[Vuejs]-Vuejs Hide a div when v-model is empty

Better to use v-show in your div:

<div class="hideResult" v-show="showSelectedInjection && selectedProduct != ''">
   {{Math.round(selectedInjection)}}
</div>

Then add @change on second select:

<select v-model="selectedInjection" @change="setShowSelectedInjection">

Also you need to add extra field showSelectedInjection with method setShowSelectedInjection and set showSelectedInjection in setSelectsToDefault:

data:{
showSelectedInjection: false,

(...)

methods:{
            setSelectsToDefault(){
                this.selectedIeProKg = 0;
                this.selectedPreisProIE = 0;
                this.showSelectedInjection = this.haufigkeitMatches.map(h => h.value).includes(this.selectedInjection);
            },
            setShowSelectedInjection(){
                this.showSelectedInjection = true;
            }

Here is a working example: JSFiddle

I don’t know how much it hits your problem because you haven’t provided an example of how the data in your application changes. If a variable depends on another variable, you must observe it and control that change. Just like me here, I follow a variable, check if it is empty and then reset the second variable. If this is still not the case, enter more data, a larger piece of code, then I will also adjust the answer.

new Vue({
  data: {
    selectedInjection: null,
    haufigkeitMatches: []
  },
  computed: {
    round() {
      return Math.round(this.selectedInjection);
    }
  },
  watch: {
    haufigkeitMatches(val) {
      if (!val.length) {
        this.selectedInjection = null;
      }
    }
  },
  methods: {
    add() {
      this.haufigkeitMatches.push({
        name: 'Fus',
        value: 1.1
      }, {
        name: 'Ro',
        value: 2.2
      }, {
        name: 'Dah',
        value: 3.3
      })
    },
    del() {
      this.haufigkeitMatches = [];
    }
  }

}).$mount('#app');

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.js"></script>
<div id="app">
  <select v-model="selectedInjection">
    <option v-for="(match,i) in haufigkeitMatches" :key="i" :value="match.value">{{ match.name }}</option>
  </select>
  <div v-show="selectedInjection">{{round}}</div>
  <div>DIV is {{selectedInjection ? 'visible' : 'invisible'}}</div>
  <button @click="add">Add</button>
  <button @click="del">Del</button>
</div>

This is working for me. It is clearing the old value everytime. Please try this.

<div id="app">
                  <select v-model="selectedProduct" @change="setSelectsToDefault">
                    <option value=""></option>
                    <option v-for="(level1,index) in products"
                            :key="index"
                            :value="level1">{{level1.name}}</option>
                </select>
                <select v-model="selectedInjection">
                    <option v-for="(match,i) in haufigkeitMatches"
                            :key="i"
                            :value="match.value" >{{ match.name }}</option>
                </select>
                <table>
                  <tr>
                  <td class="table-result-body-ipJahr"><div class="hideResult" v-if="selectedInjection> 0">{{Math.round(selectedInjection)}}</div></td>
                </tr>
                </table>
</div>


    "use strict";

    new Vue({
        el: '#app',
        data: {
            selectedPreisProIE: [],
            selectedIeProKg: [],
            selectedGewicht: [],
            selectedInjection: '',
            selectedProduct: null,
            dataJson: [],
            products: [{
                name: "ivi",
                Hint: "45-60 IE/kg alle 5 Tage\n60 IE 1x/Woche\n30-40 IE 2 x/Woche",
                frequency: [1, 2, 8]
            }, {
                name: "ynovi",
                Hint: "40-50 IE/kg\n2x/Woche im Abstand\nvon 3-4 Tagen",
                frequency: [2, 6, 7]
            }, {
                name: "octa",
                Hint: "50 (25-65) IE/kg\nalle 3-5 Tage",
                frequency: [6, 7, 8]
            }, {
                name: "eroct",
                Hint: "50 IE/kg \nalle 4 Tage",
                frequency: [7]
            }, {
                name: "ltry",
                Hint: "20-40 I.E./kg\n2-3x/Woche",
                frequency: [2, 3]
            }, {
                name: "ate",
                Hint: "20-40 I.E./kg\nAlle 2-3 Tage",
                frequency: [5, 6]
            }, {
                name: "Facto A",
                Hint: "20-40 I.E./kg\nAlle 2-3 Tage",
                frequency: [5, 6]
            }, {
                name: "Eight",
                Hint: "40-60 I.E./kg \nJeden 3.Tag oder\n2x/Woche",
                frequency: [2, 3, 5, 6]
            }, {
                name: "iq_Vima",
                Hint: "20-40 I.E./kg\nAlle 2-3 Tage",
                frequency: [5, 6]
            }, {
                name: "Afla",
                Hint: "20-50 I.E./kg\n2-3x/Woche",
                frequency: [2, 3]
            }, {
                name: "Pma",
                Hint: "20-40 I.E./kg\nAlle 2-3 Tage",
                frequency: [5, 6]
            }, {
                name: "others",
                Hint: "Individuell",
                frequency: [1, 2, 3, 4, 5, 6, 7, 8]
            }],
            haufigkeit: [{
                name: "1x / Woche",
                id: 1,
                value: 52.1428571429
            }, {
                name: "2x / Woche",
                value: 104.2857142857143,
                id: 2
            }, {
                name: "3x / Woche",
                value: 156.4285714285714,
                id: 3
            }, {
                name: "alle 1 Tage",
                value: 365,
                id: 4
            }, {
                name: "alle 2 Tage",
                value: 182.5,
                id: 5
            }, {
                name: "alle 3 Tage",
                value: 121.6666666666667,
                id: 6
            }, {
                name: "alle 4 Tage",
                value: 91.25,
                id: 7
            }, {
                name: "alle 5 Tage",
                value: 73,
                id: 8
            }]
        },
        computed: {
            haufigkeitMatches: function haufigkeitMatches() {
                var _this = this;

                if (this.selectedProduct) {
                    return this.haufigkeit.filter(function (x) {
                        return _this.selectedProduct.frequency.includes(x.id);
                    });
                }
            },
        },
        methods:{
            setSelectsToDefault(){
                this.selectedIeProKg = 0;
                this.selectedPreisProIE = 0;
                this.selectedGewicht = 0;
                this.selectedInjection='';
            }
            }
    });