الضرب والقسمة في مجموعة الأعداد الكسريّة النسبيّة Q
السنة الثامنة من التعليم أساسي
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx89Il06op63DIhNGKYP4j-KENyUdwC6qGCYV_t8Po_p6_0R3hLI8yqvHYLTcwnkYy8nWMDdpV5CJDJfOfKHSIUKaR9iqPYKPG0H-vMRAxTK0tZp4nF8Jql6BP6dnBpH_zDTIRYMUlUuxt/s1600/001.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPWeRG5tzcu2rivSLHFy-6v2EQu_j47E1r6U-kknHCgE_Eu9VEnafHOOEouscjDOMvxOxG1rCj21zVAjtb-bO26FhX08ucDA4n_CHNwLz9vG_k8UtoeFekU0ys94C0hXQYSOI0yegCWE7j/s1600/002.png)
مثال تطبيقي:
لنفترض أنّ
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuX_-8ouKhbkkR5F5Oz9GF8IHzuRnlvdn_f9OwBedbEf6ShJ4CagSgOVHXUAvmXGF0gZBr3CQ9TX6bJvX4HziDTzbrzKDswVPAGU9gErHTCH2j01Oha8d-YXbNUhg_UH10UY8hlrU98NTN/s1600/0033.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFJtx2rmJk9fX1yBRrQHVBJBmK8Id1OUaJSA_CYhlhoadaFaaegi0ueqjJRwnwI-4WV8Xei0D-v5fzc2VNwCH1pU2GhMe4_dQaNqery4E8eufn9kUTK2sdkUnvM___JublQjjA_GeqjQYz/s1600/005.png)
خاصيات عمليّة الضرب في المجموعة ِQ.
خاصيات عمليّة الضرب في المجموعة Q هي نفس خاصياتها في +Q.- فهي تبديليّة، وتجميعيّة، وتوزيعيّة على الجمع، وتوزيعيّة على الطرح.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic-XQCVqz9QUH5bLxsZtpyZuXG21nGZnPx4_rRX-3bzPzG_AMzTpu51-2AcJUwPIsrGaLZHXwEhVTbC_Sdg6u3sUYoM0WJpPrbqKqs9BKw4w6ry4vwiNoVWnjeKv68RFt6QheZyh8IhwA6/s1600/006.png)
------------------------------------
1- تبديليّة: يعني
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdJcKXIcBB5OkIq8Ehk1eC_Uksi7NK0m_h2NxBcK3uWs-yn50pj1KzTEVZtcldPGaEXocRbCfbl-VGy5ymuFRN-B0JAWITzdUUnkwyV-G3fyyvjHVeVLFnO-Cc60X0WjhOszbJi1P9nzrM/s1600/007.png)
مثال تطبيقي:
لنفترض أنّ
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuX_-8ouKhbkkR5F5Oz9GF8IHzuRnlvdn_f9OwBedbEf6ShJ4CagSgOVHXUAvmXGF0gZBr3CQ9TX6bJvX4HziDTzbrzKDswVPAGU9gErHTCH2j01Oha8d-YXbNUhg_UH10UY8hlrU98NTN/s1600/0033.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVr8UNlQYOTMQLTDUcoIhXvVnfi0PKCIbPPPJD1gO3-RVoWLn1hyeNFgAglzgxfSZFc3QnPkdRY2cjnm5no9WTGjCz4UbrP_iboCycsqxTbmlaqBxLIYx8ioMtFgcOKwTcO6lyQv-6y0LL/s1600/003.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhuFbi6K4IQlvSwKuG5OYIAVarJeG9LNl1JwaULmuG54i5zxDGJPxVuIIQT-41p_etlwsaeYWDYOxOU5NFg5h7lW2EStBZ6Sr6pw4y_Ts3vg0oIoON5J2w35wFAmd_mQeu2bZa1rCJl9CH/s1600/008.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0ogaCUt5n8w5qDr9lFRpRomGnwZD6yabevQXYUzyxng5yUaO1wD6MAV7GeHzlQIZV-4skdCpi2PLhLgN2qCdNF_nSqxQONgKbkyXUyAH8gzvofx12noRX_ZdKwLPt4tB2dbtroYCEFvIo/s1600/004.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv3iH3eZAaPxsU7A8LFFVHjUSXWE72vJBSdGe9b0-ZtcvNcQ7vjl8moAFMtQHUyU_HahxAvBaJnUvq0bpSjj4tBxUj0Dq85hP6tujPb0xvCiStgu5RZBTzsXrI-HX6HMYdvFXkXCerwwjj/s1600/009.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKqtJ9drMX1A_s0C4Rm4ACFjICHSItCy5aN4T0Cms909EAUGdfc_RscxS2JDZAk4wzWgLOaFDWoz15cQQXpx_b6ZyyrFmMbDQs-QQ-lxHNDbFz20KrnyA9D8BGmlhzr5txTB7TDgKUlNPm/s1600/007.png)
