7 szkoły podstawowej

Matematyka 7

Matematyka

Matematyka 7. Ćwiczenia podstawowe

Matematyka 7. Podręcznik cz. 1

Matematyka 7. Podręcznik cz. 2

Matematyka 7. Zestawy zadań

Matematyka wokół nas 7

Matematyka z kluczem 7

Matematyka z plusem 7

Teraz egzamin ósmoklasisty. Arkusze

Teraz egzamin ósmoklasisty. Repetytorium

a) (−12,5+(−13))+(121​⋅(−6))=(−25,5)+(1,5⋅(−6))=(−25,5)+(−9)=−34,5

Suma: −2,75+331​=−243​+331​=−411​+310​=−1233​+1240​=127​ Różnica:&nbsp;&nbsp; 331​−(−2,75)=331​+243​=310​+411​=1240​+1233​=1273​

Za mandarynki zapłaciła&nbsp; 241​⋅4,80=2,25⋅4,80=10,80 &nbsp; Za brzoskwinie zapłaciła&nbsp; 352​⋅6,50=3,4⋅6,50=22,10 &nbsp; Razem za zakupy zapłaciła&nbsp; 10,80+22,10=32,90 &nbsp; Zapłaciła banknotem 50-złotowym, więc musi odjąć od 50 zł kwotę 32,90 zł. 50−32,90=17,10 &nbsp; Odp. Otrzymała 17,10 zł reszty.

Obliczmy szerokość prostokąta, czyli 116​  długosˊci

Najpierw obliczmy liczbę a i liczbę b. a=253​+6,4:3,2+76​⋅231​=2,6+6,4:3,2+76​⋅37​=2,6+2+716​⋅371​=2,6+2+16​⋅31​=2,6+2+36​=2,6+2+2=6,6

a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b71afa3e8a4308915dfa0f8bf055807d767525673098a6b5113ee16d9e022a06_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b71afa3e8a4308915dfa0f8bf055807d767525673098a6b5113ee16d9e022a06_big.svg" type="image/svg+xml"></object> &nbsp; b) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c002c1118668344198cf3095f6ff10cd137279044491ab4bb1b31920bb3bd8e6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c002c1118668344198cf3095f6ff10cd137279044491ab4bb1b31920bb3bd8e6_big.svg" type="image/svg+xml"></object> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c002c1118668344198cf3095f6ff10cd137279044491ab4bb1b31920bb3bd8e6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c002c1118668344198cf3095f6ff10cd137279044491ab4bb1b31920bb3bd8e6_big.svg" type="image/svg+xml"></object> c) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f1aa9127ec093cdc6aef48c21097fbc6f58285a0e2dd9710ba3508e0079ecb67_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f1aa9127ec093cdc6aef48c21097fbc6f58285a0e2dd9710ba3508e0079ecb67_big.svg" type="image/svg+xml"></object> &nbsp; d) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/45b6ac7767d4a5c99a81ff4c4a5432a50e41d2e7b52122c44b0bae31554a6859_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/45b6ac7767d4a5c99a81ff4c4a5432a50e41d2e7b52122c44b0bae31554a6859_big.svg" type="image/svg+xml"></object> &nbsp; e) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5d57d8981cb70fa4f180e061fa0fd2aa5a50adf6924ba1426bffda11e0d92137_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5d57d8981cb70fa4f180e061fa0fd2aa5a50adf6924ba1426bffda11e0d92137_big.svg" type="image/svg+xml"></object> f) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8d2da6c7858dedcdc01ed15ad3166cecadfaab95fb22e2636f7cf0c615dff4ad_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8d2da6c7858dedcdc01ed15ad3166cecadfaab95fb22e2636f7cf0c615dff4ad_big.svg" type="image/svg+xml"></object> &nbsp;

a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1c2e127ac7076ea158299ffa29a99812fb7cfed4ae8492c523acc88690cb2745_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1c2e127ac7076ea158299ffa29a99812fb7cfed4ae8492c523acc88690cb2745_big.svg" type="image/svg+xml"></object> b) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5f3829cfb321a29e036cf0c29af996de94e58cd82490d92a4824edcc7bcaa3bf_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5f3829cfb321a29e036cf0c29af996de94e58cd82490d92a4824edcc7bcaa3bf_big.svg" type="image/svg+xml"></object>

