MUST REMEMBER
"If the ratio of A to B is say, 3 : 1, this means A is 3 times larger than B, or that B is a 1/3 the size of A."
"TIP#1: Try to reduce the ratio to its simplest form by dividing both sides by common factors. E.g., for the ratio 4:2, both 4 and 2 have a common factor of 2, so divide both sides to get 2:1."
"TIP#2: Remember to convert both sides to the same unit, e.g., convert days to hours, kg to g and so on."
TIP: If the question gives you a value and a ratio, like the question below, simplify the ratio so that the value's ratio is 1, For example, if the question gives you the value of green, so change the part of the ratio that is for that value 'green', which is '2' to a '1', by dividing each part by /2 to get 2.5 : 1 : 2, now you can simply use the 2.5 as the multiplier for the amount of red, and 2 as the multiplier for the amount of white."
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TIP: When dividing a value by a ratio, you need to work out how many shares there are in total by adding the proportions together, For example, in the question below, you add 3 + 5 to get 8 shares, then divide the $240/8 to get the value of one share = $30, Ann receives 3X$30 $90 and Bob 5x$30 $150, so Ann gave half to Colin which is $45 and Bob gave 1/10 to Colin which is $15, so in total Colin received $60.
"Fajar earned 1.5 times more than what Del earned (6:9 is 1:1.5). So if the gap is $36 then Del must have earned $36/1.5 = $24 so Fajar earned $60."
"a black square is 7/3 times bigger than a grey square: B = 7/3G
a white square is 9/5 times bigger than a gray square: W = 9/5G
Therefore, black to white must be:
7/3 : 9/5, Now clear the fraction using LCM of 15.
= 35 : 27
7:2 means that whatever the number of counters in each bag, the ones in A are 3.5x more, right? in other words: 7k / 2k = 3.5 (Note: we can't work out the value of K as all we know is that ratio holds)
However, we are told that if we take 5 from A and put it in B it becomes 2.66x more. this can be written as follows
7k - 5 / 2k + 5 = 8/3
if we solve for k we get = 11
So at 7 : 2 = 77 to 22
After moving 5 from A to B
72: 27
TIP: "When we say 'A is directly proportional to B,' it means that B is consistently multiplied by a fixed number to make it equal to A!"
"What is this fixed number?"
"It is ALWAYS equal to A/B."
"We can see in the example below that if A = 10, B = 2, the multiplier must be 10/2 = 5. Hence, we can write the formula as A = 5B."
当我们说'A与B成正比'时，意思是B始终乘以一个固定的数字来等于A
这个固定的数字是什么?
它总是等于A/B
在下面的例子中我们可以看到，如果A=10，B=2，乘数必须是10/2=5。因此，我们可以将公式写为A=5B
"In this case the fixed number is ALWAYS equal to A/B²."
TIP: "When we say 'A is inversely proportional to B,' it means that B is consistently the denominator in a quotient with a fixed numerator to make it equal to A!"
"What is this fixed numerator?"
"It is ALWAYS equal to A * B."
"We can see in the example below that if A = 5, B = 6, the numerator must be 5 * 6 = 30. Hence, we can write the formula as A = 30/B."
当我们说'A与B成反比'时，意思是B始终作为一个分数的分母，而这个分数有一个固定的分子，使得整个分数等于A.
"这个固定的分子是什么？"
它总是等于A*B
"在下面的例子中我们可以看到，如果A=5，B=6，分子必须是5×6=30。因此，我们可以将公式写为A=30/B
"In this case the fixed numerator is ALWAYS equal to A*B²."