USING INEQUALITIES IN BALANCING EQUATIONS

Complete the following scales and inequalities by adding greater than (>) or less then (<).

Problem 1 :

Solution :

By observing the scale, 8 x 7 should be heavier. Then, we have to use the greater than sign.

8 × 7 > 12 + 13

56 > 25

So, 8 × 7 is greater than 12 + 13.

Problem 2 :

Solution :

By observing the scale, 12 x 4 should be heavier. Then, we have to use the lesser than sign.

3 × 8 < 12 × 4

24 < 48

In these problems, you have to add both the symbol and a value that would make the equation true. Remember, just with ordinary scale, the bigger value will be lower down.

Problem 3 :

Solution :

By observing the scale, 4 x 12 should be heavier. Then, we have to use the greater than sign.

17 can be added by any thing but the number what we are going to place near 17 should be lesser than 31. Because 17 + 31 will give 48. So, the scale can be balanced.

That's why we choose lesser than 31.

4 × 12 > 17 + 10

48 > 27

Problem 4 :

Solution :

By observing the scale, 100 - ? should be heavier. Then, we have to use the lesser than sign.

7 x 7 = 49

So, 100 - ? should be greater than 49. So the unknown can be replaced by the value lesser than 51.

7 × 7 < 100 - 20

49 < 80

Problem 5 :

Solution :

By observing the scale, 9 x 9 should be heavier. Then, we have to use the greater than sign.

9 x 9 = 81

So, 120 - ? should be greater than 81. So, the unknown can be replaced by greater than 39 (120 - 81).

In case it is equal to 39, the scale can be balanced.

9 × 9 > 120 - 50

81 > 70

Problem 6 :

Solution :

By observing the scale, 9 x ? should be heavier. Then, we have to use the lesser than sign.

8 x 6 = 48

The unknown should be more than 5. Because, it is equal 5, we will get 45 and will become lighter.

8 × 6 < 9 × 6

48 < 54