Difference between revisions of "Divide a Number Problems"

Latest revision as of 17:47, 1 May 2023

[Expand]30 into 4 parts

[Expand]600 into 3 parts

Divide Ten into Two Parts

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=24+\frac{3}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(48+\frac{1}{6}\right)\sdot a\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{5}\sdot\left(a\sdot b\right)\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{1}{3}\right)\sdot\left(a\sdot b\right)\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(2+\frac{1}{4}\right)\sdot a^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{22}{49}\right)\sdot a^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=4\sdot a^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=100\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=\frac{1}{5}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6+\frac{1}{3}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot b=\left(20+\frac{1}{4}\right)b\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50-b=m^2\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50+b=m^2\end{cases}

Divide Eleven into Two Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=11\\\scriptstyle\frac{1}{2}a+\frac{1}{4}a=\frac{1}{3}b+\frac{1}{5}b\end{cases}

Divide Twenty into Two Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=20\\\scriptstyle b=4a\end{cases}

Divide Twenty-Four into Two Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=24\\\scriptstyle\frac{2}{3}a+\frac{3}{4}b=a\end{cases}

Divide Thirty into Two Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle\frac{a}{b}=27\end{cases}

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle4a=3b\end{cases}

Divide Ten into Three Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}

Divide Eighteen into Three Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b+c=18\\\scriptstyle a-\frac{1}{5}a=b+\frac{1}{3}b=c\sdot\left(2+\frac{1}{2}\right)\end{cases}

Divide Twenty-Seven into Three Parts

[Expand]

\scriptstyle a^3+b^3+c^3=27

Divide Thirty into Three Parts

[Expand]

\scriptstyle\begin{cases}\scriptstyle a+b+c=30\\\scriptstyle7a=\frac{b}{5}=\frac{c}{10}\end{cases}

@@ Line 3: / Line 3: @@
 	[[category: #divide a number]]
 	[[comment: 30 into 4 parts]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed">600 into 3 parts<div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: 600 into 3 parts]]
 }}</div></div>
 <br>
@@ Line 150: / Line 156: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, a/b+b/a=4¼]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10, a/b+b/a=√5]]
 }}</div></div>
 <br>
@@ Line 156: / Line 168: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, a/b-b/a=5/6]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10, b/a-a/b=5/6]]
 }}</div></div>
 <br>
@@ Line 162: / Line 180: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, a/b-b/a=3¾]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10, (b/a)·(b-a)=24]]
 }}</div></div>
 <br>
@@ Line 168: / Line 192: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, b²-a²=50]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10, a²-b²=80]]
 }}</div></div>
 <br>
@@ Line 212: / Line 242: @@
 }}</div></div>
 <br>
-<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}</math><div class="mw-collapsible-content">
-{{#annotask:
-	[[category: #divide a number]]
-	[[comment: a+b=10, a²-b²=80]]
-}}</div></div>
-<br>
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}</math><div class="mw-collapsible-content">
 {{#annotask:
@@ Line 246: / Line 271: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, (b/a)²·a=32]]
-}}</div></div>
-<br>
-<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}</math><div class="mw-collapsible-content">
-{{#annotask:
-	[[category: #divide a number]]
-	[[comment: a+b=10, (b/a)·(b-a)=24]]
 }}</div></div>
 <br>
@@ Line 326: / Line 345: @@
 }}</div></div>
 <br>
-<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}</math><div class="mw-collapsible-content">
-{{#annotask:
-	[[category: #divide a number]]
-	[[comment: a+b=10, a/b+b/a=√5]]
-}}</div></div>
-<br>
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}</math><div class="mw-collapsible-content">
 {{#annotask:
 	[[category: #divide a number]]
 	[[comment: a+b=10, (a/b)²+(b/a)²=3]]
-}}</div></div>
-<br>
-<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
-{{#annotask:
-	[[category: #divide a number]]
-	[[comment: a+b=10, b/a-a/b=5/6]]
 }}</div></div>
 <br>
@@ Line 350: / Line 358: @@
 }}</div></div>
 <br>
 <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}</math><div class="mw-collapsible-content">
@@ Line 393: / Line 399: @@
 	[[category: #divide a number]]
 	[[comment: a+b=10, (40/a)²·(40/b)²=625]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50-b=m^2\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10,20+a=n²,50-b=m²]]
+}}</div></div>
+<br>
+<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50+b=m^2\end{cases}</math><div class="mw-collapsible-content">
+{{#annotask:
+	[[category: #divide a number]]
+	[[comment: a+b=10, 20+a=n²,50+b=m²]]
 }}</div></div>
 <br>

Category	Comment	Link	Annotated text
word problem/divide a number	600 into 3 parts	קצור_המספר#gOdu	Similarly, if we wish to divide them by 3, so that the first gets a half, the second a third, and the third a quarter. : $\scriptstyle600=\frac{1}{2}a+\frac{1}{3}a+\frac{1}{4}a$ וכן אם אמרנו לחלקם על ג' ויהיה לראשון יחס החצי ולשני יחס השליש ולשלישי יחס הרביע
word problem/divide a number	600 into 3 parts	קצור_המספר#zdLv	For example: we wish to divide six hundred by three, so that the first gets double, the second triple, and the third quintuple. : $\scriptstyle600=2a+3a+5a$ ויהיה ‫104rהמשל בזה רצינו לחלק שש מאות על שלשה בענין שיצא לא' ביחס השנים ולשני ביחס השלשה ולשלישי ביחס הה‫'

