P6 - Solving Fraction, Ratio, Percentages Word Problems
for Primary 6 students
This course is targeted at Singapore primary school level 6, but is also suitable for primary school level 5 students.
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 5 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.
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P6FRPV1-A - learnbrill
FREE PREVIEW1) 40% of a group of 800 pupils are girls. 30% of the girls have long hair. How many girls have short hair?
2) There were a total of 1080 roses of the tulips were pink. The rest were red roses and tulips. If the total number of pink roses and pink tulips was 200, how many roses were there in the garden?
3) There are blue, red, and pink balls in a box. 40% of the balls are blue. The number of blue balls is 20 more than the number of pink balls. There are 50 red balls. What is the number of pink balls in the box?
4) In Jin’s Bike Shop, 30% of the tires were black and the rest were white. 40% of the black tires and 20% of the white tires were sold. If Jin had 148 tires left in the shop, how many white tires were there at first?
FREE PREVIEW5) The mass of a bottle when it was 14 filled with syrup was 960 g. Mary added more syrup into the bottle to make it 23 full and the mass increased to 1.86kg. Find the mass of the bottle when it is completely filled with syrup.
FREE PREVIEW6) There were 3808 biscuits, cookies and brownies on a tray. If Tim took away 1/3 of the biscuits, 1/3 of the cookies and 2/5 of the brownies, there would be an equal number of each type of snacks left.
7) Salimah bought some roses, tulips and carnations. 1/4 of them were roses, 5/12 of the remainder were tulips and the remaining flowers were carnations. Each rose cost $2.50. Each tulip cost $3 and each carnation cost $1.50.
8) Michelle spends 35% of her salary every month. Her salary for June was 20% more than that of May. As a result, her expenditure in June increased by $175. How much was Michelle’s expenditure in May?
9) Mark was training for a marathon. Each week, he jogged a distance of 10% more than the previous week. He jogged 36.3 km in Week 3. a. What distance did he jog in Week 1? b. What was the total distance Mark jog in 3 weeks?
10) The original selling price of a computer was $2800. A shop sold it at a discount of 20% during a sale. If the shop charged a 7% GST on the discounted price , a. How much was the GST?
11) The bill for a dinner for 4 friends at Sedap Restaurant is shown below. A service charge of 10% was included in the bill before a GST of 7% is added.
12) A store was having a 20% storewide discount. a. If Mrs Chan paid $55 for a blouse, what was the original price of the blouse? b. Mrs Goh wanted to buy a dress that cost $200 originally.
13) On Friday, shirts in a shop were sold at $30 each. On Saturday, a discount was given on all the shirts, and the number of shirts sold increased by 20%.
14) At a sale, Mr Chua bought an electric kettle and a fan at a discount. He paid a total of $105 for these two items. The amount paid for the electric kettle is 2/3 as much as that for the fan. How much did he pay for the fan?
15) 40% of the people who joined a newly opened fitness club were female. After one year, the number of female members decreased by 20% and the number of male members increased by 45%. In the end, the fitness club had 228 more members than a year ago.
16) DIZ Orchestra performed at the concert hall on two evenings. On the first evening, there were 70 more men than women in the audience. On the second evening, the number of men decreased by 10 % and the number of women increased by 20%.
17) Fiona had $480 more than Shixiu. Shixiu gave Fiona 20% of her money. Fiona then gave 75% of her money to Shixiu. In the end, Shixiu had $1892 more than Fiona. How much did Shixiu have at first?
18) Ted had $300 less than Amy. Amy decided to give 1/5 of her money to Ted. Ted gave 1/3 of his money back to Amy. Amy now has $400 more than Ted. How much money did Ted have at first?
19) The table below shows the number of coloured beads that Jane and Dinah had.
20) At first, jolly had 5/8 of the number of stickers Kelly had. When Kelly gave 36 stickers to Jolly, both had the same number of stickers. How many more stickers did Kelly have than Jolly at first? How many stickers were there altogether?
21) Jara used 70 beads to make a bracelet and 75% of her remaining beads to make a necklace. If she had 20% of her original number of beads left, how many beads does she have at first?
