64 2. 4. 56 26 = 30 45 is 55 less than 100

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Mental sums (2): Find then missing number in the box 1. ? 45 = 50 ? = 90 ?

2. 77 +

3. 40 is more than 4. ?

is 35 less than 80

Mental sum (2): Answers 1. 95 45 = 50 13 = 90 27

2. 77 +

3. 40 is more than 4. 45

is 35 less than 80

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Practice 2: Solve the following problems. Model-drawing is encouraged but you may also use any other method as long as the steps are clearly worked out. 1. Ken has 5 stickers. Lenny has 5b times as many as stickers. How many stickers do both of them have altogether? There are 6 rows of desks in Marys classroom. There are 5 desks in each of the first 4 rows and 3 desks in the last 2 rows. How many desks are there in Marys classroom? Mrs Brown baked some tarts. She gave 9 tarts to each of her 4 friends. Then she had 15 tarts left. How many tarts did Mrs Brown bake? Mr Roberts collected 4 piles of 10 worksheets from class 3A and 6 piles of 8 worksheets from class 3B.How many worksheets did Mr Robert collect from the 2 classes? 7 classes of students went to watch a show. Each class had 3 students and 2 teachers. How many people went to watch the show?

2.

3.

4.

5.

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Question 1: There are 424 apples in Basket A and 381 in Basket B. How many apples are there in two baskets?

There are

apples in the two baskets

Question 2: Michael has 55 stickers. James has 28 fewer stickers than Michael. How many stickers that James have?

James has

stickers

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Question 3: Eric has 350 seashells. He has 60 seashells more than Anna-Maria. How many seashells does Anna-Maria have?

Anna-Maria has

seashells.

Question 4: After lending Michiko 64 pieces of colored paper, Henry had 49 pieces left. How many pieces of colored paper did Henry have in the beginning?

Henry had in the beginning

pieces of colored paper

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Question 5: Madison completed 431 questions in her workbook. 214 of her answers were correct. How many answers were wrong?

answers were wrong.

Question 6: Ms Jackson gad some stamps. She gave 31 stamps to Kyra, 57 stamps to Darius, and had 21 stamps left. How many stamps did Ms Jackson have in the beginning?

stamps in the beginning Page | 29

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Question 7: Randy has 83 balloons. Kaylee has 21 fewer balloons than him. How many balloons does Kayle have?

Kaylee has

balloons

Question 8: Mr Gracia sold 341 eggs on Monday. He sold 291 eggs on Tuesday. How many more eggs that he sell on Monday than on Tuesday?

more eggs on Monday than on Tuesday

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Question 9: A television set costs RN581, and a DVD player costs RM289. Mr. Ito paid the cashier RM1000. a) How much does the television set and the DVD player costs altogether? b) How much change did Mr. Ito receive from the cashier?

The television set and the DVD player cost RM Mr Ito received RM in change.

Question 10: Dad gave Tyler and Emily the same amount of pocket money. Emily bought a T-shirt for RM41, and she had RM6 left. How much money did Dad give Tyler?

Dad gave Tyler RM Page | 31

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Question 11: After collecting 89 ice-cream sticks, Ahmad had 501 icecream sticks altogether. How many ice-cream sticks did What he have in the beginning?

He had beginning

ice-cream sticks in the

Question 12: Alexis has RM53. She needs RM29 more to buy a scooter. What is the cost of the scooter?

The cost of the scooter is RM Page | 32

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Question 13: Joseph has 99 marbles. He has 35 more marbles than Elijah. How many marbles does Elijah has?

Elijah has

marbles.

Question 14: Alex has 281 stickers. His sister gives him another 29 stickers. a) How many stickers does Alex have now? b) If Alex gives 99 stickers to his friends, how many stickers does he have left?

Alex has He has Page | 33

stickers now. stickers left.

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Question 15: Taneesha has 345 stamps. Stephen has 56 fewer stamps than her. Lily has 9 stamps more than Taneesha. a) How many stamps does Stephen have? b) How many stamps does Lily have?

Stephen has Lily has

stamps. stamps.

Question 16: Mr Bell baked some cookies. After selling 341 cookies, he had 39 cookies left. How many cookies did Mr Bell bake?

Mr Bell baked Page | 34

cookies.

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Question 17: Lucy had 536 stamps. She gave 312 stamps to Salima and used 102 stamps to mail greeting cards. How many stamps did she have left?

She had

stamps left.

Question 18: There are 316 boys in Green Valley Elementary School. There are 180 more boys than girls. a) How many girls are there in the school? b) What is the total number of students in the school?

There are girls in the school. The total number of students in the school is Page | 35

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Question 19: A red stick is 189 cm long. A white stick is 85 cm long. How much longer is the red stick than the white stick?

The red stick is cm longer than the white stick. Question 20: Jorge sold 350 oranges in the morning and another 81 oranges in the afternoon. He still had 65 oranges left at the end of the day. How many oranges did he have in the beginning?

He had Page | 36

oranges in the beginning.

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Question 21: There were 378 boys and 209 girls in the school choir last year. 95 boys and 35 girls joined the school choir last year. a) How many students were in the school choir last year? b) How many students joined the school choir this year?

students were in the school choir last year.

students joined the school choir this year.

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Question 22: Nicholas and his brother each have 421 marbles. Nicholas receives 59 more marbles from his friends. a) How many marbles does Nicholas have now? b) How many marbles do Nicholas and his brother have altogether?

