ISTITUTO COMPRENSIVO “ G. FALCONE – CATULLO” di Pomigliano d’Arco (Na)

Question

Here is a list of ingredients to make a potato soup

for four people:

200 g potatoes

2 onions

40 g butter

200 ml stock

Work out how much stock is needed to make a

potato soup for 14 people.

Givens

potatoes = 200 g

onions = 2

butter = 40 g

stock = 200 ml

Request

stock to prepare a soup

for 14 people= ?

stock = (200 ml : 4) x 14

stock = 50 ml x 14

stock = 350 ml

Answer

350 ml stock is needed to prepare a potato soup

for 14 people.

Question

William and Edward share 28 marbles in the ratio

of 2/5. Work out how many marbles Edward

gets.

I refer William’s marbles to segment AB and

Edward’s marbles to segment CD.

u u

A B

u u u u u

C D

u u u u u u u

A B C D

Givens

AB + CD = 28 marbles

AB = 2/5 CD

Request

AB = ? CD = ?

U =( AB + CD ) : 7

U = 28 : 7 = 4

William’s marbles = 2 x 4 = 8

Edward’s marbles = 5 x 4 = 20

Answer

William gets 8 marbles and Edward gets 20

marbles.

QUICK TEST

The ratio 6 : 18 full simplified is 1/3. True or

false?

6/18 = 3/9 = 1/3 TRUE

27.00 £ is divided in the ratio of 4/5. How

much is the share?

27.000 £ : 5 = £ 5.400

5.400 £ x 4 = £ 21.600

657 x 0,02 = 13,14. True or false? TRUE

Arrange these decimal in order of size :

6,37 – 6,49 – 6,04 – 6,371 – 6,27

6,04 – 6,27 – 6,37 – 6,371 – 6,49

EXERCISE

Work out the following power and extraction of

root:

√64 = √26= 26:2 = 23 = 8

√81 = √34 = 34:2= 32 = 9

√169 = √132 = 132:2=13

52 = 5 x 5 = 25

43 = 4 x 4 x 4 = 64

3√729 = 3√36 = 36:3 = 32 = 9

Question

362 pupils are going on a trip. A coach can seat 48

people. Work out how many coaches are needed

and how many seats are empty in the final coach.

Givens

pupils = 362

a coach = 48 seats

Request

coaches needed= ?

seats empty= ?

coach needed = 362 : 48 ≅ 8

total seats = 48 x 8 = 384

seats empty = total seats – pupils

seats empty = 384 – 362 = 22

Answer

The coaches needed are 8 and the seats empty

are 22.

Question

A train carriage can hold 126 people. If a train has

13 carriages , how many people can it hold?

Givens

a train carriage = 126

a train = 13 carriages

Request

people in the train= ?

people in a train = 126 x 13

people in a train = 1638

Answer

It can hold 1638 people.

Question

It takes Katie 25 minutes to walk to school. What

time must she leave home in order to arrive at

school at 8:50 am ?

Givens

Katie = 25m to walk to school

Request

time she must leave home=?

Time Katie must leave home = (8:50m – 0:25m) =

=8:25 m

Answer

Katie must leave home at 8:25 a.m.

Question

A garden centre buys 248 trees paying £ 68 for a

each tree. How much do they spend?

Givens

trees = 248

cost = £ 68 for a tree

Request

total cost= ?

total cost = 248 x £ 68

total cost = £ 16.864

Answer

A garden centre spends £ 16864.

Question

John’s mobile phone package includes 500

minutes and 350 text messages a month.

In February, he used 4/5 of his inclusive minutes

and 3/7 of his message allowance.

a ) How many of his inclusive minutes didn’t John

use in February?

b) How many text messages did John send?

Givens

total package = 500 minutes

and 350 text messages

minutes used = 4/5 x 500 m

ext messages allowanced= 3/7 x 350

Request

minutes not used= ? text message sent=?

minutes used = 4/5 x 500m =(500m : 5) x 4 =

= 100m x 4 = 400m

minutes Not used = 500m – 400m = 100m

text messages sent = 3/7 x 350 =(350 : 7) x 3

= 50 x 3 = 150

Answer

John didn’t use 100 minutes.

John sent 150 text message.

EXERCISE

Write the following in the index notation:

a) 6 x 6 x 6 x 6 x 6 = 65 = 7.776

b) 2 x 2 x 2 x 2 x 2 x 2 = 26 = 64

c) 8 x 8 x 8 x 8 = 84 = 4.096

QUICK TEST

Place each of these sets of decimals in order of

size, the smallest first :

a ) 4,26 – 4,31 – 4,09 – 4,29 – 4,293 – 4,02

4,06 – 4,09 – 4,26 – 4,29 – 4,293 – 4,31

b) 8,73 – 8,48 – 8,429 – 8,475 – 8,481 – 8,427

8,427 – 8,429 – 8,475 – 8,48 – 8,481 – 8,73

c) 6,92 – 6,915 – 6,902 – 6,926 – 6,925 – 6,931

6,902 – 6,915 – 6,92 – 6,925 – 6,926 – 6,931

Question

The scale of a map is 1:100.000. Work out the

real distance that 7,2 cm on the map represents.

Givens

scale of a map= 1 : 100.000

graphic distance= 7,2 cm

Request

real distance= ?

real distance = graphic distance x denominator

scale

real distance = 7,2 cm x 100.000 = 720.000 cm

Answer

The real distance is 720.000 cm.