22) Jeff spent 1/4 of his salary on an Ipad and2/9 of the remainder on a watch. If he spent $360 on his watch, what was his salary?
23) A fishmonger sold 40% of his salmon at $30 per kg on Saturday. He sold 25% of the remaining salmon on Sunday at a discount of 10%. He collected a total of $1765.50. How much salmon was left after the weekend?
24) Larry read 2/7 of a book in the morning and 2/5 of the remainder in the afternoon. He then read 3/4 of the remaining pages in the evening and found that there were still another 60 unread pages. Find the total number of pages in the book.
25) Ken spent 1/4 of his money and an additional $6 on a number of CDs. He then spent 3/5 of the remaining money and an additional $12 on magazines. Given that he was left with $18, what fraction of his money was spent on magazines?
P6FRPV1-B - learnbrill
FREE PREVIEW1) How many three-fifths are there in 9 wholes?
2) How many times of 1 2/5 is 7?
3) What is the value of 3/a2 when a = 1/2 ?
4) The difference between two numbers is 54. The sum of 1/3 the smaller number and 2/9 the bigger number is 102. Find the sum of the two numbers.
5) A television set sold at $450 incurred a loss of 10%. AT what price had the television set to be sold in order to make a profit of 10%?
6) An MP3 player was sold at $240 after a discount of 20%. This yielded a profit of 20%. What would the profit be if the MP3 player was sold at the original price?
7) Mrs Lee bought a diamond bracelet during a sale. The store was giving a discount of 30%. Mrs Lee, being a regular customer, received an additional 10% member’s discount off the discounted price. She paid $645.75 for the bracelet.
8) A shop gave different discounts at different time of the day. In the morning, Mr Lim bought a sofa for $1050 after a discount of 25%. In the afternoon, Mr Tan bought a similar sofa for $1120. Find the percentage discount given to Mr Tan.
9) At Shop A, Mr Tang bought a laptop for $2400 which was 20% more than the price that Shop B sold it for. a. How much did Shop B sell the laptop at? b. During a sale, both shops offered an equal percentage discount on the same laptop.
10) The number of girls at a camp is 3/7 the number of boys. If there are 210 children at the camp, how many more boys than girls are there?
11) In a toy shop, 46% of the toys are stuffed toys. 5/9 of the remaining toys are toy trains and the rest are toy cars. There are 280 stuffed toys and toy cars. How many toy cars are there in the shop?
12) There were 3220 spectators at a stadium. 3/7 of the male and 3/4 of the female spectators did not wear sunglasses. The number of male spectators who wore sunglasses was the same as the number of female spectators who wore sunglasses.
13. In a train, the ratio of female passengers to male passengers was 5 : 3. When 16 female passengers alighted the train, the new ratio of female passengers to that of male passengers became 11 : 9.
14) There were 369 roses and lilies at a flower shop. After 2/5 of the roses and 3/7 of the lilies were sold, there was an equal number of roses and lilies left. How many roses were left?
15) There are 1023 pupils in Ubi Primary School. 2/3 of the girls and 5/6 of the boys participated in a mass run. A total of 795 pupils took part in the mass run.
16) At a sports carnival, the ratio of the number of pupils sent by School A, School B and School C to the event was 1:2:3, The number of boys from School A and the number of girls from School B were the same.
17) There are 2300 pupils in a school this year and this number is 15% more than the number of students last year. The number of boys is 25% more than that of last year but the number of girls is 25% less than that of last year.
18) Last month, the number of workers in Restaurant A was twice that of Restaurant B. The ratio of the number of male walkers to the number of female walkers in Restaurant A and Restaurant B was 5 : 4 and 2 : 7 respectively.
19) At a concert, 3/8 of the audience were boys, 1/2 of the remaining audience were girls. There were 120 women and the number of men was 2/3 the number of women. How many people were there in the audience?
20) There were 42 people at a party. 8 of them were men and 15 of them were women. The number of women was thrice the number of girls and the remaining were boys. How many males were there at the party?
