Page 131 - NUMINO Challenge_D2
P. 131
15 Thinking Backwards
Basic Concepts Thinking Backwards
Some problems are hard to solve when figuring out the given conditions in order.
But if you know the process in the middle and the result, it may be easier to figure
out the beginning part by thinking backwards. This type of communication method
is called thinking backwards.
When finding the first number from the result of the calculation by thinking
backwards, use subtraction for addition, addition for subtraction, division for
multiplication, and multiplication for division.
Example After pouring water from dish A to dish B by following the method
below, the amount of water in dish A became the same as the
amount of water in dish B, which is 120L. How many liters of water
were in dish A and dish B respectively at first?
[First Action] Transfer water from dish A to dish B, according to the amount of
water in dish B.
[Second Action] Transfer water from dish B to dish A, according to the amount of
water remaining in dish A.
[Third Action] Transfer water from dish A to dish B, according to the amount of
water remaining in dish B.
Class Notes
Before [Third Action], there were 120 2 L of water in dish B, which is half of the
amount of water left at the end. Also, before [Third Action], there was as much more water in
dish A as the amount of water transferred from dish A to dish B. Therefore, there were
120 L of water in dish A.
Complete the table below by thinking backwards shown in .
Stage The amount of water
Present Dish A Dish B
Before the
first action 120 120
Before the
second action 180(120 60) 60(120 2)
Before the
third action (180 2) (60 )
(90 ) ( 2)
Therefore, the original amount of water in dish A was L, and the original amount of water
in dish B was L.
128 NUMINO Challenge D2
Basic Concepts Thinking Backwards
Some problems are hard to solve when figuring out the given conditions in order.
But if you know the process in the middle and the result, it may be easier to figure
out the beginning part by thinking backwards. This type of communication method
is called thinking backwards.
When finding the first number from the result of the calculation by thinking
backwards, use subtraction for addition, addition for subtraction, division for
multiplication, and multiplication for division.
Example After pouring water from dish A to dish B by following the method
below, the amount of water in dish A became the same as the
amount of water in dish B, which is 120L. How many liters of water
were in dish A and dish B respectively at first?
[First Action] Transfer water from dish A to dish B, according to the amount of
water in dish B.
[Second Action] Transfer water from dish B to dish A, according to the amount of
water remaining in dish A.
[Third Action] Transfer water from dish A to dish B, according to the amount of
water remaining in dish B.
Class Notes
Before [Third Action], there were 120 2 L of water in dish B, which is half of the
amount of water left at the end. Also, before [Third Action], there was as much more water in
dish A as the amount of water transferred from dish A to dish B. Therefore, there were
120 L of water in dish A.
Complete the table below by thinking backwards shown in .
Stage The amount of water
Present Dish A Dish B
Before the
first action 120 120
Before the
second action 180(120 60) 60(120 2)
Before the
third action (180 2) (60 )
(90 ) ( 2)
Therefore, the original amount of water in dish A was L, and the original amount of water
in dish B was L.
128 NUMINO Challenge D2