a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1a8c97b13eb552afd36b6493a94e0be0e636483c6a0ad67a92c97bfb8d4d5a14_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1a8c97b13eb552afd36b6493a94e0be0e636483c6a0ad67a92c97bfb8d4d5a14_big.svg" type="image/svg+xml"></object>

a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/3a41860cdb64d3a7dfec22905e997769ce0836095aad6cc8dd746d9706a67def_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/3a41860cdb64d3a7dfec22905e997769ce0836095aad6cc8dd746d9706a67def_big.svg" type="image/svg+xml"></object>

Suma: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/38a25383172f2a11ce0cbabd296f8514925407b5c86583eb69d8208a63891a9c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/38a25383172f2a11ce0cbabd296f8514925407b5c86583eb69d8208a63891a9c_big.svg" type="image/svg+xml"></object> Różnica:&nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/829b7b92bac226b8e4a138995db465e6270701a3b3cd2334955e976421b912fe_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/829b7b92bac226b8e4a138995db465e6270701a3b3cd2334955e976421b912fe_big.svg" type="image/svg+xml"></object>

Za mandarynki zapłaciła&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/45f4d59cd2c3ee6e1093062ceecf3ee17559361594195dfbd8209b162342a355_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/45f4d59cd2c3ee6e1093062ceecf3ee17559361594195dfbd8209b162342a355_big.svg" type="image/svg+xml"></object> &nbsp; Za brzoskwinie zapłaciła&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/bf2eb8a4c45d8b9ab1cacead61ad3d85a2094cf79f38366a65de7200bcbf794a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/bf2eb8a4c45d8b9ab1cacead61ad3d85a2094cf79f38366a65de7200bcbf794a_big.svg" type="image/svg+xml"></object> &nbsp; Razem za zakupy zapłaciła&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f2c5c4707a7effa2b1d30293e91ded5284494af0427030ec207c6f6c4b363f32_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f2c5c4707a7effa2b1d30293e91ded5284494af0427030ec207c6f6c4b363f32_big.svg" type="image/svg+xml"></object> &nbsp; Zapłaciła banknotem 50-złotowym, więc musi odjąć od 50 zł kwotę 32,90 zł. <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/151ec6e2913a23d0d996231ff4df57196d1abb5cdb1c57df9cf97a2fc601e6d4_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/151ec6e2913a23d0d996231ff4df57196d1abb5cdb1c57df9cf97a2fc601e6d4_big.svg" type="image/svg+xml"></object> &nbsp; Odp. Otrzymała 17,10 zł reszty.

Obliczmy szerokość prostokąta, czyli <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d2c3fd5f941af0e7480a90e5b4a3a42de8e90932d0fa2053ecb2c7c88643050e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d2c3fd5f941af0e7480a90e5b4a3a42de8e90932d0fa2053ecb2c7c88643050e_big.svg" type="image/svg+xml"></object>

a)&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/fa53c2eb3394f93d70fa76d142441db60c48a05d5c3be65ba669ef2fbb2128ae_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/fa53c2eb3394f93d70fa76d142441db60c48a05d5c3be65ba669ef2fbb2128ae_big.svg" type="image/svg+xml"></object>

Uwaga !!! Aby obliczyć różnicę dwóch liczb, to od większej liczby odejmujemy mniejszą liczbę. a) <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e62faee7883e97d32bc84edf1e16d5f937e873ada1f614422e6aff2c180ec660_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e62faee7883e97d32bc84edf1e16d5f937e873ada1f614422e6aff2c180ec660_big.svg" type="image/svg+xml"></object>

Najpierw obliczmy liczbę a i liczbę b. <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2460b7dc70316c79782945095abfed3a800a36389b8d68992722e3689cef1a73_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2460b7dc70316c79782945095abfed3a800a36389b8d68992722e3689cef1a73_big.svg" type="image/svg+xml"></object>

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