C + T : R = 7 : 8 = 14 : 16

**Multiply by 2 to make (C + T) the same**

**7 x ? = 3 x ? + 5 x ? [7 x 2 = 3 x 3 + 5 x 1 Guess and Check]**

CS : C = 1 : 3 = 3 : 9

**Multiply by 3 to make (C + T) the same**

TS : T = 1 : 5

RS : R = 1 : 4 = 4 : 16

**Multiply by 4 to get R = 16**

C + T + R --> 14 + 16 - 3 - 1 = 26

26 u --> 260

1 u --> 260/26 = 10

16 u --> 16 x 10 = 160 cm2.

The area of the rectangle is 160 cm2.

Alternative method

**[Given informations 1/3 and 1/5 are redundant]**

C + T : R = 7 : 8

RS : R = 1 : 4 = 2 : 8

7 + 8 - 2 = 13

**Minus 2 to remove double-counting of shaded areas.**

13 u --> 260

1 u --> 260/13 = 20

8 u --> 8 x 20 = 160 cm2.

The area of the rectanglee is 160 cm2.

Obs, I have tried to understand your solution but the thing is that i still don't know how to use addition and multiplication on problem sum....

ReplyDeleteRefer to link for examples...and hope you can enlighten me when we should use addition and multiplication...

Example 1

http://4.bp.blogspot.com/_NGNaLTzN5_U/SQxTRczo6vI/AAAAAAAAA-o/TN0PwcEVk80/s1600-h/MathsChallengingQ010.JPG

Example 2

http://4.bp.blogspot.com/_NGNaLTzN5_U/SQxR1BQlCgI/AAAAAAAAA9I/Ozy-G5mWrWQ/s1600-h/MathsChallengingQ002a.JPG

http://2.bp.blogspot.com/_NGNaLTzN5_U/SnJh1OoNA6I/AAAAAAAACWc/zD_Mpyr-0Ak/s1600-h/MathsP4NYSA2Q45ChallengingAb.JPG

In example 2, why multiply instead of addition?

Example 3

http://3.bp.blogspot.com/_NGNaLTzN5_U/SQxR00tZgEI/AAAAAAAAA9A/k1PUrm6Rxqg/s1600-h/MathsChallengingQ002b.JPG

In example 3, why you add instead of multiply?

Please look at the remarks in the red box.

ReplyDeleteAnother way is for you to list them out and you will be able to see clearly.

For example 3, besides addition, I have also shown how to can use multication - 20 x 19 / 2 [You need to divide by 2 because when A shakes hand with B or B with A, they are actually the same].

You may want to use the method taught in your school .

But how do you identify whether addition and multiplication from a question?

ReplyDeleteIt does not depend on the question. It depends on what method you are using to solve the question. Please go through the comments in red box. Try to make a list of the different ways using less number. You will be able to appreciate better why add or multiply.

ReplyDeleteThis was taught at Sec 3 (Additional Maths) during my school day. So obviously, we have less problem to understand.