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Grammar detail: わけがない

わけがない
there's no way that~; couldn't possibly~
117 words
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verb plain form
い adjective
な adjective + な
+
わけがない
means
there's no way that~; couldn't possibly~
The literal definition of わけがない is 'there's no reason that'. It is used when a speaker wishes to emphasize that X is impossible because of a set of circumstances. It can also be used when a speaker is confident that there is no reason for X to be possible and they wish to emphasize this opinion.
On its own わけ can mean 'the reason'; 'reason', or 'why'. There are several expressions that use わけ, all of which have the core meaning 'reason'.
お
かあ
母
さん
は
いま
今
しごと
仕事
が
たいへん
大変
だから、
ひま
暇
なわけがないよ。
Work is intense for mum right now, so there's no way she'll have time on her hands.
10
じかん
時間
やす
休
みなし
はたら
働
いて
から、
さんじかん
3時間
も
うんてん
運転
できるわけがない。
I couldn't possibly drive for 3 hours after having worked 10 hours without break.
あんなに
くさ
臭
い
チーズがおいしいわけがない。
There's no way a cheese that smells that bad could taste good.
あの
ふたり
2人
がすごく
なか
仲
がいい
から、お
たが
互
い
の
わるくち
悪口
を
い
言
う
わけがないだろう。
Those two get along so well, there would be now way they'd bad-mouth each other.
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Kanji used in this grammar

母
ボ   はは mother   
今
コン   キン   いま now   
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仕
シ   ジ   つかえる to attend to   
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事
ジ   ズ   こと thing; matter   
大
ダイ   タイ   おおきい big   おおいに very much   おお-    
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変
ヘン   unusual   かえる to alter, change   かわる to change   
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暇
カ   ひま free time   
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時
ジ   とき time, occasion   
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間
カン   ケン   あいだ interval, between   ま space, room   
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休
キュウ   やすむ to rest   やすまる to be rested   やすめる to suspend (use etc.)   
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働
ドウ   はたらく to work   
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運
ウン   carry; luck   はこぶ to carry   
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転
テン   ころがる to roll (intr.)   ころがす to roll (tr.)   ころげる to roll about   ころぶ to fall over   
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臭
シュウ   くさい foul-smelling   におう to smell (bad)   
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人
ジン   ニン   ひと person   
仲
チュウ   なか friend; go-between   
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互
ゴ   たがい mutual, reciprocal   
悪
アク   オ   わるい bad   
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口
コウ   ク   くち mouth   
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言
ゲン   ゴン   say; word   こと word, saying   いう to say   
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