P6 Maths - Fractions ( "Before and After" Method )

Chloe had 120 more stickers than Gladys. After Chloe lost 1/5 and Gladys lost 3/4, Chloe had 184 more than Gladys. How many did Gladys have at first?

To use this method, we have to identify a certain number of units for both Chloe and Gladys. Since 20 units can both be divided into 5 parts and 4 parts respectively, it is used here.

Chloe --> Before
= 20 units + 120
- 4 units – 24 ( lost 1/5)

--> After
= 16 units + 96

Gladys --> Before
= 20 units
-15 units ( lost ¾ )

--> After
= 5 units

Using the “After” units, Chloe will have (11 units + 96) more stickers than Gladys.

11 u --> 184 – 96 = 88
1 u --> 88 / 11 = 8
20 u --> 20 * 8 = 160.

P5 Maths - Ratio

The number of stickers Raymond had to Cadence was 5 : 3. After Cadence gave away 39 stickers, the ratio became 6 : 1. How many stickers did both of them had altogether in the end?

For this qn, there is a "Before and After" ratio given. One of the subject in the ratio will remain unchanged.


Before, Raymond : Cadence
= 5 : 3 (multiply by 6)
= 30 : 18

After, Raymond : Cadence
= 6 : 1 ( multiply by 5)
= 30 : 5

Raymond did not have any changes made to his stickers. Hence the before and after units are made the same.

Cadence,

18u – 5u = 13u
13u --> 39 stickers ( Cadence gave away)
1 u --> 3 stickers

In the end,

30u + 5u = 35u
35u --> 35 * 3 = 105 stickers

P6 Maths - Speed

Mr Tan sends his son to school every morning at 6.15am. If he drives at an average speed of 60km/h, his son will be 10 min late. If he speeds at 120km/h, his son will be 10 min early. What speed should he drive at to arrive on exactly on time?

When the distance covered is the same, the ratio of time taken is opposite to the ratio of the speed.

Speed ratio = 60 : 120 = 1 : 2
Time ratio = 2 : 1

Difference = 2 - 1 = 1 unit

(Difference between 10 min early and 10 min late = 20 min)



1 unit --> 20 min
2 units --> 40 min

When he travels at 60 km/h, he will take 40 min, or 2/3 hr.

Distance to school = 60km * 2/3h
= 40 km

To be on time, the time taken is 30 min, (10 min less than 40min)

Hence Speed = 40km / 1/2h
= 80km/h.

P6 Maths - Speed, Fractions

A motorist travelled 2/5 of his journey in 4/5 hr. He travelled the remaining 84 km in 1 1/5 hr.

Find the avergage speed for his whole journey.


To find average speed, we need 2 things, “ total distance” and “total time”.

1 – 2/5 = 3/5 -> remaining journey

3/5 of his journey = 84 km
1/5 of his journey = 84 / 3 = 28 km
5/5 of his journey = 28 * 5 = 140 km ( total distance )

Total time taken = 4/5 + 1 1/5 = 2 hrs

Hence

Average speed = Total distance / total time
= 140 / 2
= 70 km / h.

P5 Maths - Numbers ( Going Backwards Method )

A, B & C has 204 erasers altogether. A gave some to B and B’s erasers doubled. B gave some to C and C’s erasers doubled. In the end, they have equal number of erasers. How many does A have at first?

For this qn, we have to use the “ Going Backwards” method. We have to start from the end, and move backwards step by step.

204 / 3 = 68 (A,B,C has the same at the end)

68 / 2 = 34 ( This is C before his erasers doubled)

68 + 34 = 102 ( This is B before he gave C some eraser)

102 / 2 = 51 (This is B before his erasers doubled)

68 + 51 = 119 ( This is A before he gave B some eraser)

Ans: 119

P6 Maths - Percentage, Decimals

Conversion of percentage to decimal.

Convert ½% to decimal.

If your answer is 0.5, you are wrong. This question may look simple, but it always managed to get students tricked!

Whenever we convert percentage to a decimal, we have to divide by 100.

½% = ½ / 100
= ½ * 1/100
= 1/200

Hence the answer is 1/200 or 0.005.