Learning Outcomes
Translate 'the ratio of 9 more than x to x' into an algebraic expression. Okay; 'the ratio of (this) to (that)' means '(this) divided by (that)', so I know I'll be ending up with a division. But the items being divided aren't simple.
- Translate statements into algebraic equations involving addition, subtraction, multiplication, and division
Translate Word Phrases to Algebraic Equations
Remember, an equation has an equal sign between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals. Some words that translate to the equal sign are:
- is equal to
- is the same as
- is
- gives
- was
- will be
Google's free service instantly translates words, phrases, and web pages between English and over 100 other languages. Translate from English to French. Be it words, phrases, texts or even your website pages - Translate.com will offer the best. Translate Word Phrases to Algebraic Equations. Remember, an equation has an equal sign between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals. Some words that translate to the equal sign are: is equal to; is the same as.
It may be helpful to put a box around the equals word(s) in the sentence to help you focus separately on each phrase. Then translate each phrase into an expression, and write them on each side of the equal sign.
We will practice translating word sentences into algebraic equations. Some of the sentences will be basic number facts with no variables to solve for. Some sentences will translate into equations with variables. The focus right now is just to translate the words into algebra.
example
Translate the sentence into an algebraic equation: The sum of [latex]6[/latex] and [latex]9[/latex] is [latex]15[/latex].
Solution
The word is tells us the equal sign goes between 9 and 15.
The word is tells us the equal sign goes between 9 and 15.
Locate the “equals” word(s). |
Write the = sign. |
Translate the words to the left of the equals word into an algebraic expression. |
Translate the words to the right of the equals word into an algebraic expression. |
example
Translate the sentence into an algebraic equation: The product of [latex]8[/latex] and [latex]7[/latex] is [latex]56[/latex].
Show SolutionSolution
The location of the word is tells us that the equal sign goes between 7 and 56.
The location of the word is tells us that the equal sign goes between 7 and 56.
Locate the “equals” word(s). |
Write the = sign. |
Translate the words to the left of the equals word into an algebraic expression. |
Translate the words to the right of the equals word into an algebraic expression. |
example
Translate the sentence into an algebraic equation: Twice the difference of [latex]x[/latex] and [latex]3[/latex] gives [latex]18[/latex].
Show SolutionSolution
Locate the “equals” word(s). | |
Recognize the key words: twice; difference of …. and …. | Twice means two times. |
Translate. |
Translate to an Equation and Solve
Now let’s practice translating sentences into algebraic equations and then solving them. We will solve the equations by using the Subtraction and Addition Properties of Equality.
example
Translate and solve: Three more than [latex]x[/latex] is equal to [latex]47[/latex].
Show SolutionSolution
Three more than x is equal to [latex]47[/latex]. | ||
Translate. | [latex]x+3=47[/latex] | |
Subtract [latex]3[/latex] from both sides of the equation. | [latex]x+3color{red}{-3}=47color{red}{-3}[/latex] | |
Simplify. | [latex]x=44[/latex] | |
We can check. Let [latex]x=44[/latex] . | [latex]x+3=47[/latex] | |
[latex]44+3=47[/latex] | ||
[latex]47=47[/latex] |
So [latex]x=text{}44[/latex] is the solution.
example
Translate and solve: The difference of [latex]y[/latex] and [latex]14[/latex] is [latex]18[/latex].
Show SolutionSolution
The difference of y and [latex]14 is 18[/latex]. | ||
Translate. | [latex]y-14=18[/latex] | |
Add [latex]14[/latex] to both sides. | [latex]y-14color{red}{+14}=18color{red}{+14}[/latex] | |
Simplify. | [latex]y=32[/latex] | |
We can check. Let [latex]y=32[/latex] . | [latex]y-14=18[/latex] | |
[latex]32-14=18[/latex] | ||
[latex]18=18[/latex] |
So [latex]y=32[/latex] is the solution.
In the following video we show more examples of how to translate an equation into words and solve. Note that this is different from the written examples on this page because we start with the mathematical equation then translate it into words.
Number to Letter A1Z26 Converter
Letter to Number A1Z26 Encoder
Calculate a word's value
Tool to convert letters to numbers and vice versa. The Letter-to-Number Cipher (or Number-to-Letter Cipher) consists in replacing each letter by its position in the alphabet, for example A=1, B=2, Z=26, hence its over name A1Z26.
Answers to Questions
How to encrypt using Letter-to-Number/A1Z26 cipher?
A1Z26 encryption requires to count the positions/ranks of letters in the alphabet. If it is the Latin alphabet of 26 characters here is the correspondence table letter ↔ number/value: Itube studio 7 4 0 52.
A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Replace each letter with its position in the alphabet (A = 1, B = 2, .. Z = 26)
Example:DCODE is encrypted 4-3-15-4-5 by alphanumeric substitution
Often the space character is also encoded with the number 0
How to decrypt Number-to-Letter cipher?
Decryption requires taking each number and replace it with the letter of same position in the alphabet: 1 = A, 2 = B, .. 26 = Z
A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Translator 1 2 1 Equals Grams
Example:1.12.16.8.1.2.5.20 gives ALPHABET
Translator 1 2 1 Equals 2/3
How to recognize Letter-to-Number ciphertext?
The crypted message is made of numbers between 1 and 26, sometimes the number 0 is used to code a space. Disk graph 2 1 15 inch.
The digit 5 for E is supposed to appear regularly for an english text.
This encryption is sometimes called alphanumeric code.
What are the variants of the Letter-to-Number cipher?
Shift of numbers: the alphabet can start with A = 0 or A = 1, but also A = 65 or A = 97 (ASCII code).
Use of a supplementary character for space (usually 0 or 27)
Use of leading zeros to be able to concatenate numbers AB = 0102, else AB = 12 and 12 = L.
Use of a custom alphabet, or reversed alphabet (A=26, Z=1)
Bookends 12 7 4 download free. Use of modulo 26 in order to get 1=A,2=B,..26=Z then 27=A, 28=B etc.
Source code
dCode retains ownership of the online 'Letter Number (A1Z26) A=1, B=2, C=3' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Letter Number (A1Z26) A=1, B=2, C=3 download for offline use on PC, tablet, iPhone or Android !
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