Lesson Arithmetic word problems to solve them MENTALLY

Arithmetic word problems to solve them MENTALLY

Problem 1

Even if you are 2-nd grade student and do not know equations yet,
you can easy solve this problem using only your common sense and skills calculating whole numbers.


From 20 animals, take out 2 tigers and 3 bears, for a minute (mentally in your mind).


You will get 15 animals, lions, tigers and bears in equal amount.


What you will do next ? - But of course, you will distribute 15 animal in 3 equal groups.


In other words, you will divide 15 by 3 and will get 5 animals in each group.


After that, you will return back 2 tigers and 3 bears and will get the final answer this way.


ANSWER.  5 lions, 7 tigers and 8 bears.

Problem 2

Mentally in your mind, make your greater number 20 units less.


Then you will have two equal numbers with the sum of 92 - 20 = 72.


Hence, the smaller of the two original numbers is 72/2 = 36.


Then the greater of the two original numbers is 36 + 20 = 56.


ANSWER.  The numbers are 36 and 56.


To complete the solution, check  mentally that the difference is of the found numbers is 20 and the sum is 92.

Problem 3

As the problem says, for every one 20c coin, there are two 50c coins.
    (In particular, the number of 50c coins is even).


Next, the problem says that for every 50c coin, there are five 10c coins.


So, you can group the coins in sets, placing one 20c coin, two 50c coins 
and ten 10c coins into each set.


Thus, every such set of coins is worth 20c + 2*50c + 10*10c = 220 cents.


The number of such sets (groups) is   = 7.


Since each set contains two 50c coins, the number of the 50c coins is 2*7 = 14.    ANSWER

Problem 4

The container filled with water weighs 5 kg.


When half of the water is emptied, the container and the remaining water weigh 2.6 kg.  
So, the weight of the half volume of water that was emptied is (5-2.6) = 2.4 kg.


The weight of the other half volume of water that remains in the container is also 2.4 kg.
Since the combined weight of the container and the remaining half gallon of water is 2.6 kg, 
the weight of the container alone is (2.6-2.4) = 0.2 kg.


ANSWER: The container weights 0.2 kg.

Problem 5

When Matthias was on 8-th floor,  the number of the remaining floors to climb was 12/2 = 6, according to the condition.


Hence, Clara lives on the 8+6 = 14 (fourteenth) floor.


ANSWER.  Clara lives on the 14-th floor.


CHECK.  Then Matthias lives at the 14-12 = 2 (second) floors.  
        14-8 = 6 floors,  and 8-2 = 6 floors, which is consistent with the problem's description.

Problem 6

Divide 101 by (3+5) = 8 :  101:8 = 12*8 + 5.


For each group of 8 sandwiches, Jane pays for only 5 sandwiches; the rest 3 sandwiches of this group 
she gets for free.


So, Jane pays for 5*12 + 5 = 65 sandwiches, only.

Problem 7

As you read the problem, you should notice in your mind, that the difference 
between work done in the morning and in the afternoon is 4-3 = 1 bush and 28-24=4 strands of lights.


So, you conclude that Xavier uses 4 strands of lights to decorate each bush.


Thus this morning he used 4*4 = 16 strands of lights to decorate 4 bushes,
and the rest 28-16 = 12 strands of lights to decorate one tree.


ANSWER.  4 strands of lights for each bush and 12 strands of lights for each tree.


CHECK the number of strands of lights at the afternoon:  4*3+12 = 24.   ! correct !

Problem 8

After reading the condition, a student should notice that the difference between
the morning production and the afternoon production is 20-15 = 5 deluxe wreaths
and 168-138 = 30 pinecones.


Hence, each deluxe wreath has 30/5 = 6 pinecones.


Then each regular wreath has   = 4 pinecones.