------------------------------------
2- تجميعيّة: يعني
مثال تطبيقي:
لنفترض أنّ ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwRIDuXzx0id85246qRFSP8aHp1vgyvr70t4IpSptKwxPaKaw6IBUV7TdsDEj34em_tRClv3qKqO7DFz4uRM0f3h3ZqjbLiL4YRlay6D6xQpq4CABDSNn2G7aNlvptlACWtjKl-Fle11gD/s1600/011.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwRIDuXzx0id85246qRFSP8aHp1vgyvr70t4IpSptKwxPaKaw6IBUV7TdsDEj34em_tRClv3qKqO7DFz4uRM0f3h3ZqjbLiL4YRlay6D6xQpq4CABDSNn2G7aNlvptlACWtjKl-Fle11gD/s1600/011.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwZV6DaS_K9Xz32fwc4csobNXm3Jfl7lmazT1ZNQBq9gBUaavd0Sg6dT08s8xbyWmYUKtryW8O8JpEK2dKjCqvaqkWsgIW4E9x1sfZpQJjXdQLr15R-2K3WVxJ-KA83l4XroaYndvxiEur/s1600/012.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp2HbVcg_0XlaL4ludktEoTlkpG7nHElj-KwKnCj7Y2p01LV1ZY6QYmIG6ew4Iqwxs6vwh1kkwyLSbSwac18k_-3PP20mFHbLmLJXzHcA8lxDwRp1QdIKZydcQdg3knRFeYXvBl_qOUh4Q/s1600/013.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz5Jxdli_whiMTiV0HeWUJjdh5XnR4fSB2UjYimISDuMJqPpXt_qlGV3Nha0BLKQtIaQ9RFnachqR6FjfdvHJG_whdYIaRlbTOaB_e7n3te3G4qKEyTNobEwePOElgDh6sHW0vJd9OoY7c/s1600/014.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPmYPuiTbjEQt2dKHCZeQB2JXOnQzR6GlqcqS7H_tB_JZajSKkpuTey7nU3AOl1TU8sv2jog6DcdDJki9Wifa7WrqwW-6LU9Jj6l6hzEHoI9wEsRyhrIuB7RRGxRZqxGCRIKRog0f0P0af/s1600/015.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-pVgBTQYozQc_bvUmdKrUf1gmlSRC7vPNBYGacLz3V0Nf2ZxlXa78_yUT2ZTjNx5axesEFGfw84a_YE0-K1AyhPlJblX5gdum0yQ2OyPlMMASBTU2nc1w5Fvg-KW7FPbos2QBCk7xNlhu/s1600/010.png)
------------------------------------
3- توزيعيّة على الجمع: يعني
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4zHLWU0Aq2pNQWrKyCtFeKo7zGVFRwahQe_YXymIYX1nArKyPx1I2xdJtP6k1QiJ5n49PC_txmwBwlxLKXs1_SiG60aLhiZ1PCCAKgzuRoL_n4uUfqCdmf97cBlZ58Nb2dUUWXsTutfiz/s1600/016.png)
مثال تطبيقي:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUjQKY68kX1vLC2uCVVZE-Pl_jBrmdn6LOTsKtbE_BU1KjmlESqKPqdqcje6MIdg9-pvFK3NQAhvA3o0d_r4Lsis1uUaYU6R-K14bhvIFS2CzT4itu3cH39fzxTH2bHLHmuj-8sz8lBQOP/s1600/018.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ7FTOcM7pP93RQ7dlCphZxblsG0GgGrkpx59oQs4y0uZutQWQWNEBfQC9it83HW8EfZhdlUcg9u0u1n2rkzTPJDenRRcFWZVx06hIZEKMnCchkymyaG0uR82VVc2uCfJOkbCAdqLZp2oZ/s1600/019.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzIRUu9VwKlpjbr71hcN_7Qgi1Xb7oV_2mOB6glwTV0bNX541pm06VRZewvCZzt6_azx35b41OY7uS-CUXs8_zO3m7C-57d16YqwJGRPf1ANgS5R4YGP5g4q4KExBVJ4uLv0df_05lFMKT/s1600/020.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxiaUgwX0aTxIBm6CRv2UDrpCIxj69KMWLASSSEQX-Bnk_ulRCHogCoNtOlcoOxs0Zde_B-r3MaxSYUjQ0w0eB4c0NBHqEKy1kqfwHxz4DewCO8BW3EQalbP4EkURBEKZ6tg3CHcOZE29k/s1600/016.png)
