Chapter 16 - Preparation for Algebra
Problem Set 36
Write the following mixed fractions in decimal form and read them aloud.
(1) 3 \(\large \frac {9}{10}\)
Ans:
3 \(\large \frac {9}{10}\) = 3.9
Read as: Three point nine
(2) 1 \(\large \frac {4}{10}\)
Ans:
1 \(\large \frac {4}{10}\) = 1.4
Read as: One point four
(3) 5 \(\large \frac {3}{10}\)
Ans:
5 \(\large \frac {3}{10}\) = 5.3
Read as: Five point three
(4) \(\large \frac {8}{10}\)
Ans:
\(\large \frac {8}{10}\) = 0.8
Read as: Zero point eight
(5) \(\large \frac {7}{10}\)
Ans:
\(\large \frac {7}{10}\) = 0.7
Read as: Zero point seven
Problem Set 37
Write the following mixed fractions in decimal form and read them aloud.
(1) 9 \(\large \frac {1}{10}\)
Ans:
9 \(\large \frac {1}{10}\) = 9.1
Read as: Nine point one
(2) 9 \(\large \frac {1}{100}\)
Ans:
9 \(\large \frac {1}{100}\) = 9.01
Read as: Nine point zero one
(3) 4 \(\large \frac {53}{100}\)
Ans:
4 \(\large \frac {53}{100}\) = 4.53
Read as: Four point five three
(4) \(\large \frac {78}{10}\)
Ans:
\(\large \frac {78}{10}\) = 0.78
Read as: Zero point seven eight
(5) \(\large \frac {5}{100}\)
Ans:
0.05
\(\large \frac {5}{100}\) = Read as: Zero point zero five
(6) 5/10 \(\large \frac {5}{10}\)
Ans:
5/10 \(\large \frac {5}{10}\) = 0.5
Read as: Zero point five
(7) \(\large \frac {2}{10}\)
Ans:
\(\large \frac {2}{10}\) = 0.2
Read as: Zero point two
(8) \(\large \frac {20}{100}\)
Ans:
\(\large \frac {20}{100}\) = 0.2
Read as: Zero point two
(1) (23 + 4) = (4 + 23)
Ans:
27 = 27
∴ The given equation is right
(2) (9 + 4) > 12
Ans:
13 > 12
∴ The given equation is right
(3) (9 + 4) < 12
Ans:
13 \(\not<\) 12
∴ The given equation is wrong
(4) 138 > 138
Ans:
138 \(\not>\) 138
∴ The given equation is wrong
(5) 138 < 138
Ans:
138 \(\not<\) 138
∴ The given equation is wrong
(6) 138 = 138
Ans:
138 = 138
∴ The given equation is right
(7) (4 × 7) = 30 – 2
Ans:
28 = 28
∴ The given equation is right
(8) \(\large \frac {25}{5}\) > 5
Ans:
5 \(\not>\) 5
∴ The given equation is wrong
(9) (5 × 8) = (8 × 5)
Ans:
40 = 40
∴ The given equation is right
(10) (16 + 0) = 0
Ans:
16 ≠ 0
∴ The given equation is wrong
(11) (16 + 0) = 16
Ans:
16 = 16
∴ The given equation is right
(12) (9 + 4) = 12
Ans:
13 ≠ 12
∴ The given equation is wrong
2. Fill in the blanks with the right symbol from <, > or =.
(1) (45 ÷ 9) ___ (9 – 4)
Ans:
5 = 5
∴ (45 ÷ 9) = (9 – 4)
(2) (6 + 1) ___ (3 × 2)
Ans:
7 > 6
∴ (6 + 1) > (3 × 2)
(3) (12 × 2) ___ (25 + 10)
Ans:
24 < 35
∴ (12 × 2) ___ (25 + 10)
- Fill in the blanks in the expressions with the proper numbers.
(1) (1 × 7) = ( __ × 1)
Ans:
1 × 7 = 7
and 7 × 1 = 7
∴ (1 × 7) = ( 7 × 1)
(2) (5 × 4) > (7 × __ )
Ans:
5 × 4 = 20
∴ 7 × __ should be less than 20
∴ (5 × 4) > (7 × 2)
(3) (48 ÷ 3) < ( __ × 5)
Ans:
48 ÷ 3 = 16
∴ __ × 5 must be greater than 16
∴ (48 ÷ 3) < (4 × 5)
(4) (0 + 1) > (5 × __ )
Ans:
0 + 1 = 1
∴ 5 × __ must be less than 1
∴ (0 + 1) > (5 × 0)
(5) (35 ÷ 7) = ( __ + __ )
Ans:
35 ÷ 7 = 5
∴ __ + __ must be equal to 5
∴ (35 ÷ 7) = (2 + 3)
(6) (6 – __ ) < (2 + 3)
Ans:
2 + 3 = 5
∴ 6 – __ must be less than 5
∴ (6 – 4) < (2 + 3)
Problem Set 56
1. Use a letter for ‘any number’ and write the following properties in short.
(1) The sum of any number and zero is the number itself.
Ans:
Let the number be x.
∴ According to the property,
x + 0 = x
(2) The product of any two numbers and the product obtained after changing the order of those numbers is the same.
Ans:
Let the two numbers be × and y.
∴ According to the property,
x × y = y × x
(3) The product of any number and zero is zero.
Ans:
Let the number be x.
∴ According to the property,
x × 0 = 0
2. Write the following properties in words :
(1) m – 0 = m
Ans: Subtracting zero from any number, gives the number itself.
(2) n ÷ 1 = n
Ans: Dividing any number by 1, gives the number itself.