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, ab=21	חשבון_השטחים#uEcK	We divided ten into two parts, then we multiplied the one [part] by the other and the result was 21. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$ חלקנו עשרה לשני חלקים והכינו האחד על האחר והיה עשרים ואחד
word problem/divide a number	a+b=10, ab=21	תחבולות_המספר#Wntm	[5] He said: the fifth problem is as if you are told: divide ten into two parts, such that when we multiply one part by the other the result is 21. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$ אמ' והשאלה החמישית כמו אם יאמרו לך תחלק עשרה לשני חלקים באופן שכאשר נכה החלק האחד באחר יעלה עשרים ~~ורביע~~ ואחד
word problem/divide a number	a+b=10, ab=21	אגרת_המספר#W549	5) We divided ten into two parts. :We multiplied one part by the other [part] and [the product] was 21. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\\\end{cases}$ החמישית עשרה חלקנום לשני חלקים והכינו אחד מהם בשני והיה כ"א
word problem/divide a number	a+b=10, ab=21	ספר_המספר_/_אליהו_מזרחי#EcDu	The example: if you want to divide ten into two parts, so that the product of the two parts by each other is 21? :: $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$ המשל בזה אם רצית לחלק העשרה לשני חלקים שיעלה מהכאת ב' החלקי' זה עם זה כ"א
word problem/divide a number	a+b=10, ab=21	ספר_ג'יבלי_אלמוקבאלא#Ibmi	Divide ten into two parts such that when one [part] is multiplied by the other the result is 21. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$ תעשה לי מעשרה שני חלקים שכשהוכה האחד באחר יעשה כ"א

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, a²=9b	אגרת_המספר#KEkF	4) We divided ten into two parts. :We multiplied one part by itself, we multiplied the other part by the nine, and the [products] are equal. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\\\end{cases}$ הרביעית עשרה חלקנום לשני חלקים והכינו החלק האחד בעצמו והשני הכינוהו בתשעה והם שוים
word problem/divide a number	a+b=10, a²=9b	חשבון_השטחים#X9cD	We divided ten into two parts, then we multiplied the smaller part by nine and the larger part by itself and the [products] were equal. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}$ חלקנו עשרה לשני חלקים והכינו החלק הקטן על תשעה והגדול על עצמו והיו שוים
word problem/divide a number	a+b=10, a²=9b	ספר_המספר_/_אליהו_מזרחי#IfkV	The example: if you want to know how to divide ten into two parts in such a way that the square of the greater part of it is equal to the product of the smaller part by 9? :: $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9\sdot b\end{cases}$ המשל בזה אם רצית לדעת היאך נחלק העשרה לשני חלקים באופן שיהיה מרובע החלק הגדול ממנו שוה לעולה מהכאת החלק הקטן ממנו עם ט‫'
word problem/divide a number	a+b=10, a²=9b	תחבולות_המספר#7Ia4	[4] He said: the fourth problem is as if you are told: divide ten into two parts, such that the product of the larger part by itself is the same as the product of the smaller part multiplied by nine. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}$ אמ' והשאלה הרביעית היא כמו אם יאמרו לך תחלק עשרה לשני חלקים באופן שיהיה העולה מהכאת החלק הגדול בעצמו כמו הכאת החלק הקטן בתשעה

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, a²=1½ab	תחבולות_המספר#nJqx	[1] He said: the first problem is as if you are told: divide ten into two parts, such that the product of the larger by itself is the same as one time and a half of the product of the one part by the other. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(a\sdot b\right)+\frac{1}{2}\sdot\left(a\sdot b\right)\end{cases}$ אמ' והשאלה הראשונה היא כמו אם יאמרו לך תחלק עשרה לשני {{#annot:term\|606,1259\|Vr9G}}חלקים{{#annotend:Vr9G}} באופן שתהיה הכאת החלק הגדול בעצמו כמו פעם וחצי מהעולה מהכאת החלק האחד באחר
word problem/divide a number	a+b=10, a²=1½ab	חשבון_השטחים#Dmzf	The first problem of the six is: If you are told: divide ten into two parts, then multiply one part by the other and multiply the larger part by itself. The [product] of the part that is multiplied by itself is the same as the product of the one part by the other and as its half. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(a\sdot b\right)+\frac{1}{2}\sdot\left(a\sdot b\right)\end{cases}$ והשאלה הראשונה מן הששה היא אם יאמרו לך תחלק עשרה לשני חלקים ותכה החלק האחד על האחר ותכה החלק הגדול על עצמו ויהיה החלק המוכה על עצמו כמו הכאת החלק האחד על האחר וכמו חציו