------------------------------------
4- توزيعيّة على الطرح: يعني
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX1oOKwT_7Kikg8ngVO9AwaXv2_bmdNGzqyj-AHsJoknvnvQ60r3EAhJ6-Xq1PJxaE6VdrA5f5638N5XEVfhe7hxUhLrZrgpXvDmHk-6NcccQ_cAgVBboMrxIRqxHfCBtvosJDBMfEafoF/s1600/021.png)
مثال تطبيقي:
لنفترض أنّ ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwKPWW5yD89Qzn9vknqOclPvBeaWIk0rzMjwcz-tzZUqQK3ppqSGbQdIp4gF1hym4hY-V5eLM0j5YYWpsAQj56LV4fG4SWJb2vdqmDbFv-GPHFsb3Uk4VSCSZ7rKQfaGVo0iZwIy_TmZp4/s1600/017.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwKPWW5yD89Qzn9vknqOclPvBeaWIk0rzMjwcz-tzZUqQK3ppqSGbQdIp4gF1hym4hY-V5eLM0j5YYWpsAQj56LV4fG4SWJb2vdqmDbFv-GPHFsb3Uk4VSCSZ7rKQfaGVo0iZwIy_TmZp4/s1600/017.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCsD9WSRj-f43goEK8kKXcvkfW-5DHwgrmCIBmZMjaEId4_cHTLFgaJ5CNs9pXXCGWh8VaNlMTX6cU0G0rKFU25J_ynCC8CDrKi2r9kpuiK8uJnRxkuY6avoJ2IqCfjNpWf8F9-gii2bgF/s1600/022.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEim7w33p1HrsVD1eo57SDPtnf6MsIhlQQcBX05__LsPCs0l7Db6fRWzIR4NDn7-LBb6jpOnlb6M1wcA_6jffLsvYBy-VEVGH_me-J4GNs9AzXHfr9Ep4j4m2i9o7vdpYTegbtlA6cTYzcos/s1600/024.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfHmZI95_5Gpi45pekAxZx-jfTCcCNlqoVXdNS2G79lo0lGhCrONGrMlv29UHQiPbvakK13EDWTECAVZfR7Ekol7Hsg116YFDB05p0lIQ7JUfnIXPLLkeq6CWdQ0UX7YotXCBC7SBqceBy/s1600/021.png)
------------------------------------
- مهما كان العدد الكسري النسبي
فإنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZDv9BwmMV-KSS99aRde3PqdVzUk9eTlkqjV0royECmCEK5odlHs56kRbeAspV29GPbAekYM4Ke64sdDqty0GjSCDrDf2OX8Wt6bXtPGZ31-r0W2y169z2yP0LNaJpH7cSDAO8gTmM3xu3/s1600/026.png)
مثال تطبيقي:
لنفترض أنّ ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfLxqQfUUlPSZbqcmN_I8XkxrvqCw-213TRV28_yaDPXZjq0dV9Xb0EDsXYTECd-WdAH9I7hdExqkQL3VzkKMVbAzl9Lsjvl4qwXCqduPM4JjrlVmco38I7asYALhBh2OxGfuCkJU-VCkO/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfLxqQfUUlPSZbqcmN_I8XkxrvqCw-213TRV28_yaDPXZjq0dV9Xb0EDsXYTECd-WdAH9I7hdExqkQL3VzkKMVbAzl9Lsjvl4qwXCqduPM4JjrlVmco38I7asYALhBh2OxGfuCkJU-VCkO/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGNmDlBUqvQQOw8ABzEtGNEB8kuOwdsJgSemZ87wAw4hSE0XyfmnZ3EKl2wlIFO8WNZDd5Jc2i2qbYDnkD0poeFjJp0IaxYX_2HzJg0gKDFc9UPtsTPBC3WoQ0kjO33T6GFI7bBcUhauqr/s1600/028.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG2G9UBKMOksS-5RPdRkfRS0j6Pxq2zEwn0I5vqqmSSyColELN5tYXcZ5jBUoAZCYeiTw1nj_n-r2b_HIQZNOygqL68l_gzDg0Qhm67QyRHwlAW7m8U25v3PB0K2bGUtl1NMm2uE_ZVVYE/s1600/029.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwuMXfBwITg2Qjk9lV5gl2ilFAlokTykXDCGgzl3WsJQ-JlmlOrbMtyNEO-g6dSyT2ViPdmJo2ybXx10OHD6sD4bGo5-E_KxTBNY2HZBtcnmMlVmbJ1-Hu7GXqEF0_WR29oW5UCXJDjIiq/s1600/030.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVI7VobzjaVw4z5uqbFVBtk3Kgbeo4PY5m-yFLAIxHQajYpBM8xg1l_lBpg2Z_LzZlsOvLmUEbenT6ol12Lb29vmmkrEt8e4AlH7_smXBAoCEvP4nGvDQqqanYkQhnm5R9yulJhSqSb5jT/s1600/026.png)
