Ratio and Proportion

Ratio and Proportion:

Work out the following:

1. Share £35 in the ratio of 3:2
2. Share £156 in the ratio of 5:1
3. Share £1800 in the ratio of 7:2
4. Share £684 in the ratio of 5:4
5. Share £560 in the ratio of 5:3

1. Write 24:48 in ts simplest form.
2. Write 17:51 in its simplest form.
3. Write 78:390 in its simplest form
4. Flower bouquets were made with daisies and carnations. In total, 56 daisies and 84 carnations were used. What is the ratio of daisies to carnations?

5.  Lulu and Tom are sharing a packet of sweets in a ratio of 1:5. If there were 60 sweets in the packet, how many sweets would Tom get?

6. Green paint is made from tins of blue and yellow paint. To make 1 bucket of green paint you need 2 tins of blue paint and 5 tins of yellow paint  How many tins of blue paint is needed to make 5 buckets of green paint?

7. 50 children were swimming in a pool.  4 out of every 10 children were boys. How many girls were swimming in the pool?

8. 28 passengers were travelling in a coach. There was 1 child for every 3 adults. How many children were there in the coach?

9. Sam went for strawberry picking and picked 56 strawberries. 1 out of every 8 strawberries was spoiled. How many strawberries were spoiled?

10. Citrus punch is made by adding 350 ml orange juice and 150 ml lemonade. How much lemonade do you need to make 5 litres of citrus punch?

Rounding up and Money Problems

Round up the following numbers to the nearest 10 and 100:

1)  343                    6)  573              11)  1001

2)  708                    7)  499              12)  2347

3)  528                    8)  189              13)  7699

4)  479                    9)  653              14)  4441

5)  276                   10)  849             15)  6056

Write the following amounts of money as decimals:

1) 3 pounds and 45 pence          6) 100 pounds and 50 pence

2) 46 pounds and 7 pence          7) 54 pounds and  49 pence

3) 73 pounds and 9 pence          8) 80 pounds and 0 pence

4)  12 pounds and 90 pence       9) 69 pounds and 99 pence

5) 103 pounds and 5 pence       10) 39 pounds and 1 pence

Convert the pence to pounds (and pence):

After you finish these questions, explain how you worked the answers out and what operation you used:

1)  534 pence               6) 65 pence               11) 4008  pence

2)  709 pence               7) 330 pence             12) 6900 pence

3)  1450 pence             8) 403 pence             13) 7805 pence

4)  5699 pence             9) 760 pence             14) 4503 pence

5)  6740 pence            10) 999 pence            15) 6000 pence

Work out:

1. A pair of trainers cost £53. It was on sale for 1/2 off. How much will it cost now?

2. John had £9 to spend in his school trip. He spent 1/4 of his money to buy an ice-cream.

How much did he have after buying the ice cream?

3. Selena gets £12 pocket money every week. She decides to save 2/3 of the pocket money every week. How much will she save in 10 weeks?

4. John, James and Joe are brothers. They have a piggy bank (common for all of them). John puts £1.10, James puts 65p and Joe puts 75p in it every week. How much money will be there in the piggy in 20 weeks?

5. 4 lollipops cost £2.50. How much will 10 lollipops cost?

  

Word Problems

Read the questions carefully, understand what is being asked and work them out.

Show your working out clearly.

1. 9 Litres of juice cost £27. How much does 1 Litre cost? 
2. Jack ran 5475m in 15 minutes. How many metres did he run in 1 min? 
3. Jan buys soft toys for £25. 1 Soft toy cost £2.50.How many soft toys does he buy? 
4. One lollipop costs 15p. How many lollipops can be bought for £3? 
5. 5 Birds can fit in one bird cage. How many cages do you need for 175 birds? 
6. One egg costs 35p. How many eggs can be bought for £7? 
7. 1 adult ticket for a trip to London from Manchester cost £45. 1 Child ticket costs 1/2 of the adult ticket. What is the cost of the tickets for family of 2 adults and 2 kids?
8. Emily is 32 years old. Her son is 1/4th of her age. How old is Emily's son?
9. Jessie wants to save £30 to buy her favourite video game. If she saves £1.50 a week, after how many weeks will she be able to buy the game?
10. A juice bottle holds 5 litres of apple juice. How many 250ml cups can be filled from the bottle?.