21) Melissa collected some beads. 20% of them were golden beads. 9/20 of them were silver beads and the rest were bronze beads. There were 300 more bronze beads than golden beads. How many beads did she collect altogether?
22) At a party, there were twice as many boys as adults, thrice as many adults as girls. Every boy was given 12 sweets, every girl was given 26 sweets and the adults were not given any.
23) A group of pupils registered for a mass run conducted by their school. There were 9 fewer pupils in the lower primary than the upper primary who registered for it. 2/3 of all those registered were boys. 3/7 of the lower primary pupils were girls.
24) In a boutique, 40% of the clothing are dresses. 70% of the remainder are skirts and the rest are pants. There are 30 more skirts than dresses. After some dresses are sold, 25% of the remaining clothing in the boutique are dresses.
25) The number of students who do not wear spectacles is 80% of the number of students who wear spectacles. 36% of the students who wear spectacles are girls and 2/5 of the students who do not wear spectacles are boys.
26) There were some people in a school hall attending a talk. 70% of the people were adults. 3/5 of the children were girls. There were 174 more adults than boys.
27) There are roses and carnations altogether. 6/7 of the roses and 5/6 of the carnations are pink. There are 39 pink flowers in total. How many roses are not pink? How many carnations are pink?
P6FRPV1-C - learnbrill
FREE PREVIEW1) Joseph had a collection of toys. He gave half of his toys to his sister and 1/5 of the remaining toys to his brother. If he had 48 toys left, how many toys did he have at first?
2) Shawn spent $120 on a bag and 1/3 of the remaining money on a cap. If he had 2/5 of the original sum of money left, how much money did he have at first?
3) Patrick spent 25% of his savings on a bag and 40% of the remainder on a pair of shorts. He was left with $135. How much savings did Patrick have at first?
4) Mrs Gupta spent $8 more than 1/5 of her original amount of money on a book. She then spent $4 more than 3/4 of her remaining money on stationery. Given that Mrs Gupta had $12 left, how much did the book cost?
5) Mr Koh had some money. He spent 1/5 of it on a watch and 3/8 of the remainder on a golf set. The amount of money left was $1492 more than the golf set.
6) I have $495 in the form of dollar notes. 1/6 of them are $2 notes and 1/10 of the remainder are $5 notes. The rest are $10 notes. How many $10 notes do I have?
7) Shirley weights 30% more than Alice. If Shirley weighs 6 kg more than Alice, what is their average weight?
8) Kaden is 6 times as old as John. Haikal is 2/3 the age of Kaden. What fraction of Haikal’s age is John’s age?
9) 1/4 of Abdullah’s age is equal to 2/3 of Hussein’s age. The ratio of Hussein’s age to Siti’s age is 2 : 3. Abdullah is 42 years older than Siti. How old is Hussein?
10) Aysha has 1/2 as much money as Keira. Keira has 1/2 as much money as Hairul. What is the ratio of Hairul’s money to Keira’s money to Aysha’s money? How much more money does Hairul have than Aysha if Hairul has $792?
11) Ronn’s savings was 2/7 that of Wayne’s savings in January. In February, Ronn saved another $37 and Wayne saved another $82. Wayne’s savings then became thrice that of Ronn’s. What was Wayne’s savings at the end of February?
12) Alice’s salary was 45% less than Bella’s salary at first. After Alice spent $668 and Bella spent $752, Bella had 4 times as much left as Alice. What was the sum of their salaries?
13) Sally had 3/4 as much money as Zoey. Sally and Zoey shared the cost of a present in the ratio 2 : 3 respectively. Sally used 50% of her money to pay for her share. Zoey had $84 left after paying for her share.
14) A shopkeeper has some $2 notes and $5 notes in his cash register. At first, he had 2/7 as many $5 notes as $2 notes. After exchanging 10 of the $2 notes for $5 notes, he had 2/5 as many $5 notes as $2 notes.
15) Gerald had some green and yellow beads. The number of green beads was 1/3 the number of yellow beads. He gave each of his friends 2 green beads and 3 yellow beads. He then had 42 green beads and 270 yellow beads left.
