Class 6 Knowing Our Numbers Exercise 1.9

\begin{array}{l} \text {Simplify each of the following:}\\\text {Q1. } \quad 7 \times 109\text {Sol. } \quad 7 \times 109 \\ = 7 \times (100+9) \\ = 7 \times 100 + 7 \times 9 \\ = 700 + 63 = 763 \\ \\\text {Q2. } \quad 6 \times 112 \\ \\\text {Sol. } \quad 6 \times 112 \\ = 6 \times (100 + 12) \\ = 6 \times 100 + 6 \times 12 \\ = 600 + 72 = 672 \\ \\\text {Q3. } \quad 9 \times 105 \\ \\\text {Sol. } \quad 9 \times 105 \\ = 9 \times (100 + 5) \\ = 9 \times 100 + 9 \times 5 \\ = 900 + 45 = 945 \\ \\\text {Q4. } \quad 17 \times 109 \\ \\\text {Sol. } \quad 17 \times 109 \\ = 17 \times (100 + 9) \\ = 17 \times 100 + 17 \times 9 \\ = 1700 + 153 = 1853 \\ \\\text {Q5. } \quad 16 \times 108 \\ \\\text {Sol. } \quad 16 \times 108 \\ = 16 \times (100 + 8) \\ = 16 \times 100 + 16 \times 8 \\ = 1600 + 128 = 1728 \\ \\\text {Q6. } \quad 12 \times 105 \\ \\\text {Sol. } \quad 12 \times 105 \\ = 12 \times (100 + 5) \\ = 12 \times 100 + 12 \times 5 \\ = 1200 + 60 = 1260 \\ \\\text {Q7. } \quad 102 \times 103 \\ \\\text {Sol. } \quad 102 \times 103 \\ = 102 \times (100 + 3) \\ = 102 \times 100 + 102 \times 5 \\ = (100 + 2) \times 100 + (100 + 2) \times 5 \\ = 10000 + 200 + 500 + 10 = 10506 \\ \\\text {Q8. } \quad 101 \times 105 \\ \\\text {Sol. } \quad 101 \times 105 \\ = 101 \times (100 + 5) \\ = 101 \times 100 + 101 \times 5 \\ = (100 + 1) \times 100 + (100 + 1) \times 5 \\ = 10000 + 100 + 500 + 5 = 10605 \\ \\\text {Q9. } \quad 109 \times 107 \\ \\\text {Sol. } \quad 109 \times 107 \\ = 109 \times (100 + 7) \\ = 109 \times 100 + 109 \times 7 \\ = (100 + 9) \times 100 + (100 + 9) \times 7 \\ = 10000 + 900 + 700 + 63 = 11663 \\ \\\end{array}