DAY 1. Translating Real Life Verbal Phrases into Algebraic Expressions ADDITION (+) Added to, Increased by, Sum, more than, total of SUBTRACTION (-) less than, subtracted from, difference, minus, Diminished by, fewer by MULTIPLICATION (X) percent of, times, multiplied by, product DIVISION (/) quotient, per, divided by, ratio Algebraic Expression - a set of symbols resulting from applying one or more fundamental operations, namely, addition, subtraction, multiplication, and division of constants and variables. Constant - a symbol that has a fixed value Variable - a symbol with no fixed value and is usually represented by an English alphabet. Expressing verbal phrases into mathematical symbols. Verbal Phrase | Mathematical Symbol ---|--- Six increased by two | 6 + 2 Twelve diminished by three | 12 - 3 Fifteen decreased by eleven | 15 - 11 Express the following verbal phrases into mathematical symbols. The quotient of nine and 3 The sum of five and seven Translating verbal phrases into algebraic expressions. Verbal Phrases | Algebraic Expressions ---|--- Six times a number | 6x A number divided by five | n ÷ 5 Translating verbal phrases into algebraic expressions. Verbal Phrases | Algebraic Expressions ---|--- 1. The difference between twenty and a number 2. The product of a number and twelve 3. A number decreased by two DAY 2: Writing Algebraic Equations For Simple Real-Life Situations An algebraic equation is a statement of the equality of two expressions formulated by applying to a set of variables, algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Base Fare is the price to be paid before additional fees are added. Perimeter of a rectangle is the total distance around its outside edges represented by the formula P = 2l + 2w
Answer (1)
To translate verbal phrases into mathematical symbols and algebraic expressions, we need to identify the operations described by the phrases and use the appropriate symbols. Let's go through each of the examples provided:
The quotient of nine and 3 :
In mathematics, the word 'quotient' refers to division.
So, the quotient of nine and 3 is expressed as: 3 9
The sum of five and seven :
The word 'sum' refers to addition.
So, the sum of five and seven is expressed as: 5 + 7
Next, let's express the verbal phrases given in the form of algebraic expressions:
The difference between twenty and a number :
'Difference' indicates subtraction.
Let the unknown number be represented by the variable 'n'.
This expression is written as: 20 − n
The product of a number and twelve :
'Product' denotes multiplication.
Using 'n' to represent the unknown number, the expression is: 12 n
A number decreased by two :
'Decreased by' indicates subtraction.
Let 'n' be the unknown number.
The expression is written as: n − 2
These examples help us understand how to convert verbal descriptions into mathematical language using constants (fixed values) and variables (symbols representing numbers with no fixed value). This skill is essential in solving real-life mathematical problems and equations.