16) At a fruit stall, the number of watermelons was 3/5 of the number of pineapples. In the morning, 1/3 of the watermelons and 1/3 of the pineapples were sold. In the afternoon, 8 watermelons and 8 pineapples were sold.
17) At first, Frank had 7/12 of the number of cards Gary had. Then, Gary gave Frank 70 cards and both had the same number of cards
18) Alice, Beth and Charles shared a sum of money. Alice received 4/9 of what Beth received. Charles received 2/3 as much as Beth. Beth gave $420 to Alice and another sum of money to Charles. As a result, all the three had the same amount of money.
19. Mel, Nancy and Omega shared some shiny cards. Mel had one-third of what Nancy and Omega had. Nancy had one-fifth of what Mel and Omega had. Mel had 32 fewer shiny cards then Omega. a. What is the ratio of shiny cards between Mel, Nancy and Omega?
20) A sum of $2345 was distributed to Aaron, Bill and Cavin. 1/2 of Aaron’s share was 1/3 of Bill’s share. 1/4 of Bill’s share was 1/5 of Cavin’s share. What was the ratio of Aaron’s share to Bill’s share to Cavin’s share? How much did Bill get?
21) 4/5 of David’s cards is equal to 2 1/2 of Ali’s cards. When David lost 400 cards and Ali bought another 75 cards, the ratio of David’s cards to Ali’s cards became 5:3. How many cards did David have at first?
22) At first, Huimin had only ten-dollar notes and Jim had only two-dollar notes. The number of notes Huimin had was 2/3 the number of notes Jim had. After Huimin gave Jim $3600, the number of notes Huimin had became 1/6 the number of notes Jim had.
23) 4 poles of different lengths were found in a park. The length of pole A is 1/8 of the total length of poles B, C and D. The length of pole B is 2/3 of the total length of poles C and D. The length of pole C is 1/5 of the length of pole D.
P6FRPV1-D - learnbrill
1) The pie chart represents the number fruits sold at a fruit stall. 650 apples were sold. How many oranges were sold?
2) The pie chart below shows the number of different coloured beads Jenny bought. Jenny bought 57 more blue beads than green beads. How many beads did Jenny buy altogether?
3) The pie chart shows the different nationalities of tourists at the River Safari on a particular day. If there are 135 Korean tourists, how many European and Indian tourists are there altogether?
4) The pie chart below shows the amount of money collected from the sales of different types of items in a supermarket in a week.
5) Some people participated in a survey to select their favourite of ice-cream flavour. The pie chart below shows the results of the survey. The ratio of the number of people who prefer vanilla to chocolate flavour is 1 : 3.
6) The bar graph below shows the number of food items sold at a carnival.
7) The graph below shows the number of cars sold from July to December.
8) The table below shows Mrs Lau’s expenditure on groceries and transportation from January to May in a year. a. In which month was the expenditure on groceries 150% of that in May?
9) There were some pies and cakes for sale in a pastry shop. 1/4 of the pastries were pies. The pastry chef then baked an equal number of pies.
10) On a farm, the number of cows was 4/5 the number of goats. After some goat were sold, the number of goats decreased by 60% and there were 360 cows and goats left. How many goats were sold?
11. The ratio of the mass of sugar in packet A to the mass of sugar in packet B is 5 : 6. After the mass of sugar in packet A is increased by 30%, by what percentage must the mass of sugar in packet B be decreased
12) In a factory, the first batch of toy cars and toy bears were produced in the ratio 5: 8. In the second batch of production, the number of toy bears produced increased by 40%. If 455 toys were produced during the first batch,
13) The ratio of Anna’s salary to Ben’s salary to Colin’s salary is 4 : 7 : 10. If Anna’s salary is increased by 20% and Ben’s salary is reduced by 20%, the new total salary is $5100. Find the total salary of the three children.
14) Last year, there were 120 pupils in the computer club. 40% of the pupils were boys. Some boys joined the computer club this year. The percentage of the pupils who are boys has increased to 52%. How many boys joined the computer club this year?
