1.1 Foundations & Classification of Numbers

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Key Formulas

Solved Examples

Step 1

Make denominators the same. LCM of 5 and 3 is 15.

Step 2

Convert fractions:

35=915,23=1015\frac{3}{5} = \frac{9}{15}, \quad \frac{2}{3} = \frac{10}{15}

Step 3

The gap between 9 and 10 is not enough for 5 integers. Multiply numerator and denominator by n+1=6n+1 = 6.

Step 4

Scale up:

9×615×6=5490,10×615×6=6090\frac{9 \times 6}{15 \times 6} = \frac{54}{90}, \quad \frac{10 \times 6}{15 \times 6} = \frac{60}{90}

Step 5

Select integers between 54 and 60: 55, 56, 57, 58, 59.

Final Answer

The numbers are 5590,5690,5790,5890,5990\frac{55}{90}, \frac{56}{90}, \frac{57}{90}, \frac{58}{90}, \frac{59}{90}.

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