This document provides examples and explanations of algebraic expressions and equations. It begins by defining variables in expressions and equations. Examples are then given of translating sentences to algebraic expressions and equations. The document also distinguishes between expressions and equations. Several word problems are presented and solved, writing the corresponding algebraic equations. The key steps are to understand the problem, plan by identifying the variables and mapping words to symbols, solve the resulting equation, and check the work.

1. ALGEBRAIC
EXPRESSIONS AND
EQUATIONS
ARTURO D. DEL ROSARIO JR.
Mathematics 6 Quarter 3 Week 4

2. What you need to learn?
1. Translate real-life verbal expressions
and equations into letters or symbols
and vice versa.
2. Define the variables in the given
expressions and equations.

3. REVIEW 1
1. Represent the sentence: “The
sum of a number and four is
twelve.” as an algebraic
equation.
a. n + 4 = 12 b. 12 + 4 = n
c. n + 4 d. n + 12

4. 2. “Twice a number decreased by
five” when written in algebraic
expression is _______________.
a. n - 5 × 2 b. n - 5
c. 5 - 2n d. 2n - 5

5. 3. Translate: “the sum of a
numbers and 50” into
algebraic expression.
a. n - 50 b. n + 50
c. n × 50 d. n ÷ 50

6. REVIEW 2
Direction: Identify each of the following statements
if it is an Expression or an Equation. Write your
answer in the space before the number.
__________ 1. Seven more than twice a number.
__________ 2. Nine subtracted from a number.
__________ 3. The sum of a number and 8 is twelve.
__________ 4. Twice a number decreased by five is
equal to 19.
__________ 5. Twice the sum of a number and 3 is
twenty-five.
Expression
Equation
Expression
Equation
Equation

7. Whats New?
PROBLEM OPENER:
An electrician earns ₱150.00 per
hour and spends ₱200.00 a day on
gasoline. Write an algebraic
expression that represents his
remaining earnings for one day if
he works for n hours on that day.

8. GIVEN:
₱150.00
n
₱200.00
Guide Questions:
1) How much does the
electrician earn per hour?
2) If he works for n hours on
one, how much will he earn?
3) How much does he spends
for gasoline?
4) After spending on gasoline,
how much will be his
remaining earnings for one
day?

9. GIVEN:
₱150.00
₱200.00
n
n150-200
PROBLEM OPENER:
An electrician earns ₱150.00 per hour
and spends ₱200.00 a day on gasoline.
Write an algebraic expression that
represents his remaining earnings for
one day if he works for n hours on that
day.

10. MORE EXAMPLES
Claudine saved ₱200.00 this week
from her allowance. This amount is
₱100.00 more than twice the amount
she saved last week.
If n is the amount she saved last
week, write an algebraic equation
that represents this situation.

11. Claudine saved ₱200.00 this week from her
allowance. This amount is ₱100.00 more than
twice the amount she saved last week.
Saved this week twice the amount last week
is more than
100
₱200.00 = n
2x
+
₱100.00

13. If thrice a number is decreased
by 15, the result is 12. What is
the number?
3n – 15 = 12
3n – 15 = 12
3n = 12 + 15
3n
=
27
3 3
n = 9
+

14. Annie bought 2 kilos of meat at
₱370.00 per kilo and 3 kilos of
fish. She paid a total of ₱1,370.00.
Let n be the cost of a kilo of fish.
What is the correct equation for
the problem?

15.  Solution: Translate the following keywords/phrases to symbols
 2 kilos of meat at ₱370.00 per kilo ⇒
 3 kilos of fish that cost n kilo ⇒
 Total amount paid ⇒ ₱1, 370.00
2 x 370
3 x n
Annie bought 2 kilos of meat at ₱370.00
per kilo and 3 kilos of fish. She paid a
total of ₱1,370.00. Let n be the cost of a
kilo of fish. What is the correct equation
for the problem?

16. Therefore, the algebraic equation that represents the problem is:
(2 x 370) + (3 x n) = 1 370
740 + (3 x n) = 1, 370
740 3 x n =1, 370 -
(3 x n) = 630
3 = 3
(3 x n) =630
N= 210

17. Mr. Dela Cruz own a water refilling
station. He had 143 customers
this week, 15 fewer than last week.
Write an algebraic equation that
will give the number of customers
they had last week if x be the
number of customers, they had
last week.

18. Mr. Dela Cruz owns a water refilling station. He had 143 customers
this week, 15 fewer than last week. Write an algebraic equation that will
give the number of customers they had last week if x be the number of
customers, they had last week.
Solution: Translate the keywords/phrases to symbols.
Fifteen fewer than the number last week is 143
x - 15 = 143
Therefore, the algebraic equation that represents the problem is
x – 15 = 143
Computation : x – 15 = 143
: x = 143 + 15
: x = 158 customers
Therefore: Mr. Dela Cruz has 158 costumers last week.

20. 5
4
3
2
1

21. UNDERSTAND
PLAN
SOLVE
CHECK