- مهما كان العدد الكسري النسبي
فإنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoENkZMSQfarPwpHMeMUXlmvkJq8wqlRZM0KBd-8QimqatwcS5Y15o_AaAWy-nKlBfIdVegGdBznYaaCoNrH-DAowdvRdmsMrKpqRMKfPzD7_B3A5fEJjUaTKoiHS6kH1oOjo_qSCG8Zg_/s1600/031.png)
مثال تطبيقي:
لنفترض أنّ ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjQya3utNb9M4lBDTljrevJLqJ2yxQOxd2HmQqaxv1lKbVgweTuD84DyGNa0j-zv1qhw0cJxK7W-tFfB3UOrV5E21g6-FM5ywNgiZ-Ge4_P67xwpKqUchcfZwUFslTWHATqXoDSc6Ozl15/s1600/032.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwmW6jcvga5cjc3vgszhZuV6zvQcKgzx_ZVu6JSrCHC2ZfbUR7QcYIlwm4zJRmb57zYxB3-4Cb_9F9KUdUWunG-9sRCwMHwxcxn1h9RrMRX1coC_OkelsOnhdLPtRRW5ReDjEq6m-iHR9a/s1600/033.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisINiQfV8s1DnyyyEVapCJYiJFbs4DO5qDvPBl2y16HBfvH7J-xR8WQlN3AMjrzNJwdW5ilNURwNZAQyCJ3kDYz3ucHbxBBZZbQM-BZpFVMlmV2j583mi5WRFZaeipRooKk9kkmc4K6BWF/s1600/034.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDBukhqDxi2Yz1Srsis0z-w0oGshSWvkno44JysksnEDf6X3-nPZRyVIuelbrwS-ESfStTEvm4yAofEB5S1q_f0yhDMoh1X5G4knNRc7O65UoTt9bSuoe4yUsyoj6vy1VX6OjkN4dFMuKy/s1600/031.png)
- مهما كان العدد الكسري النسبي
فإنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioDMDn5GWOX49u1_25Zp9Qsmyu8m5niHCyn0sAQcyqDwvYH1mGNr-DAjd5qasHYBs3N_3dL_e_YTJWH0b8kmKEJF8UUyWLxNcTqQhajAMNDE3VOTBQXvYFxh0d_MBynOuYfC9Es9K6cAUE/s1600/035.png)
مثال تطبيقي:
لنفترض أنّ ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSmxa-V68wL-_CHBx2VwscKWKJII7XZBJtakiBy5z5Jqv0FUSR3nhCWvTN6B-rxOHrwYSyRord5q85bS2W6AXTbKAOb3GSWHbUcKSixSDLrUrA3zivyXo5Bfj3K2XG4Q2STzBdAIaZqKKq/s1600/036.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjr9YD_aP4nX3u84edfO-qINCnoYn8VNayvozHg-5mVNL2VBCGe_SjQjXOmtjmj_0SySUu-vIYzjv8Tkm7bsFUWjdjL1CgIc1_YlCRALo_w8aLH1jEE2WEjSzBcLNhgVaiVa0vMQsVOiFB-/s1600/037.png)
إذا
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHaPS0OsOVY9B1Y1TWZN14CVemEcMG9F-qlMvMpy2zNGIhsI73egIFsDV_4oyGaCo1CyDZ9PrTjqbnW4S2jOHWTAZ89sOzNsqx1yt8Y8CCgg0aFAXbTi09Fae6duTrKYvO5mtODsvrdmq8/s1600/038.png)
ونستنتج أنّ:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEif6YprDXzyK4F8WOgufT6kqofu_bTI_C6LeEvSYOBB0-7lxXT8VFw9EuRWvHwZ3qmtbwzVa1rStZYUOCbUiPIIRU94hEj9T0fq14RLfrzwqhsk8zOdIRJxd7lFIIVPYWZvhF5KX3Dk-X3D/s1600/035.png)
خاصيات عمليّة الضرب في المجموعة ِQ.
