Course description
Overview
This course is targeted at Singapore primary school level 5, but is also suitable for primary school level 6 students. Primary 4 students who are keen to work on harder questions will also find this useful.
Based on feedback, many parents have used the videos to learn the methods to help their children to learn faster.
Math Arena students gain an edge using techniques that we teach here in our videos, these methods provide accuracy and speed. We believe it also provides better understanding of their solution to the question that they are solving.
It can also be used as independent learning or for revision.
There are a total of 4 PDF sets for this series. They are arranged by similarity for easy question pattern recognition.
The Number of stars indicates level of difficulty. One star is fundamental, 2 stars are moderate. 3 and 4 stars are difficult and challenging. Note due to the student’s ability he may experience difficult questions as easy and easy questions as difficult. So do not be over anxious, if an “easy question” stumped you, just keep practicing.
Course Content
You will :
- get 4 (Set A, B, C and D) PDF files that you can print
- be able to watch and learn from 100 videos
- learn fast, accurate methods in solving Fraction, Ratio Percentage Questions
Course Pre-requisites
You will need to know:
- Basic ideas of Fraction, Ratio and Percentages,
- How to watch videos on your computer
Notes:
- PDF files contain the questions, the videos are the solutions to the questions.
- Question header may not contain the full question as it it limited to 255 characters.
- Our Videos complements the student’s math lessons in Math Arena.
- Fraction, Ratio, Percentages (FRP) are the main bulk of of questions for PSLE.
- It is common that parents do learn from our videos and work with their children too.
- The bar model is good for understanding but may be less useful for more complicated questions. It can also lead to harder transition to algebra in their secondary schools.
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Course Curriculum
FRP - Set A
Fractions, Ratio, Percentage Set A
FREE PREVIEW
1) A box contained some blue and red marbles in the ratio of 3: 8. When 144 blue marbles were added in, the ratio became 3: 4. Find the number of marbles in the box at first.
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2) The number of erasers Jay had to the number of erasers Ray had was 7: 5. After Ray gave away 40 erasers, the ratio of the number of erasers Jay had to the number of erasers Ray had become 3: 1.
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3) Alexia had some blue pegs and green pegs in the ratio 2:3. 15 green pegs and 26 blue pegs broke and the number of blue pegs is now 1/3 the number of green pegs. Find the number of blue pegs at first.
4) The number of hats in Javier’s shop is six times the number of scarves. After selling 9 hats and buying 66 more scarves, the ratio of the number of hats to the number of scarves is now 3:5. How many hats and how many scarves were there at first
5) In café Moon, the number of females is 20% of the number of males. In café Eclipse, the number of males is 25% of the number of females. The ratio of the number of females in café Moon to the number of males in café Eclipse is 3:5.
6) Phoebe has 128 more stamps than Eugenia at first. If Phoebe buys another 20 stamps and Eugenia buys another 60 stamps, Phoebe will have twice the number of stamps Eugenia has. How many stamps does Eugenia have at first?
7) May had a collection of 224 bookmarks. After May threw away 32 bookmarks, June had 2/3 of what May had left.
8) Ethan has $120 more than Dilton. After Ethan spent 80% of his money and Dilton spent 60% of his money, they still have $270 left altogether. How much money does Ethan have left in the end?
9) Siti and Aslinda had 198 stickers altogether. Siti gave away 1/2 of her stickers and Aslinda gave away 3/5 of hers. In the end, they had an equal number of stickers left. How many stickers did they give away altogether?
10) David spent 5/12 of his money on some books and Mary spent 3/4 of her money on some files. After paying for their purchases, they had an equal amount of money left.
11) Min Jung and Min Ho each received some bonus. Min Ho spent 7/12 of his bonus. Min Jung spent 5/9 of his bonus on a wallet. The wallet cost $1250. Finally both of them had the same amount of bonus left.
12) Lucas and Leonard had 439 marbles. Lucas gave 3/11 of his marbles to his friends while Leonard gave 40 marbles to his friends. If they have an equal number of marbles left, how many marbles did Leonard have at first?
13) Joy spent 3/4 of her money on 3 blouses and Grace spent 4/9 of her money on 2 skirts. They were each left with an equal amount of money. One blouse cost $9 more than one skirt. How much money did they have altogether at first?
