Math  /  Numbers & Operations

Question1. List five rational numbers between: (i) -1 and 0 (ii) -2 and -1 (iii) 45\frac{-4}{5} and 23\frac{-2}{3} (iv) 12-\frac{1}{2} and 23\frac{2}{3}
2. Write four more rational numbers in cach of the folloming pattems: (i) 35,610,915,1220,.\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}, \ldots .. (ii) 14,28,312,\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}, \ldots.

Studdy Solution

STEP 1

1. A rational number is any number that can be expressed as the quotient or fraction pq\frac{p}{q} of two integers, where pp is the numerator and qq is a non-zero denominator.
2. The task is to find rational numbers within given intervals and extend given sequences of rational numbers.

STEP 2

1. Find rational numbers between given pairs.
2. Extend the given sequences of rational numbers.

STEP 3

(i) Find five rational numbers between 1-1 and 00.
Choose numbers like 0.9,0.8,0.7,0.6,0.5-0.9, -0.8, -0.7, -0.6, -0.5.

STEP 4

(ii) Find five rational numbers between 2-2 and 1-1.
Choose numbers like 1.9,1.8,1.7,1.6,1.5-1.9, -1.8, -1.7, -1.6, -1.5.

STEP 5

(iii) Find five rational numbers between 45\frac{-4}{5} and 23\frac{-2}{3}.
Convert to decimals: 45=0.8\frac{-4}{5} = -0.8 and 230.6667\frac{-2}{3} \approx -0.6667.
Choose numbers like 0.79,0.78,0.77,0.76,0.75-0.79, -0.78, -0.77, -0.76, -0.75.

STEP 6

(iv) Find five rational numbers between 12-\frac{1}{2} and 23\frac{2}{3}.
Convert to decimals: 12=0.5-\frac{1}{2} = -0.5 and 230.6667\frac{2}{3} \approx 0.6667.
Choose numbers like 0.4,0,0.2,0.4,0.5-0.4, 0, 0.2, 0.4, 0.5.

STEP 7

(i) Extend the sequence 35,610,915,1220,\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}, \ldots.
Notice the pattern: 3n5n\frac{-3n}{5n}.
Next four terms: 1525,1830,2135,2440\frac{-15}{25}, \frac{-18}{30}, \frac{-21}{35}, \frac{-24}{40}.

STEP 8

(ii) Extend the sequence 14,28,312,\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}, \ldots.
Notice the pattern: n4n\frac{-n}{4n}.
Next four terms: 416,520,624,728\frac{-4}{16}, \frac{-5}{20}, \frac{-6}{24}, \frac{-7}{28}.
The rational numbers and extended sequences are:
1. Between 1-1 and 00: 0.9,0.8,0.7,0.6,0.5-0.9, -0.8, -0.7, -0.6, -0.5.
2. Between 2-2 and 1-1: 1.9,1.8,1.7,1.6,1.5-1.9, -1.8, -1.7, -1.6, -1.5.
3. Between 45\frac{-4}{5} and 23\frac{-2}{3}: 0.79,0.78,0.77,0.76,0.75-0.79, -0.78, -0.77, -0.76, -0.75.
4. Between 12-\frac{1}{2} and 23\frac{2}{3}: 0.4,0,0.2,0.4,0.5-0.4, 0, 0.2, 0.4, 0.5.
5. Sequence: 1525,1830,2135,2440\frac{-15}{25}, \frac{-18}{30}, \frac{-21}{35}, \frac{-24}{40}.
6. Sequence: 416,520,624,728\frac{-4}{16}, \frac{-5}{20}, \frac{-6}{24}, \frac{-7}{28}.

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