* ليكن![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0yGCqYQy_59AnT2FBx7PRzXK3hopaxVnNxHimKrfiondwO1Nlzw1VxR5gtez7XLswvJbaADYZEw6hgXy4hM7-BKycHHA_6Ca2gCJlv3mQSuqqyk8FhucW-a_mSCrEIVSAaG4IgP5Ste_Q/s1600/025.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOBmFFNH_qf-R_Rkcj1pVpSt6rGVEfR6iXxgMRV5IhZk7j9F_vXhhlazrT66o-lppzk4D5x5uZ3YhoRx_Mn5mqFQ3VEe513Xg2-AE0ceXXDXYIRfM7Vib3nwtz_Zi1eLC25qPmyK-ac7q0/s1600/039.png)
مثال تطبيقي:
لنفترض أنّ
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzkkG4zOYh55ofpf9-fMxmhsc7BY5UDjwYIQfijL8GMZNTAKxvVyOPM0nayZ42tq1A9XScY94mIw97WqPgPAJ7nF54tvWpvsGb8UKAmMJ8watlU8egIIEuv5xkpVOGQ7sSdFbb8kf5Dath/s1600/040.png)
إذا
ونستنتج أنّ:
* نقول أنّ العددين
عددان مقلوبان أو أحدهما مقلوب الآخر.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyZnzAWW-lATSoc0mbghfSGaAeTFjYMvPw09iQzz1VpiReOdI4ozFGdLzbz6CJz1Y8Kkh9BHfwYXMpGzmVcO0sZrvU8kW5LM0_GfFnRqz0IvvdCqhdQiz3gGXkJZzbTCRmTk7t_augAk6R/s1600/042.png)
* العدد
يسمى مقلوب العدد
ونرمز له بـ:
.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPoiKaOpWlC0CUVCLSiUhkpYORdjyuiUns2qpezLaKaaivHndsesRLtKZxysnK1Ss2RXxbPmWcwn4PIXKuczYlW0a_M75H8rmFGUHLvgnj716-VS4WSBjMeVF92DHXlSe2y6fIHG9jn95l/s1600/043.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinSPskbqSm4chELSerBLobEMMRhEK7r-DSGcsYjN8cD1NEsqpBhmwc9RCBv9keutRgAFloxdnWLQofwJeoTew3161mqQbdKKlUElRtLXfBl0sIaoJIgtUdWKtwFkaOaRNDI5S47DFcLKzt/s1600/025.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJD8fXVNTyPKD8q5u_VcqzIJ6j-aWGDK-O6Pa66-u_j4cx9d64R8mRCGs1qGWYvpbshz6auhug9qpTmPIU_j3lt6kpQmvOSvJGsI7eTnur1r9m6lME_THME_9PT7rS0_afRO1J63cPX7Ge/s1600/045.png)
كما أنّ العدد
يسمى مقلوب العدد
ونرمز له بـ:
.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinSPskbqSm4chELSerBLobEMMRhEK7r-DSGcsYjN8cD1NEsqpBhmwc9RCBv9keutRgAFloxdnWLQofwJeoTew3161mqQbdKKlUElRtLXfBl0sIaoJIgtUdWKtwFkaOaRNDI5S47DFcLKzt/s1600/025.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPoiKaOpWlC0CUVCLSiUhkpYORdjyuiUns2qpezLaKaaivHndsesRLtKZxysnK1Ss2RXxbPmWcwn4PIXKuczYlW0a_M75H8rmFGUHLvgnj716-VS4WSBjMeVF92DHXlSe2y6fIHG9jn95l/s1600/043.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVKoDeKAICsm9kIal6Q1-FQLK5OxKCcZPi9RRzEBQkKJoXBvUeLzUxYOVLUX2rgFyYw_OUpJwc-xIBuviX4Al2QKvmKzEiG6e15XljL4WCJGBLBHJAKNe2oIKfupDWx4xIGxGG8Wxd1fwg/s1600/046.png)
لنفترض أنّ