14) Angie spent 5/6 of her money on 5 packets of chicken rice and Bob spent 3/8 of his money on 3 curry puffs. They were each left with an equal amount of money. The cost of one packet of chicken rice is $2.80 more than a curry puff.
15) Kim had 5 times as much money as Boon Yong at first. After Kim spent $68 and Boon Yong receive another $36, they had an equal amount of money. How much did Kim have in the end?
16) Kenneth’s savings was 7/10 of Eric’s savings. After Kenneth increased his savings by 10% and Eric’s savings decreased by 25%, Kenneth’s savings was $900 more than Eric’s. What was Kenneth’s savings in the end?
17) Nicole had 4 times as many beads as Audrey. After they each bought an equal number of beads, Audrey had 162 beads and Nicole had three times as many beads as Audrey
18) Vernon has 2/5 as many stamps as Walsh at first. They then sold the same number of stamps each. Vernon now has 57 stamps which is one-third the number of stamps Walsh have. Find the number of stamps each of them had at first.
19) Catherine had thrice as much money as Andy at first. After Catherine gave Andy $450, Andy had 7 times as much money as Catherine. How much money did Catherine have at first?
20. There were 750 golf balls in Bag A and Bag B altogether. If Megan transferred 45 golf balls from Bag B to Bag A, the number of golf balls left in Bag B will be four times the number of golf balls left in bag A. How many golf balls are there in Bag B?
21) 1/4 of Dana’s savings is equal to 2/5 of her sister’s savings. 21) The difference in the amount of their savings is $171. What is the total amount of savings that Dana and her sister have?
22) 3/5 of Claire’s muffins is equal to 6/7 of Melody’s muffins. Claire has 39 more muffins than Melody. How many muffins do they have altogether?
23) After Sharon spent 40% of her money, the amount of money she had left was $48 more than the amount she had spent. How much money had Sharon left?
24) Benny received the same amount of salary in January and February. In both months, he spent part of his salary and saved the rest. In January, he saved 2/3 of the amount that he spent. In February, he saved 4/5 of the amount that he spent.
25) 25% of Henry’s savings is $65 more than 20% of Jane’s savings. If Henry’s savings is $450, how much is Jane’s savings?
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FRP - Set B
Fractions, Ratio, Percentage Set B
FREE PREVIEW
1) 1 file and 1 notebook cost $10. 1 file and 1 pen cost $6. Each notebook costs thrice as much as a pen. How much does 1 file cost?
2) The ratio of the number of boys to the number of girls in a camp is 4: 7. The camp fee for each child is $45. There are 112 boys in the camp. Find the total amount of fees paid by all the children.
3) Elsa was given 1/3 of a pizza. Anna was given 2/5 of the remaining pizza. The rest of the pizza was distributed equally among 4 children. What fraction of the pizza did each of the 4 children get?
4) Angela had some stickers. She gave 110 of them to her sister and 162 of them to her brother. She then gave 2/3 of the remaining stickers to her friend. She was left with 1/7 of the stickers she had at first.
5) Alisa sold 168 cupcakes on Monday. She sold 2/7 of the remainder on Tuesday and had half of her cupcakes left. Find the number of cupcakes she sold altogether
6) A tailor had some cloth. She used 2/9 of the cloth to make dresses and 3/14of the remaining cloth to make trousers. She bought another 126m of cloth and then found out that she had as much cloth as she had at first.
7) A shopkeeper imported 480kg of rice. He packed 1/4 of it into 2-kg packets and 7/12 of the remainder into 3-kg packets. Then he packed the rest into 5-kg sacks. He sold each 5-kg sacks at $11.20 per sack.
8) Fanny shared a sum of money with 3 of her sisters, Mandy, Helen and Anne. She gave 1/3 of the money to Mandy, then 3/8 of the remainder to Helen and 1/3 of what was left and an additional $135 to Anne. Fanny was left with $275.
9) Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder on a belt. He had 2/5 of his money left in the end.
10) Shaun spent $360 of his pocket money on a bicycle, 2/3 of the remainder of food, and saved the rest. Given that he saved 1/5 of his pocket money, how much as his pocket money?
