Chapter 16 Preparation for Algebra Problem Set 55 Solutions

(1) (45 ÷ 9) [ ] (9 – 4)

(2) (6 + 1) [ ] (3 × 2)
Answer:
6 + 1 = 7,
3 x 2 = 6
7 > 6
so, (6 + 1) > (3 x 2)

(3) (12 × 2) [ ] (25 + 10)
Answer:
12 x 2 = 24,
25 + 10 = 35
24 < 35
so, (12 x 2) < (25 + 10)

(1) (1 × 7) = ( [ ] × 1)

(2) (5 × 4) > (7 × [ ] )
Answer:
5 x 4 = 20, 7 x ………… must be less than 20.
7 x 2 = 14
so, (5 x 4) > ( 7 x 2)

(3) (48 ÷ 3) < ( [ ] × 5)
Answer:
48 – 3 = 16,
5 x 4 = 20
5 x 3 = 15
16 > 15 and 16 < 20 so, (48 + 3) <(4 x 5)

(4) (0 + 1) > (5 × [ ] )
Answer:
0 + 1 = 1,
5 x 1 = 5
5 x 0 = 0
1 < 5 and 1 > 0 so, (0 + 1) > (5 x Q)

(5) (35 ÷ 7) = ( [ ] + [ ] )
Answer:
35 ÷ 7 = 5,
3 + 2 = 5 so, (35 + 7) = (3 + 2)

(6) (6 – [ ] ) < (2 + 3)
Answer:
6 – < 2 + 3 = 5
5 > 6 – 2
so, (6 – 2) < (2 + 3)

Using letters
Symbols are frequently used in mathematical writing. The use of symbols makes the writing very short. For example, using symbols, ‘Division of 75 by 15 gives us 5’ can be written in short as ‘75 ÷ 15 = 5’. It is also easier to grasp.

Letters can be used like symbols to make our writing short and simple.

While adding, subtracting or carrying out other operations on numbers, you must have discovered many properties of the operations.

For example, what properties do you see in sums like (9 + 4), (4 + 9)?

The sum of any two numbers and the sum obtained by reversing the order of the two numbers is the same.

Now see how much easier and faster it is to write this property using letters.

Changing the order of those numbers will make the addition ‘b + a’. Therefore, the rule will be : ‘For all values of a and b, (a + b) = (b + a).’

Let us see two more examples.

In short, if a and b are two different numbers, then (a ÷b) ≠ (b ÷a).

Take the value of a as 8 and b as 4 and verify the property yourself.

Preparation for Algebra Problem Set 54 Additional Important Questions and Answers

Say whether right or wrong.

(1) (15 ÷ 3) =5
Answer:
5 = 5 is right.

(2) (2 x 1) = 1
Answer:
2 = 1 is wrong.

(3) (16 ÷ 8) = (2 x 2)
Answer:
2 = 4 is wrong.

(4) (13 – 7) = 6
Answer:
6 = 6 is right.

(5) (1 x 0) = 1
Answer:
1 = 1 is wrong.

(6) (1 + 0) = 1
Answer:
1 = 1 is right.

Fill in the blanks with the right symbol from <, >, or =.

(1) (12 + 6) (10 X 2)
Answer:
12 + 6 = 18,
10 x 2 = 20
18 < 20
so, (12 + 6) < (10 x 2)

(2) (4 X 5) (10 X 2)
Answer:
4 x 5 = 20,
10 x 2 = 20
20 = 20
so, (4 x 5) = (10 x 2)

(3) (7 + 3) ………….. (3 X 3)
Answer:
7 + 3 = 10,
3 x 3 = 9
10 > 9
so, (7+ 3) > (3 x 3)

Fill in the blanks in the expressions with the proper numbers.

(1) (8 + ………….. ) = (8 x 1)
Answer:
8 + ……………. = 8,
8 x 1 = 8
8 + 0 = 8
so, (8 + 0) = (8 x 1)

(2) (5 x 6) > (14 x ……….. )
Answer:
5 x 6 = 30,
14 x 1 = 14
14 x 2 = 28
14 x 3 = 42
30 >28
so, (5 x 6) >(14 x 2)

(3) (6 X 7) < ( x 5)
Ans.
6 x 7 = 42,
9 x 5 = 45
42 < 45, 50, 55
so, (6 x 7) < (9 x 5)