Fractions - Simple word problems

Word Problems:

Read the problems carefully. Show you working out clearly.

1. John bought a pizza. He cut it into 8 equal pieces. He ate 2 pieces and gave his friend 2 pieces. What fraction of the pizza is left? (Give the answer in the simplest form).

2. Maria had a box of chocolates. 1/6 of the chocolates had nuts in them. What fraction of the chocolates did not have nuts?

3. Year 3 had 90 children. 1/3 were girls.
What fraction of them were boys?
How many were girls?
How many were boys?

4. Year 5 had 84 children. 1/7 of them brought packed lunch.
How many children brought packed lunch?
What fraction of the children ate school dinner?
How many children ate school dinner?

5. Year 6 had 96 children. 1/6 of them did not hand in them homework on time.
How many children did not hand in their homework on time?
What fraction of the children handed in their homework on time?
How many children handed in their homework on time?

6. 50 children were swimming in a pool. 20 children were not wearing hats.
What fraction of the children were not wearing hats?
What fraction of the children were wearing hats?

7. 150 passengers were travelling in a double decker bus. 100 passengers were sitting in the lower deck. What fraction of the passengers were sitting in the lower deck? What fraction were sitting in the upper deck?

8. Jack had 168 marbles. He gave 1/4 of the marbles to John and another 1/4 to James. What fraction of the marbles would have John now?

9. Peter has 180. 1/4 were red. 1/2 were blue. Rest were green.
What fraction of the marbles were green?
How many marbles were green?

10. Jessica had 10 plants in her garden. 1/5 of them had red flowers. 2/5 of them had yellow flowers. Rest had pink flowers.
What fraction of the plants had pink flowers?
How many plants had pink flowers?

Decimals

Ordering Decimals: (from the smallest to the biggest)

1.  0.7,   0.65,   0.43,  1.2,  0.09
2. 1.2,   1.03,   1.24,  1.09,  0.74
3. 6.3,   6.03,   3.6,   3.06,   3.66
4. 1.39,  2.96,  1.9,   2.6,    2.06
5. 4.04,  4.4,   4.44,  4.14,  4.64
6. 25.5,  2.55,  20.5,  2.05,  21.5
7. 7.3, 7.32,  4.3,   4.23,   4.32
8. 2.65,  2.5,  2.6,  6.25,  5.62
9. 8.9,  2.8,  2.89,  2.98,  9.28
10. 1.67,  1.7, 1.67, 7.16,  6.17

 Use the three numbers and make the smallest and the biggest numbers possible:

Example: 1, 2,  3

Smallest number: 1.23

Biggest number:  32.1

1.    8,  0,  4
2.    4,  5,  1
3.    8,  2,  3
4.    5,  6,  4
5.    7,  2.  3

Fill in the blanks:

1.  1.5  +  ________ =   2.5

2.  3.25 +  0.75  =  _________

3.  1.25  +  1.25  =  ________

4.   4   -    0.5  =  _____

5.   1.2   -  0.4  =  _______

6.  5  - 0.2 =  _________

7.  5.4  +  3.6  = _________

Word Problems:

1. Find the difference between  23.93 and  14.5

2. Tommy's pet dog gave birth to three puppies. The first puppy weighed 1.23 kg. The second puppy weighed  1.2 kg. The third puppy weighed 1.3 kg. How much did the puppies weigh in total?

3. Cakes cost £1.42 each. Maria buys 4 cakes.
a)How much does Maria spend?
b)How much change will she get if she pays with a £10 note?

4. The hedge around Brian's home was 89.45 cm tall. His dad cut 12.25 cm off it. How tall is the hedge now?

5. John buys a jacket for £39.99, a pair of shoes for 29.99 and a watch for 19.99.
a)How much does he spend in total?
b) If he pays with two £50 notes, what will he get?

6. Kate's wants to buy a toy that costs £25. If she saves £2.50 a week, after how many weeks can she buy the toy?

7. A juice bottle holds 3.5 litres. Emma and her family drink 1.25 litres of juice for breakfast. How much juice is left in the bottle?