11) Mr Lee spent 1/5 of his bonus on a mobile phone and 5/8 of his remaining money on a vacation package. He then gave $600 to his wife and saved then remaining $580. How much did Mr Lee spend on the mobile phone?
12) James spent 3/4 of his money on a book and 2/3 of the remainder on a pen. He had $1.25 left. What fraction of his money did he spend altogether? How much money did he have at first?
13) Lyna had some money. She spent $292.80 on a printer and 3/10 of the remaining amount on a study desk. Finally, she was left with 1/2 of the amount of money she had at first. How much money did Lyna have left?
14) Ginny spent 1/8 of her money to buy a carton of milk, 2/7 of the remainder to buy a box of cereal and spent the remaining amount equally on 3 tins of biscuits. One tin of biscuits cost $8 more than a carton of milk.
15) Alvin had some money at first. He spent 1/4 of it on a T-shirt and 2/5 of the remainder on a pair of shoes. After that, his parents gave him $120.
16) Joel brought a sum of money for his trip. On the first day, he spent 1/4 of his money and misplaced $4. On the second day, he spent 1/4 of his money on 2 identical boxes of tea leaves.
17) Miss Lanny borrowed $78000 from a bank to buy a car. She paid an interest of 3.4% to the bank in the first year. How much interest did she have to pay per month in that year?
18) Sharon bought laptop which cost $2128 before a 15% discount. In addition, she had to pay 7% GST after the discount. How much did she pay for the laptop? Correct your answer to 2 decimal places.
19) During a sale, 20% discount was given for all items. a.The discounted price of a wardrobe, inclusive of 7% GST, was $1391. Find the original price of the wardrobe, excluding GST. b. If Mrs Shanta bought a dining table with an original price of $499.
20) During a sale, notebooks were sold at a 20% discount. Nat wanted to buy 20 notebooks but was short of $26.20. After borrowing $6.36 from his mother, he had enough to buy exactly 12 notebooks. a.What is the usual price of the notebook?
21) Desmond went for dinner with his 4 friends at a restaurant. They each ordered set meals of the same price and the dinner cost $200. In addition, they had to pay 10% service charge and a 5% tax on top of that. a.How much did they each pay for dinner?
22. There were a total of 90 apples and oranges in a basket. There were 4 times as many apples as oranges. After some apples were removed, there was an equal number of oranges and apples left. How many apples were removed from the basket?
23) A farmer had the same number of sheep, ducks and cows at first. After 75 cows, some sheep and ducks were sold, there were 170 animals left. There were twice as many sheep as ducks left.
24) Hazel had the same number of purple beads, red beads and yellow beads. After giving away 152 yellow beads, some purple beads and red beads, she had 324 beads left. The remaining red beads were three times as many as the remaining purple beads.
25) Yong Hoon baked 240 pineapple tarts and lemon tarts. 40% of them were lemon tarts. He gave away 36 lemon tarts and 2/3 of pineapple tarts to his friends. He then gave some of the remaining pineapple and lemon tarts to his sister.
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FRP - Set C
Fractions, Ratio, Percentage Set C
FREE PREVIEW
1) The price of tickets for a concert is as shown in the table below. [Price per ticket] Pupil [$9.50] Teacher [$15]. A total of 420 tickets were sold. 1/6 of the tickets sold were bought by teachers.
2) The table below shows the entrance fee to enter the Singapore Art Museum. The ratio of the number of adults to the number of children who visited the Museum is 5: 3. How many adults visited the Singapore Art Museum if a total of $6500 was collected?
3) Mrs Tan bought a new bottle of olive oil. She used an equal amount every day to cook her meals. At the end of the 12th day, 1/4 of the bottle was left. At the end of the 13th day, there were 240ml of olive oil left.
4) Sumei had some money. She spent an equal amount of money every day. At the end of the fourth day, she had 2/3 of her money left. At the end of the seventh day, she had $20 left. How much money did she have at first?
5) A calculator cost $15 and a watch cost 3 times as much as a calculator. Jenny bought some calculators and watches for $600. She bought 4 more watches than calculators. How many watches did she buy?
