Mathematics P5 & P6

By : NICCO ALYSSHA PARIKH

INTERNAL TRANSFER MORE THAN LESS THAN / TOTAL UNCHANGED

There were two groups of students at a gathering . Group1 had 22 more students than group 2 . When 5 students from group 2 joined group 1 , the number of students in group 1 was thrice the number of students in group 2 . How many students were there in group 1 at first ?

Group 1

Group 2

1unit

1unit

5

-5

22 +5

Therefore 2 units 22+5+5=32 1 unit 32/2 = 16

Number of students in Group 1 at first 1 unit+5+2216+27=43

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DIFFERENCE UNCHANGED Mrs Lim is 32 years old and her son 5. In how many years’

time will she be four times her son’s age ?

Mrs Lim Son Age difference(27) 1U

Therefore 3 units 27 years 1 unit 27/3=9 1 unit 9 Number of years : 9-5= 4 years’ time #

MULTIPLICATION OF VALUE AND UNITS Mdm Tan had a total of $360 , consisting of $10 and $2 notes . Given

that she had four times as many $2 notes as $10 notes , how many notes did she have?

NUMBER OF NOTES X VALUE OF EACH NOTE TOTAL$(U)$10 notes 1 UNIT X $10 = $10 UNITS $2 notes 4 UNITS X $ 2 = $ 8 UNITS

Total amount $10 + $8 = $18 UNITS $18 UNITS $360 1 UNIT $360/$18 = 20 NOTES

TOTAL NUMBER OF NOTES : 5 UNITS 5X20 = 100 PIECES #

PART-WHOLE RELATIONSHIP (TYPE 1)David spent ¼ of his money on a pack of cards . He spent 1/3 of the remaining

money on a pencil case . a) What fraction of his money was left ?b) If he spent $9 on the pencil case , how much money did David have at first ?

1unit – cards

Pencil case

Remainder

a) Fraction of money left 2/4 = ½

b) 1unit $9 Amount of money he had at first 4 units 4units x 9 = $36

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PART-WHOLE RELATIONSHIP (TYPE 2 )Caroline spent $75 of her money on a number of CDs.She spent ¼ of the remaining money on a number of Batteries . Given that she was left with 1/3 of the original sum of money , how much

money did Caroline have at first ?

$75 1 unit

2/3 of Total

Remainder

1/3 of total

Since 1/3 of Total 3 units or 3 boxes 2/3 of Total 6 units or 6 boxes

Therefore the remaining 5 units $75 1 unit $75/5 =$15

Amount of money Caroline had at first 9 units 9 x $15 = $135 #

PART-WHOLE RELATIONSHIP (TYPE 3)Hanson spent ¼ of his money and an additional $3 on a number of CDs . He then

spent 3/5 of the remaining money and an additional $6 on a number of batteries. Given that h was left with $24 , how much money did Hanson have at first ?

TOTAL

¼ OF TOTAL + $3 (CDS)

¾ OF TOTAL-$3 (REMAINING $ )

3/5 OF REMAINDER+$6(BATTERIES )

2/5 OF REMAINDER - $6 =$24

2/5 OF REMAINDER $6 + $24 = $30 1/5 OF REMAINDER $15 REMAINDER 15 X 5 = 75¾ OF TOTAL – 3 75 ¾ OF TOTAL + 3 78 ¼ 78/3 = 26 TOTAL – 26 X 4 = $104 #

EQUAL FRACTIONS In a class gathering of 39 students , ¼ of the boys is equal to 2/5 of the

girls . How many more boys than girls are there in the gathering ? BOYS GIRLS

Total unit – 13 units 39 pupils 1 unit 39/13 = 3 Difference between the number of boys and girls 3 units 3x3 = 9 pupils #

REPEATED IDENTITY Samantha had 2/7 as many sweets as Zoey . Melvin had ¾ as many

sweets as Zoey , If Melvin had 39 more sweets than Samantha, find the total number of sweets that was shared among the three children at first .

Samantha : 2 units x 4 8 units Zoey : 7 units x 4 28 units

Melvin : 3 units x 4 12 units Zoey : 4 units x 4 28 units

Difference between Melvin and Samantha 21 units – 8 units = 13 units

13 units 39 1 unit 39/13 = 3 Total number of sweets 57 units 57 x 3 = 171 sweets #

Samantha8 units Zoey28 units Melvin 12 units

EXTERNAL UNCHANGED In a basket , ¾ of the fruits are oranges and the rest are apples . After I

gave away 10 oranges , there are now ½ as many oranges as apples . How many apples and oranges are there in the basket at first?

Before.) ORANGES APPLES

After.) ORANGES APPLES

DECREASE

Decrease in the number of oranges 5units 10 1 unit 10/5=2Total number of fruits left 3 units 3x2=6 #

TOTAL UNCHANGED Janet has ¼ as many rubber bands as Kumar . After Kumar gave

Janet 8 rubber bands , Janet now has 1/3 as many rubber bands as Kumar . How many rubber bands did Janet have in the end ? Before.) Janet 1unit x 4 = 4 units Kumar 4 units x 4 = 16 units After.) Janet 1unitx5 = 5 units Kumar3units x 5= 15 units

TOTAL UNCHANGED – MAKE THEM THE SAME USING COMMON MULTIPLE WHICH IS 20 BECAUSE 4X5=20

Transfer 1 unit 8 Number of rubber bands Janet had in the end5 units 5x8=40#

CONSTANT DIFFERENCEOn a coach to Genting highlands , there were 2/5 as many adults as

children . After 14 children and 14 adults boarded the bus at Johor baru , there were ¾ as many adults as children in the bus . How many adults were there in the bus stop at first?

Before .) Adults 2 units Children 5 units Difference 3 units After .) Adults 3 units x3 = 9units Children 4unitsx3=12 units Difference 1 unit

MAKE THE DIFFERENCE THE SAME INCREASE EACH 7 UNITS (2+5)/(4+3) : 14 1 UNIT : 14/2=7

NUMBER OF ADULTS AT FIRST 2 UNITS 2 X 2 = 4 #