Translation (Algebra)

TRANSLATION OF VERBAL PHRASES/SENTENCES

INTO

MATHEMATICAL PHRASES/SENTENCES

You will be able to familiarize yourself in translating VERBAL PHRASES/SENTENCES into MATHEMATICAL PHRASES/SENTENCES

You will AT LEAST realize that translating phrases/sentences in Math is EASY

Added to

(the) sum of

Total of

Increased by

MORE THAN

(the) difference of

Subtracted from

Decreased by

Diminished by

Reduced by

LESS THAN

(the) product of

Multiplied by

Doubled/tripled/quadrupled

“of”

Twice/thrice (of)

(the) ratio of

(the) quotient of

“over”-when using FRACTION BARS

ADDITIONThe sum of a NUMBER and

8.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let x = the NUMBER

∴ x + 8

15 MORE THAN a NUMBER.

---0O0---0O0--- 0O0---0O0---

SOLUTION

Let m = the NUMBER

∴ m + 15

ADDITIONA number INCREASED by 4.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let r = the NUMBER

∴ r + 4

25 added to a NUMBER.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let p = the NUMBER

∴ p + 25

SUBTRACTION2 LESS THAN a number.

---0O0---0O0--- 0O0---0O0---

SOLUTION

Let c = the NUMBER

∴ c - 2

SUBTRACTION7 diminished by a NUMBER.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let f = the NUMBER

∴ f - 7

A number subtracted from 12.

---0O0---0O0--- 0O0---0O0---

SOLUTION

Let L = the NUMBER

∴ L - 12

SUBTRACTIONA NUMBER decreased by

10.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let a = the NUMBER

∴ a - 10

The difference of TWO numbers.

---0O0---0O0--- 0O0---0O0---

SOLUTION

Let p = the 1st NUMBERb = the 2nd NUMBER

∴ p - b

MULTIPLICATIONThe product of TWO

numbers .---0O0---0O0--- 0O0---0O0---

SOLUTION

Let g = the 1st NUMBERd = the 2nd NUMBER

∴ gd

The TWICE of a number.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let u = the NUMBER

∴ 2u

MULTIPLICATION15 percent of a NUMBER .---0O0---0O0--- 0O0---0O0---

SOLUTION

Let h = the NUMBER

∴ 0.15h

The SQUARE of a number.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let y = the NUMBER

∴ y²

DIVISIONThe RATIO of 7 and y.

---0O0---0O0--- 0O0---0O0---

∴ 7 y

ONE-HALF of a number.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let t = the NUMBER

∴ t 2

DIVISIONThe QUOTIENT of TWO

NUMBERS.---0O0---0O0--- 0O0---0O0---

SOLUTION

Let s = the 1st NUMBERw = the 2nd NUMBER

∴ s w

The SUM of

FOUR CONSECUTIVE INTEGERS.

~~~~~~~~~~~~~~~~~~~~~~~~Solution:

Let x = The 1st INTEGER

x + 1 = The 2nd INTEGER

x + 2 = The 3rd INTEGER

x + 3 = The 4th INTEGER

∴ x + (x + 1) + (x + 2) + (x + 3) + (x + 4)

example 2.1

The SUM of

three consecutive ODD integers.

~~~~~~~~~~~~~~~~~~~~~~~~Solution:




∴ x + (x + 2) + (x + 4)

example 2.2

The SUM of

three consecutive EVEN integers.

~~~~~~~~~~~~~~~~~~~~~~~~Solution:




∴ x + (x + 2) + (x + 4)

example 2.3

TRY to manipulate the phrase by means of SUBSTITUTING an ODD number (e.g. 1)

And you’ll have an ODD number PATTERN~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~

ex. Let x = 1 (The 1st CONSECUTIVE ODD INTEGER)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~

∴ ([1] + 2) = 3-the 2nd CONSECUTIVE ODD INTEGER

([1] + 4) = 5-the 3rd CONSECUTIVE ODD INTEGER

([1] + 6) = 7-the 4th CONSECUTIVE ODD INTEGER

TRY to manipulate the phrase by means of SUBSTITUTING an EVEN number (e.g.

2)And you’ll have an EVEN number PATTERN~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~

ex. Let x = 2 (The 1st CONSECUTIVE ODD INTEGER)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~

∴ ([2] + 2) = 4-the 2nd CONSECUTIVE ODD INTEGER

([2] + 4) = 6-the 3rd CONSECUTIVE ODD INTEGER

([2] + 6) = 8-the 4th CONSECUTIVE ODD INTEGER

Oronse, O. & Mendoza, M./ e-MATH I: Elementary Algebra/ Rex Publishing Inc./ Sampaloc, Manila/ Revised Edition/ ©2010.

WRITTEN NOTES in MATHEMATICS 2

Education

Translation (Algebra)