6) Natalie spent $5390 on some bracelets and anklets for her shop. The ratio of the price of a bracelet to the price of an anklet is 4:1. An anklet cost $7. If the number of bracelets bought is 60% of the total number of bracelets and anklets,
7) A box contains chocolate and sweets in the ratio 2: 5. When 36 chocolate are added to the box, there are 60 more sweets than chocolate in the box.
8) Winston has a box of stamps. 23% of the stamps are Singapore stamps. The rest are Malaysia and Australia stamps in the ratio of 6:5. If Winston bought another 28 Malaysia stamps,
9) The total mass of 8 tables and 7 benches is 603 kg. The mass of 2 benches is 8 kg more than the mass of each table. Find the total mass of 1 table and 1 bench.
10) Roy’s coin box contained the same number ten-cent coins and fifty-cent coins. He took out 20 ten-cent coins and exchanged them for fifty-cent coins of the same value and put them back into the coin box.
11) John was sitting for a Mathematics test which consisted of some questions. In the first 20 minutes, he had completed 1/4 of the test.
12) Jared ran 4/5 km during a race. Tim ran thrice of Jared’s distance. Myra ran 2/3 of Tim’s distance. How many kilometres did Myra run? Leave your answer as a mixed number in its simplest form.
13) Andy had 650 stickers. Bernice had 3/5 as many stickers as Andy. Cindy had 150 more stickers than Bernice. How many stickers did they have altogether?
14) Ali had 27 marbles more than Ben. Charles had 2/3 as many marbles as Ali. They had 165 marbles altogether. How many more marbles did Charles have than Ben?
15) Charles, Dawn, Esther and Francis collect stamps. Charles has 80 stamps and Dawn has 160 more stamps that Charles, Esther and Francis have.
16) Ali, Bob and Caden shared 2040 trading cards among themselves. Ali received 1/4 as many trading cards as Bob. Caden received thrice as many trading cards as Bob. How many trading cards did Caden receive?
17) Melvin has 78 more guppies than Rafi. Hui Lin has 4/5 as many guppies as Melvin. Hui Lin has 26 more guppies than Rafi. How many guppies does Rafi have?
18) Aaron, Bala and Charles shared some money. Aaron received 1/3 of the total amount of money. Bala received the same amount of money as the total amount of money received by Aaron and Charles.
19) Anis, Belinda and Carol shared some stickers. The ratio of the total number of stickers received by Belinda and Carol to the number of stickers received by Anis was 3: 4.
20) Jancy, Belle and Linda donated a total of $2150 to a nursing home. Belle donated $226 more than Jancy but $861 less than Linda. How much did Jancy donate?
21) Angeline has $8. Belinda has $12 more than Angeline. Belinda has $6 less than Cindy. Find the ratio of Cindy’s share to Belinda’s share.
22. Sharon and Alex had a number of erasers in the ratio of 3: 1. Sharon and Roy had a number of erasers in the ratio of 4: 5. Sharon, Alex and Roy had a total of 155 erasers altogether. How many more erasers did Roy have than Alex?
23) Melvin has 155 stamps more than Danny. Edward has thrice the total number of stamps that Melvin and Danny have. The 3 boys have 2780 stamps altogether. How many stamp does Melvin have?
24) Alex, Ben and Caleb had some stamps. Alex had 90 stamps more than Ben, and Ben had 10 stamps more than Caleb. After Alex had given Ben 95 of his stamps and Caleb bought some stamps,
25. Alan, Ben, Carl each had some marbles. Ben had 1168 fewer marbles than Alan. After Alan and Ben each gave 355 marbles to Carl, Alan had 5 times as many marbles as Ben. a. How many marbles did Alan have at first? b.
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FRP - Set D
Fractions, Ratio, Percentage Set D
FREE PREVIEW
1) In the class library, 3/5 of the books are fiction books. 2/3 of the remaining books are non-fiction books. The rest are magazines. There are 10 fewer magazines than non-fiction books in the class library. How many fiction books are there altogether?
2) Mrs Tan had a crate of fruits. 3/5 of the fruits in the crate were apples. 1/4 of the remainder fruits in the crate were oranges and the rest were pears. There were 54 more pears than oranges. What was the total number of fruits in the crate?
3) Jessie used some rose syrup, milk and water to make a drink. She used three times as much water as milk to make the drink. The amount of rose syrup used is 2/3 the amount of milk used.
