query: Why is it that $\frac ab\times\frac1c=\frac a{bc}$?
positive_passages.docid: 41510
positive_passages.text: Multiplying and adding fractions
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 61666
negative_passages.text: Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
negative_passages.docid: 123136
negative_passages.text: Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
negative_passages.docid: 123555
negative_passages.text: Proving that if $ab=e$ then $ba=e$
negative_passages.docid: 77902
negative_passages.text: If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
negative_passages.docid: 150320
negative_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?
negative_passages.docid: 118507
negative_passages.text: Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 80684
negative_passages.text: Counter example for $(A \times B) \cap (C \times D) = (A \cap C ) \times (B \cap D)$
negative_passages.docid: 118809
negative_passages.text: If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
negative_passages.docid: 64941
negative_passages.text: Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
negative_passages.docid: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
negative_passages.docid: 65503
negative_passages.text: Identity involving LCM and GCD: $\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$
negative_passages.docid: 88268
negative_passages.text: show $\frac{1}{15}< \frac{1}{2}\times\frac{3}{4}\times\cdots\times\frac{99}{100}<\frac{1}{10}$ is true
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 119964
negative_passages.text: Prove: $1/2(a+b) \times (a - b) = b \times a$ - in three space