15) Mr Ng earned a fixed monthly salary last year. He spent 25% of his salary in November. In December, he spent 50% less than what he spent in November.
16) Aishah had a collection of coins from Malaysia, India and China. She had 248 from Malaysia. 30% of her coins were from India. She had 24 fewer coins from China than from India. a. What was the total number of coins in Aishah’s collection?
17) Mr Lin always saves 30% of his monthly salary. When his salary increased by 10%, his savings increased by $189. Find Mr Lin’s salary before the increase.
18) Mrs. Chan baked chocolate, strawberry and vanilla puffs. She baked 132 chocolate puffs. 35% of her puffs were strawberry puffs. She baked 12 more vanilla puffs than strawberry puffs.
19) 35% of the marbles in a box are blue. The rest of the marbles are green, red and black in the ratio of 3 : 5 : 4. There are 78 more red marbles than green marbles. How many marbles are in the box altogether?
20) Stella bought some red, yellow and white bows. The ratio of the number of red bows to the number of yellow bows was 4 : 1. The ratio of the number of red bows to the number of white bows was 5 : 2. If there were 165 more red bows than yellow bows,
21) In a basket, there were balls of three different sizes: large, medium and small. 2/3 of the balls were large, 1/5 of the balls were medium and the rest were small. There were 128 more large balls than small balls. How many small balls were there?
22) Last month, the number of supervisors was 3/14 of the number of workers in a factory. This month, the company employed 12 more supervisors and 42 more workers. As a result, the number of supervisors became 25% of the number of workers.
23) Sally had some money at first and she spent 1/7 of her money on a wallet. She spent the rest of the money on 2 chairs and a fan. The 2 chairs cost $491 more than the wallet. The fan cost $97 more than the wallet. How much did the fan cost?
24) Lili, Ariel, Elsa and Kolette bought a present for Mr Kumar. Lili paid 1/5 of the total amount paid by Ariel, Elsa and Kolette. Finally, Lili and Ariel paid $84 altogether while Elsa paid 20% more than Kolette.
25) A train left the terminal with some passengers. At Station A, 1/3 of them alighted and 50 others boarded the train. At Station B, 114 passengers alighted and 15 passengers boarded the train. Then,
26) Mr Lee had some apples and Mangoes. On Day 1, he sold 136 mangoes and threw away 30 rotten ones. Three-quarters of the mangoes were left. On Day 2, he sold three-fifths of the apples.
27) Charlotte and Su Ying had a total of 864 tokens. Charlotte lost 2/5 of her tokens to Su Ying and then Su Ying lost 1/4 of the total number of tokens she had to Charlotte.
P6FRPV1-E - learnbrill
1) The ratio of Ken’s savings to Belle’s savings is 2 : 3. After each of them had spent $18 on food, Ken has 3/5 as much money as Belle. Find their total savings at the end.
2) Sally and Dahua had some stamps in the ratio of 5 : 6. After Sally gave away 20 stamps and Dahua bought 32 stamps, the ratio became 3 : 5. How many stamps did Sally have at first?
3) Bee Heng spent 1/4 of his money and Calvin spent 1/6 of his money. They had the same amount of money left. If Bee Heng has $36 more than Calvin at first, how much does Calvin have at first?
4) Ann and Susan went for a dinner. Ann paid 25% of the bill and Susan paid the rest. After paying for the dinner, Susan had 1/4 of her money left and Ann had $63 left.
5) Mr Ng had a total of 150 red pens and blue pens. After he bought another 50 more red pens and gave away 1/3 of his blue pens, he had the same number of red pens and blue pens lefts.
6) Mary and Jane each had a sticker album. After Jane gave away 30% of her stickers and Mary lost 25% of her stickers, they had the same number of stickers left. If Jane had 6 more stickers than Mary at first,
7) Jane and Iris had 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris and was left with twice as many sweets as Iris. How many sweets did Iris give away?
8) Mrs Bala had a total of 128 apples, oranges and mangoes in the ratio of 7 : 5 : 4 respectively. After she gave away some apples and 15 mangoes, the ratio of the number of oranges to the total number of fruits left became 1 : 2.