Nicholas has Nicholas and his brother have marbles altogether.

marbles now.

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Question 23: Mrs. Spisak baked 250 chocolates cookies. She baked 79 fewer strawberry cookies than chocolate cookies. How many strawberry cookies did she bake?

She baked cookies.

strawberry

Question 24: There are 458 girls and 641 boys in the school auditorium. How many more boys are than girls are there in the auditorium?

There are the school auditorium. Page | 39

more boys than girls in

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Question 25: Max, Noel, Yoko, and Julia shared 36 grapes equally. How many grapes did each of them get?

Each of them got grapes. Question 26: Mrs, Cook has 3 bags of oranges. Each bag contains 4 oranges. a) How many oranges does she have altogether? b) If she takes all the oranges out of the bags and puts an equal amount on 2 plates, how many oranges will there be on each plate?

She has There will be plate. Page | 40

oranges altogether. oranges on each

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Question 27: Jasmine had some money in her purse. She used RM251 to buy a ring and had RM25 left. How much money did she have in the beginning?

She had RM

in the beginning.

Question 28: 1lb. of fish costs RM9. What is the cost of 3 lb. of fish?

The cost of 3 lb. of fish is RM Page | 41

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Question 29: A red notebook costs twice as much as a pink notebook. If the red notebook costs RM 18, what is the price of the pink notebook?

The price of pink notebook is RM Question 30: There are 5 pencils in a bag. There are 3 times as many as pencils in the same bag. How many pens are in the bag?

There are

pens in the bag

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Question 31: Clara bought a dress for RM16. She gave the cashier RM20 and got back the change in 1 dollar bills. How many dollar bills did she get back?

She got

1- dollar bills back.

Question 34: Lim put 128 red marbles into Bag A, 215green marbles into Bag B, and some white marbles into Bag C. He put a total of 500 marbles into the 3 bags. a) How many marbles were there altogether in Bag A and Bag B? b) How many white marbles did he put into Bag C?

a)

There were marbles altogether in Bag A and Bag B. b) He put white marbles into Bag C. Page | 43

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Question 35: There are 250 adults, y60 girls and 30 boys on a train. How many more adults are there than children?

There are children.

more adults than

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Question 36: Uncle Sam had 3 apple trees. He picked 8 apples from each tree. a) How many apples did he pick altogether? b) Uncle Sam shared all the apples equally among his 4 children. How many apples did each child get?

He picked Each child

apples together got apples.

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Question 37: Meena, Lauran, and Minh shared 30 crackers equally among themselves. a) How many crackers did each girl get? b) How many crackers did Meena and Lauran have altogether?

Each girl got Meena and Lauran had altogether

crakers crackers

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Question 38: Boxes A, B, and C have a total weight of 85kg. Boxes A and B have a total weight of 46kg. a) Find the weight of box C b) If box C is 21 kg heavier than Box A, find the weight of Box A.

a) The weight of Box C is b) The weight of Box A is

kg kg

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Question 39: Mr Rulaski gives RM30 to Bailey and Jenny. If Bailey gets twice as much as money as Jenny, how much will Jenny get?

Jenny will get RM

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Question 41: Tierra has 7 flowers. Megan has twice as many as Tierra. How many flowers do the girls have altogether?

They have

flowers altogether.

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Question 41: Emilio bought a pen and a watch. The watch cost three times as much as the pen. If Emilio paid RM5 for the pen, how much did he pay for the watch?

He paid RM

for the watch.

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Question 43: Kimiko had 18 colored pencils. She shared equally with her sisters. How many colored pencils did Kimiko get?

Kimiko got Question 56:

colored pencils

Every day, Mrs Romano mixes 22gal of water with 11 gal of lemon syrup to make drinks to sell. How many gallons of drinks does she make every day?

She makes every day.

gallons of drinks

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Question 57: Jacks weight is 29kg. Binh is 9kg heavier than Jack. Cooper is 8kg lighter than Binh. a) what is Binhs weight? b) what is Coopers weight?

a) Binhs weight is b) Coopers weight is

kg kg

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Question 58: Luis had 100 oranges. 30 of them were rotten. He packed the rest equally into 10 boxes.

a) How many good oranges were there? b) How many oranges were there in each boxes?

There were There were

good oranges oranges in each box.

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Question 58: Natasha has RM10. Zoe has twice as much as Natasha. Allison has RM40 more than Zoe. a) How much money does Zoe have? b) How much money does Allison have?

Zoe has RM Allison has RM

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Question 60: A workbook costs 70 cents. A box of colored pencils costs 90 cents more than the workbook. How much do the workbook and the box of colored pencils cost altogether?

They cost

cents altogether.

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Question 61: Simon has 8 five-cent coins and 5 ten-cents coins. a) How much money does he have in five-cent coins? b) How much money does he have in ten-cent coins?

He has He has

cents in five-cent coins cents in ten-cent coins

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Question 62: 12 people took part in a race. Jonah was 7th from the front. He later overtook 3 people. How many people were behind Jonah at the end of the race?

people were behind Jonah at the end of the race.

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Question 63: Malik has 10 stamps. Kevin has 3 times as many stamps as Malik. How many stamps do they have altogether?

They have

stamps altogether

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Question 64: 4 teachers and 40 girls went on an overnight trip. There were 5 girls in each room. The 4 teachers slept in 2 rooms. How many rooms did the group use altogether?

The group used altogether.

rooms

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