EXERCISE

Find…

a) 2/3 of 30 ml = (30 ml : 3) x 2 =

= 10 ml x 2 = 20 ml

b) 5/7 of 49 Kg = (49 Kg : 7) x 2 =

= 7 Kg x 2 = 14 Kg

c) 3/8 of £ 40 = ( £ 40 : 8) x 3 =

= £ 5 x 3 = £ 15

d) 7/12 of 1200 Kg = (1200 : 12) x 7 =

= 100 Kg x 7 = 700 Kg

e) 8/9 of £ 81 = ( £ 81 : 9) x 8 =

= £ 9 x 8 = £ 72

f) 7/10 of £ 640 = ( £ 640 : 10) X 7 =

= £ 64 x 7 = £ 448

QUICK TEST

The following distances were thrown in a javelin

competition. Arrange the distances in order of

size, the smallest first:

7,37 m – 12,63 m – 12,06 m – 12,39 m – 12,41 m –

12,04 m

7,37 m – 12,04 m – 12,06 m – 12,39 m – 12,41 m –

12,63 m

Question

Reece spends 25 minutes doing Maths

homework, 38 minutes doing English homework

and 42 minutes doing piano practice. How long

does Reece spend in total doing his homework

and piano practice?

Givens

time spent for Maths homework = 25 m

time spent for English homework= 38 m

time spent for piano practice= 42 m

Request

How much time does he spend for her homework = ?

total time = ( 25 + 38 + 42 )m = 105m = 1h 45m

Answer

Reece spends in total 1h45m.

Question

There are 1200 students in a school. 2/5 of these

students eat school lunches. Work out how many

students eat school lunches.

Givens

Students = 1.200

students that eat school lunches = 2/5x 1200

Request

students that eat school lunches = ?

students that eat school lunches = 2/5 x 1200 =

= (1200 : 5) x 2 = 240 x 2 = 480

Answer

There are 480 students that eat school lunches.

Question

A car drives steadily for 8 hours covering 304

miles.

a ) How far does the car travel after 6 hours?

b) How far does the car travel after 11 hours?

Givens

a car drives for 8 h = 304 miles

Request

miles covered after 6 h = ?

miles covered after 11 h = ?

after 6 h = (304 miles : 8) x 6 = 36 miles x 6 =

= 228 miles

after 11 h =(304 miles: 8)x 11 = 38 miles x 11 =

= 418 miles

Answer

After 6 hours the car covers 228 miles.

After 11 hours the car covers 418 miles.

Question

Calculating with ratio. George won £ 85.000 in

the lottery and decided to share it between

Samuel and Thomas in the ratio of 2:3. How

much do Thomas and Samuel receive?

Givens

George = £ 85.000

Samuel= 2/3 Thomas

Request

Money received = ?

u u

A B

u u u

C D

u u u u u

A B C D

I refer Samuel’s money to segment AB and Thomas’s money to segment CD.

Samuel = (£ 85.000 : 5) x 2 = £ 17.000 x 2 =

= £ 34.000

Thomas = (£ 85.000 : 5 ) x 3 = £ 17.000 x 3 =

= £ 51.000

Answer

Samuel receives £ 34.000 and Thomas receives £

51.000.

Question

6 water bottles cost £ 6,90. How much do 11

water bottles cost ?

Givens

6 water bottles = 6,90 £

Request

cost of 11 water bottles = ?

1 water bottle costs = £ 6,90 : 6 = £ 1,15

11 water bottles cost = £ 1,15 : 11 = £ 12,65

Answer

11 water bottles cost £ 12,65.

Question

A garden buys 174 bags of bulbs at 79p for a bag.

How much is the total cost of the bulbs?

Givens

bags of bulbs = 174

1 bag = 79p

Request

total cost = ?

Total cost = 174 x 79p = £ 13.746

Answer

The total cost of the bulbs is £ 13.746.

Expressions

1. 7 x (5 - 3) = 2. (27 - 52) x 2 =

= 7 x 2 = = (27 - 25) x 2 =

= 14 = 2 x 2 =

= 4

3. (15 x 2) : ( 2 x 3) = 4. 20 : (7 - 3) =

= 30 : 6 = = 20 : 4 =

= 5 = 5

EXERCISE

Find the HCF and the LCM of :

a) 42 and 20

b) 16 and 36

a) 42 = 2 x 3 x 7

20 = 2 x 2 x 5

LCM= 22 x 5 x 3 x 7 = 4 x 5 x 3 x 7 = 420

HCF = 2

b) 16 = 24

36 = 22 x 32

LMC= 24 x 32 = 16 x 9 = 144

HCF= 22 = 4

Question

Rupinder gets £ 10 pocket money for a week.

She spends 3/5 of her pocket money on

magazines. How much does Rupinder spend on

magazines each week?

Givens

pocket money for a week = £ 10

expense on magazines = 3/5 of £ 10

Request

money spent on magazines each week = ?

Rupinder spends = 3/5 x £10 = (£10 : 5 ) x 3

= £2 x 3 = £ 6

Answer

She spends £ 6 on magazines each week.

Skill Practice

An architect is designing a play area. 1/5 of the

area will be a children’s playground 3/10 of the

area will be a swimming pool. How much of the

area has the architect used and how much has he

left?

Givens

area for children’s playground = 1/5 of total area

area for swimming pool = 3/10 of total area

Request

area used by the architect = ?

area left = ?

Area used = + = = = total area

Area left = total area

Answer

The architect has used of total area and he has

left of the total area.

This work has been produced by Lorena and Fatima

Classe 2^D

-Plesso Catullo-