3 Mark Question

Question 13 Marks

Without using division, can we tell from the denominator of a fraction, whether the decimal form of the fraction will be a terminating decimal? Find out.

Answer

If the prime factorization of the denominator of a fraction has only factors as 2 or 5 or a combination of 2 and 5 then the decimal form of that fractional will be a terminating decimal form.
Consider the fractions $\frac{17}{20}$ and $\frac{19}{6}$
Now, $20=2 \times 2 \times 5$, and $6=2 \times 3$
$\therefore \frac{17}{20}$ is terminating decimal form while $\frac{19}{6}$ is recurring decimal form.

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Question 23 Marks

Answer the following questions :

1. Write all the natural numbers between 2 and 9 .
2. Write all the integers between -4 , and 5 .
3. Which rational numbers are there between $\frac{1}{2}$ and $\frac{3}{4}$ ?

Answer

1. $3,4,5,6,7,8$
2. $-3,-2,-1,0,1,2,3,4$
3. $\frac{1}{2}=\frac{1 \times 2}{2 \times 2}=\frac{2}{4}=\frac{2 \times 10}{4 \times 10}=\frac{20}{40}$
$\frac{3}{4}=\frac{3 \times 10}{4 \times 10}=\frac{30}{40}$
$\therefore$ The rational numbers between $\frac{1}{2}$ and $\frac{3}{4}$ are $\frac{21}{40}, \frac{22}{40}, \frac{25}{40}, \frac{27}{40}$ etc.

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Question 33 Marks

Discuss the characteristics of various groups of numbers in class and complete the table below. In front of each group, write the inference you make after carrying out the operations of addition, subtraction, multiplication and division, using a (✓) or a (x).
Remember that you cannot divide by zero.

Group of Numbers	Addition	Subtraction	Multiplication	Division
Natural Numbers	✓	X (7- 10 =-3)	✓	\begin{gathered} x \\ (3 \div 5= \left.\frac{3}{5}\right) \end{gathered}
Integers
Rational Numbers

Answer

Group of Numbers	Addition	Subtraction	Multiplication	Division
Natural Numbers	✓	X (7- 10 =-3)	✓	\begin{gathered} x \\ (3 \div 5= \left.\frac{3}{5}\right) \end{gathered}
Integers	✓	✓	✓	\begin{gathered} x \\ (4 \div 9= \left.\frac{4}{9}\right) \end{gathered}
Rational Numbers	✓	✓	✓	✓

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Question 43 Marks

Complete the table given below.

	$-3$	$\frac{3}{5}$	$-17$	$\frac{-5}{11}$	$5$
Natural Numbers	$x$				$\checkmark$
Integers	$\checkmark$
Rational Numbers	$\checkmark$

Answer

	$-3$	$\frac{3}{5}$	$-17$	$\frac{-5}{11}$	$5$
Natural Numbers	$\chi$	$\chi$	$\chi$	$\chi$	$\checkmark$
Integers	$\checkmark$	$\chi$	$\checkmark$	$\chi$	$\checkmark$
Rational Numbers	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

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