9) Justina had 72 more Singapore stamps than Malaysian stamps. She gave away some Singapore and Malaysian stamps. The number of Singapore stamps she gave away was 3/4 of the number of Malaysian stamps she had at first.
10) There were 156 more silver balloons than gold balloons at a party. After 5/6 of the silver balloons and 3/4 of the gold balloons burst, there were 106 balloons left. How many balloons were there altogether at first?
11) Jason and Eileen had a total of 255 goldfish. After Jason gave away 1/4 of his goldfish and Eileen gave away 34 of hers, the ratio of the number of goldfish Jason had left to that of Eileen’s became 1:3.
12) Alex and Benson each have some stickers. If Alex used 12 stickers, Benson would have half as many stickers as Alex. If Benson used 18 stickers, Alex would have 5 times as many stickers as Benson. How many stickers did they have altogether?
13) Edison is reading a novel. The ratio of the number of pages he has read to the number of pages he has not read is 3 : 8. If he reads another 182 pages, the number of pages he has read will become 70% of the number of pages he has not read.
14) At a conference, when 10 women left for the washroom, the ratio of the number of men to the number of women that remained became 1 : 1. If 10 men were to leave for the washroom instead,
15) Janice and Marissa had some money. If Janice spends $40 per day and Marissa spends $80 per day, Marissa would have $500 left by the time Janice spends all her money. If Janice spends $80 per day and Marissa spends $40 per day,
16) A fruit seller has some apples and pears. If he sells twice as many pears as the apples, he would have 207 apples left when all the pears are sold. If he sells twice as many apples as the pears,
17) Two groups of people, A and B are working on a project. If 18 people move from group A to group B, then group B will have 3 more people than group A. If we take away 18 people from both groups,
18) Maxie had, 1900 ml more fruit juice than Nick. After Maxie gave Nick 500 ml. of fruit juice, the ratio of Maxie's juice to Nick's juice became 5: 2. How much fruit juice did Maxie have at first?
19) The ratio of Charlie’s stickers to Mary’s stickers was 7:4 at first. If Charlie gives 1/3 of his stickers to Mary, what will be the ratio of Charlie’s stickers to Mary’s stickers in the end?
20) Douglas had some stamps. He sold 2/7 of the stamps and then gave 162 stamps to his best friend. He was left with 1/5 of the stamps he had at first. How many stamps did Douglas have at first?
21) Mrs Tan’s ribbon was 300 m longer than Mrs Ng’s. When Mrs Ng gave 120m of her ribbon to Mrs Tan, the length of Mrs Ng’s ribbon became 1/5 of the length of Mrs Tan’s ribbon. Find the length of Mrs Ng’s ribbon at first.
22) The number of toy cars Keith had was 1/5 the number of paper aeroplanes. After he gave 1/2 of his paper aeroplanes and 1/3 of his toy cars to his brother, he had 286 more paper aeroplanes than toy cars.
23) At first, Jane had 160 more beads than Olivia. Jane first gave 25% of her beads to Olivia, and then Olivia gave 60% of her beads to Jane. In the end, Jane had 200 more beads than Olivia. How many beads did Jane have at first?
24) Four children, Angela, Belinda, Christobel and Dorothy shared $450. Angela received 1/2 of the total amount of money received by Belinda, Christobel and Dorothy. Belinda received 4/11 of the total amount of money received by Angela,
25) Mark and Tina shared some stickers. Mark gave 25% of his stickers to Tina. Then Tina gave 50% of her stickers to Mark. In the end, the ratio of the number of stickers Mark had to the number of stickers Tina had was 14 : 5.
26) Joy and Ken earned $7960 altogether. Joy earned $600 less than Ken. Joy gave 4 times as much money as the amount Ken gave to their mother. Then Ken had twice the amount of money that Joy had left.
27) Jake had some gold coins and gave one-third to Clubby. Clubby had some silver coins and gave one-third to Jake. Jake lost 64 of his gold coins, while Clubby lost 52 of his silver coins. After that,