4) A jug is 3/4 filled with water. The amount of water is equal to 5 cups. After 3 cups of water have been poured out from the jug, what fraction of the jug is still filled with water?
5) Mrs Lim had 3 containers of flour. The ratio of the mass of flour in Container A to the mass of flour in Container B to the mass of flour in Container C is 2: 5: 8. Container B contained 600g of flour.
6) At Satay Ria stall, 3/5 of all the satay were chicken satay and the rest were mutton satay. After selling 180 sticks of mutton satay and 5/6 of the chicken satay, there was 2/5 of all the satay left. How many sticks of chicken satay were sold?
7) There are different types of flowers in a vase. 3/10 of the flowers are roses, 2/5 of them are orchids and the rest are sunflowers and lilies. The number of lilies half the number of sunflowers.
8) Joanne had white, purple and yellow beads. The ratio of the number of white beads to the number of purple beads to the number of yellow beads was 3: 5: 6. She had a total of 288 white and purple beads.
9) Mum gave Clare, Dena and Eden some money in the ratio of 3:8:9. Dean used his money to buy a skateboard and a helmet. The cost of a helmet is 5/7 the cost of the skateboard which Dean paid $44 more than the helmet.
10) A company held an annual dinner and the ratio of the number of men to women was 6:7 at first. During the middle of the dinner, 1/3 of men left and 12 more women turned up. Given that the total number of people remained the same,
11) Excel Primary School held a sports carnival and the ratio of the number of girls to boys was 5:9 at first. In the afternoon, the number of girls decreased by 3/15 and 57 more boys turned up.
12) In the morning, Evelyn and Ashley went fishing and Evelyn caught 141 more fish than Ashley. After another 2 hours of fishing after lunch, they each caught another 36 fish and ended their day.
13) Auntie Ann baked 256 muffins for friends during last year’s gathering. The ratio of the number of chocolate muffins to the number of strawberry muffins baked was 3:5.
14) Kimberly and Jennifer made a total of 448 cookies in the morning. In the afternoon, each of them made another 32 cookies each and the total number of cookies made by Jennifer was 5/11 of what Kimberly made.
15) Matilda had some 50¢ and $1 coins in the ratio 3:2. After exchanging 7 $1 coins for 50¢ coins, the ratio of the number of 50¢ coins to $1 coins became 5:1. Find the amount of money Matilda had.
16) There are some frogs and tadpoles in the pond. The number of tadpoles is 4/7 the number of frogs. 24 frogs died and 13 more tadpoles appeared. The ratio of the number of tadpoles to the number of frogs became 5:6.
17) There are thrice as many males as females at the start of the seminar. Halfway through it, 18 males left and 63 females joined in. The number of males is now 20% more than the number of females.
18) At a carnival, 1/3 of the people are children and 1/9 of the people are men. The rest are women. There are 400 women. How many people are there at the carnival?
19) At a theme park, 2/3 of the visitors were children and the rest were adults. 1/( 4) of the adults were men and 3/8 of the children were girls. Given that there were 320 more women than men, how many boys were there at the theme park?
20) At an exhibition, 2/7 of the visitors were children. The ratio of number of men to the number of women then was 3: 7. There were 120 more women than children. What is the total number of visitors at the exhibition?
21) At a seminar, 4/9 of the people are students and the rest are parents. 3/5 of the parents are women and 5/8 of the students are girls. If there are 374 women and girls altogether, how many boys are there at the seminar?
22) In a funfair, 5/6 of the people were children and the rest were adults. 1/3 of the adults were women. 2/3 of the children were girls. If there were 869 women and girls altogether, how many boys were there at the funfair?
23) On a camping trip, 60% of the group were adults and the rest were children. 80% of the children were girls. There were 48 girls. a. How many boys were there? b. How many adults and children were there altogether?
24) At a carnival, the ratio of the number of males to the number of females was 6: 5. There were twice as many girls as women. There were 1/2 as many boys as men. There were 60 more girls than boys. How many people were there at the carnival?
25) In class 5A, there were 1/2 as many girls as boys. In class 5B, there were 1/3 as many boys as girls. The number of boys in class 5B was 2/3 as many as the number of girls in class 5A. There were 32 pupils in class 5B.
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