Difference between revisions of "Divide a Number Problems"

Latest revision as of 17:47, 1 May 2023

Contents

Divide Ten into Two Parts

Divide Eleven into Two Parts

Divide Twenty into Two Parts

Divide Twenty-Four into Two Parts

Divide Thirty into Two Parts

Divide Ten into Three Parts

Divide Eighteen into Three Parts

Divide Twenty-Seven into Three Parts

Divide Thirty into Three Parts

Navigation menu

Personal tools

Namespaces

Variants

Views

More

Search

Navigation

Tools

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, 10²=6¼a²	ספר_המספר_/_אליהו_מזרחי#dVaD	The example: if you want to divide ten into two different parts, so that the square of 10 is 6 and a quarter times as the square of one of the two parts of ten. :: $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}$ המשל בזה אם רצית לחלק העשרה על ב' חלקים מתחלפים באופן שיהיה מרובע הי' ו' ורביע פעם כמרובע החלק האחד משני חלקי העשרה
word problem/divide a number	a+b=10, 10²=6¼a²	חשבון_השטחים#jgC7	You divide ten into two parts, then multiply one of them by itself and multiply the ten by itself. :The product of ten by itself is the same as the product of one of the parts by itself 6¼ times. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle10^2=a^2\sdot\left(6+\frac{1}{4}\right)\end{cases}$ עשרה תחלקהו לשני חלקים ותכה אחד מהם על עצמו ותכה העשרה על עצמו ויהיה העולה מהכאת עשרה על עצמו כמו העולה מהכאת אחד החלקים על עצמו ששה פעמים ורביע
word problem/divide a number	a+b=10, 10²=6¼a²	תחבולות_המספר#LNn6	[2] He said: and the second problem is as if you are told: divide ten into two parts, such that the product of ten by itself is the same as the product of one of the parts by itself 6¼ times. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle10^2=a^2\sdot\left(6+\frac{1}{4}\right)\end{cases}$ אמ' והשאלה השנית כמו אם יאמרו לך תחלק עשרה לשני חלקים באופן שיהיה העולה מהכאת עשרה בעצמו כמו הכאת העולה מהכא' אחד החלקי' בעצמו ששה פעמים ורביע

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, b/a=4	חשבון_השטחים#PsKJ	Divide ten into two parts, then divide the larger part by the smaller part and the result is four. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}$ תחלק עשרה לשני חלקים ותחלק החלק הגדול על החלק הקטן ויגיע לחלק ארבעה
word problem/divide a number	a+b=10, b/a=4	אגרת_המספר#xiQN	3) We divided ten into two parts. :We divided one [part] by the other [part] and the result of division is 4. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\\\end{cases}$ השלישית עשרה חלקנום לשני חלקים וחלקנו האחד על השני יצא בחלוקה ד‫'
word problem/divide a number	a+b=10, b/a=4	תחבולות_המספר#ogdI	[3] He said: the third problem is as if you are told: divide ten into two parts, such that when you divide the larger part by the smaller part the quotient is four. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}$ אמ' והשאלה השלישית היא כמו אם יאמרו לך תחלק עשרה לשני חלקים באופן שכאשר תחלק החלק הגדול על החלק הקטן יגיע לחלק ארבעה

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, b/a=5	מלאכת_המספר#JKp7	Question: if ten is divided into two parts, such that when one is divided by the other the result of division is 5. שאילה אם יחלקו העשרה בב' חלקי' שהאחד נחלק באחר שיצאו מהחלוקה ה‫'
word problem/divide a number	a+b=10, b/a=5	ספר_ג'יבלי_אלמוקבאלא#xcyr	Divide ten into two parts, such that when we multiply the one by the other it yields five. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}$ עשה לי מעשרה שני חלקי' אשר כשנחלק האחד באחר יעשה חמשה
word problem/divide a number	a+b=10, b/a=5	ספר_האלזיברא#LwGM	Question: I want to divide the number ten into two parts, so that when the one part is divided by the other part the quotient is five. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}$ שאלה רציתי לחלק מספר עשרה לשני חלקים כאשר {{#annot: term \| #to divide, #חולק \| p2Os}}חלק{{#annotend:p2Os}} החלק האחד בחבירו הגיע בחלוק ה‫'

Category	Comment	Link	Annotated text
word problem/divide a number	a+b=10, a/b+b/a=√5	חשבון_השטחים#t2zn	This is as if we said: you divided ten into two parts, then divided each part by the other, and [the sum of the quotients] is the root of five. :: $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}$ והוא כמו שאמרנו חלקת עשרה לשני חלקים וחלקת כל אחד מהם על האחר ועלה שרש חמשה
word problem/divide a number	a+b=10, a/b+b/a=√5	חשבון_השטחים#BWTC	[41] If you are told: you divided ten into two parts, then you divided each part by the other, and summed the quotients, and [the sum] is a root of five dirham. : $\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}$ ואם יאמרו לך חלקת עשרה לשני חלקים וחלקת כל חלק על האחר וקבצת מה שעלה לכל חלק ויהיה שרש חמשה דרהמי