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1btWK3hVJPaisTHsxNxIGNnOV8yJWnOnfQyn7eRHyg3L_agjUxMN_7u2kYUhoCqQwYcnD-tVTbi8Hk5BR58Jw1s-RJLh8GOxd7tAcKnDA9L1aWeIPIDAgTP6xYN376_vG6Hhd6vsOxkOW/s1600/027.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT4SWXgMhUxfZDqZiJRG6pgG1JT98CDePek3FSYxXt01bDvofYme-c95bJ9Yl6SxuxaW_s5dDICZ1asn7YROdwbSPBZQcCwB0lIBiZA_tCJJ753NGzSsPGIfPScMiDXg9NQJSXp2j9r9H_/s1600/048.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_MSSjqVpGr-MP6mXMsXfZHuX7ErB5dDvIVuso6fsrO-BFLjY4UzQI1pdUiIoiQ3W0hpyXhuTDayy3boMFlV8y4FwV34xwKAbhw68K6xdF3l2mY163MBbHkbdBKhYIgpwgy4eDocv6kxRx/s1600/049.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcjVf70TTDFzeSCprb9vynC9zYN7-ZMsCqtA0iNzPC014_ibJ7yp1Sj6PFZsmia9yrp8dVt9pqsAWS9rEK-SZcdIQ4PyEue9Czu2sKVx9Ah6OxlPlJUQTPdRW4XfYhD-DvwCroWoup6bpt/s1600/050.png)
يعني ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK8DcUIIkEmmYKjn2NzWX7nVSjoWiTKfNEg_zlfr4XIAoNiVWD76KGHlL-xvvof7Kb9Z3PaiOw4g1bg8Cg0uZtZo3tikYFgDYqc0-1yjmGEQJuhgUP7xHCAx7YaSs8HIuj3RWjx0kzhe4W/s1600/051.png)
كما أنّ العدد ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK8DcUIIkEmmYKjn2NzWX7nVSjoWiTKfNEg_zlfr4XIAoNiVWD76KGHlL-xvvof7Kb9Z3PaiOw4g1bg8Cg0uZtZo3tikYFgDYqc0-1yjmGEQJuhgUP7xHCAx7YaSs8HIuj3RWjx0kzhe4W/s1600/051.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_MSSjqVpGr-MP6mXMsXfZHuX7ErB5dDvIVuso6fsrO-BFLjY4UzQI1pdUiIoiQ3W0hpyXhuTDayy3boMFlV8y4FwV34xwKAbhw68K6xdF3l2mY163MBbHkbdBKhYIgpwgy4eDocv6kxRx/s1600/049.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT4SWXgMhUxfZDqZiJRG6pgG1JT98CDePek3FSYxXt01bDvofYme-c95bJ9Yl6SxuxaW_s5dDICZ1asn7YROdwbSPBZQcCwB0lIBiZA_tCJJ753NGzSsPGIfPScMiDXg9NQJSXp2j9r9H_/s1600/048.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimohH08sI7t3m529dex21A9Utg25Xl8JsxhY66F6AL5p9-AUmIUDIQEmVv6npKWWK8RAmQG9OJNez1De2euZaAjM5UX5Zbikt1QrDEqAtmOLSiucmf8NFcqYNg5JH6MyfyzPgIVTb6Gfh_/s1600/0522.png)
يعني
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrvrXwVdvWDI3lR8apVYemZM336PdIRifKplk7rxdRJ7DMFPEMRchlMgP0E2zcfzOt9Bpncw-mppPlf6vZWgUqw6EkWStBmNxoa5maD8YMpxoVUDDpa8aXaFpGzSxJUA8jLHKIH1K2CuYp/s1600/052.png)
* عددان مقلوبان هما عددان جذائهما يساوي 1.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc2_-1Q7he17FnriCs1iRBrIbWZwraNfxRyhoi8ASYKNkUqOe4xgV-CbnpCIeejjhQT53fVVZlAUjDwJGvu-k515HHNee9kxBFESW8MnLDs6c_yi7T5QeT8ulIm5jLqZOXF-6_JlmaDxSq/s1600/039.png)
قسمة عدد كسري على آخر مخالف للصفر.
إذا كان
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx89Il06op63DIhNGKYP4j-KENyUdwC6qGCYV_t8Po_p6_0R3hLI8yqvHYLTcwnkYy8nWMDdpV5CJDJfOfKHSIUKaR9iqPYKPG0H-vMRAxTK0tZp4nF8Jql6BP6dnBpH_zDTIRYMUlUuxt/s1600/001.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhW7drSCokEh0ldVR-5U0sBLfdT3UVIik8oh_T-CQ14dGRojTDmdPX3kDgs8FcBkyZN9wnmAFLpEj6kuGldTBx-ONJf6pwY51GEXeSiTUoujrj98fmvxLkxbAHSoTGevWYOJEFaydKN0eKa/s1600/054.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinSPskbqSm4chELSerBLobEMMRhEK7r-DSGcsYjN8cD1NEsqpBhmwc9RCBv9keutRgAFloxdnWLQofwJeoTew3161mqQbdKKlUElRtLXfBl0sIaoJIgtUdWKtwFkaOaRNDI5S47DFcLKzt/s1600/025.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhW7drSCokEh0ldVR-5U0sBLfdT3UVIik8oh_T-CQ14dGRojTDmdPX3kDgs8FcBkyZN9wnmAFLpEj6kuGldTBx-ONJf6pwY51GEXeSiTUoujrj98fmvxLkxbAHSoTGevWYOJEFaydKN0eKa/s1600/054.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkqPqq7vEA-5LIxz0tOA1d3CuyJR5wfSctdJ_mHKc0TjbAHscFqgNqqJosbCgtU1pOwlC8mMlSMapcWINAb-lifQ40L-BW9uyiXXokhV03epINQn2_mgxymqUpyYpoucXQOnB81px0pXGd/s1600/055.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiKQ52MMBmIlZdsMDgcoPELWH0W8mssbwzJXeKf9hV9u-bw8lIrU7hcrqke9PELgkmVxdRpXlfGi2No_tPb_ZhK788g4xxJdW31067Zk8uX-SLIloMQ0Jty7HKoruumFBF4PehvTJ-GD_7/s1600/056.png)
مثال تطبيقي:
لنفترض أنّ
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbB2Lrq_FJUx_tpvSa6g6fT1mttbS5I0mfXYZfMziuXZ2W82MSoDWDGhWeZzf3_buhup2I4BTMKbFzDci3-2E3qdLC5nvm6ZPqv4_gqZdoepH2zqwNvbbU9QUwnXhtK1Z1sUbWRj4iua3L/s1600/057.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7Q1gXPzcx5zdSOrsL2K9I-7dTL2AmyAoaMwFiToLooMuLNEQOh6ist6EaI5ZO0ea9tQ3gqbzvhve5OukZqiUZ9f16EcpZlWwxDsch4q0kKscUV6T_6IkKtahyzPiWTbLcvTuVUzTqICdf/s1600/058.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDNTOR1AvrvjXKcclJWw7XDselRJ7ZnVxN_D0OZekQnjVkSUqVjmNQIP6vFPHnXt6357haEtVSr-fUm0SHcRWlHcxy08Lzc3kcEL2anakV5MDNFsfkzTxKn4JJd2nXTiYJ6qoR3Nu1tnzD/s1600/059.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRi19Ti2TsLYx33bwMu01JoNEOyp0oQntGohQLwdyjAu_bBzqaig41ZW7JTZ2ApYSxjfu7_wERQXQX_upbMtUNxS27cZusbP7xxR64kZ2Lm6c6AsmsZjWalKt5QW3U7_RViV3P8CtOrDqe/s1600/060.png)
ونستنتج أنّ:
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