Skip to main content

Grade 7 Mathematics Learner’s Book

INNODEMS

Section 2.1 Algebraic Expressions

What is an Algebraic Expression?
🔗
An algebraic expression is a combination of numbers, letters (variables), and mathematical operations such as addition, subtraction, multiplication, and division.
🔗
Why use letters?
🔗
Watch this!
🔗

Subsection 2.1.1 Formation of Algebraic Expression from Real Life Situations

Remember?
🔗
In primary school you learned about algebra. Can you discuss with your friend what you learned?
🔗

Activity 2.1.1.

Group Activity:
🔗
Instructions:
🔗
Form groups of 4-5 students.
🔗
Each group will be given different real-life scenarios.
🔗
Discuss and write algebraic expressions to represent the given situations.
🔗
Discuss your solutions and explain your thoughts win the groups.
🔗
🔗

Example 2.1.1.

An exercise book costs \(ksh 30\text{,}\) and a pen costs \(ksh 15\text{.}\) Jeff buys \(p\) books and \(b\) pens, write an algebraic expression for the total cost.
🔗
Solution.
The cost of one book = ksh 30
🔗
The cost of one pen = ksh 15
🔗
Jeff buys \(p\) books, the total cost of books:
\begin{equation*} = 30 \times p \end{equation*}
🔗
\begin{equation*} = 30p \end{equation*}
🔗
and \(b\) pens, the total cost of pens:
\begin{equation*} = 15 \times b \end{equation*}
🔗
\begin{equation*} = 15b \end{equation*}
🔗
The total cost now is the sum of the two amounts:
🔗
\begin{equation*} = 30p + 15b \end{equation*}
🔗
🔗
🔗

Example 2.1.2.

A boda boda rider charges \(ksh 50 \) for the first \(2 km \) and \(ksh 20 \) for each extra kilometre. If Joy travels \(k \) extra kilometres, form an expression for the total fare for the whole journey.
🔗
Solution.
The fixed charge for the first \(2 km \) = \(ksh 50\)
🔗
Each extra kilometer costs \(ksh 20 \)
🔗
Joy travels \(k \) extra kilometers, the extra charge;
🔗
\begin{equation*} 20 \times k = 20 k \end{equation*}
🔗
The total fare Joy paid is:
🔗
\(fixed charge for the first 2 km + Extra kilometres charges \)
🔗
\begin{equation*} = 50 + 20 k \end{equation*}
🔗
🔗
🔗

Checkpoint 2.1.3.

  1. A farmer has \(t \)cows. The number of goats on his farm is twice the number of cows. Form an algebraic expression for the number of goats.
    🔗
    🔗
  2. Precious Academy buys \(5 \) textbooks at \(b \)shillings each and \(3 \) exercise books at \(50 \) shillings each. Form an expression for the total cost of the books.
    🔗
    🔗
  3. The school bus fuels \(t \) litres of diesel before leaving for a school trip. The trip consumes 12 litres of the fuel. Form an expression for the amount of fuel left after the trip.
    🔗
    🔗
  4. Mama Mwangi’s shop sells \(2 kg \) of sugar at \(y \) shillings per kg and a loaf of bread for \(60 \) shillings. What is the expression for the total amount you can pay for both items from the shop.
    🔗
    🔗
  5. In grade 7, each student contributes \(ksh 20 \) for a class maths project. If there are \(n \) students, form an algebraic expression for the total amount collected from the class.
    🔗
    🔗
🔗
🔗
🔗

Subsection 2.1.2 Formation of Algebraic Expressions from Simple Algebraic Statements involving Addition and Substraction

Activity 2.1.2.

Group Activity:
🔗
Georg has some pencils. He buys \(4\) more pencils from a shop. Later, he gives \(2\) pencils to his friend.
🔗
  1. Use a letter to represent the number of pencils Brian originally had.
    🔗
    🔗
  2. Write an algebraic expression for the total number of pencils Georg has after buying \(4\) more.
    🔗
    🔗
  3. Write an algebraic expression for the number of pencils Georg has after giving away \(2\text{.}\)
    🔗
    🔗
  4. Discuss and compare your answers with other groups.
    🔗
    🔗
🔗
🔗

Example 2.1.4.

Steph is 3 years younger than her sister. If her sister is \(w \) years old, form an algebraic expression for Steph’s age.
🔗
Solution.
Let the age of Steph’s sister be \(w \) years.
🔗
Since Steph is \(3 \) years younger, we subtract \(3 \) from her sister’s age.
🔗
The algebraic expression for Steph’s age is:
🔗
\begin{equation*} (y - 3) \end{equation*}
🔗
Steph’s age is \((y-3) \) years
🔗
🔗
🔗

Checkpoint 2.1.5.

  1. Moraa is \(6 \) years younger than his brother Eric. If Moraa’s age is \(m \) years, write an expression for Moraa’s age
    🔗
    🔗
  2. A farmer has \(b \) bags of beans. After selling \(10 \) bags, write an algebraic expression for the number of bags remaining.
    🔗
    🔗
  3. Maria had \(m \) shillings in her purse. After buying a notebook for \(180\) shillings, write an expression for the amount of money left after buying the notebook.
    🔗
    🔗
  4. A table is \(L \) cm long. A wooden bench is \(30 cm \) shorter than the table. Write an expression for the length of the wooden bench.
    🔗
    🔗
  5. Ken and Sam are playing. The Sam is \(130 cm \) tall, while Ken is \(h cm \) shorter. Write an expression to represent Sam’s height.
    🔗
    🔗
  6. A fisherman from Oriwo banks rows his boat \(d \) kilometers from the shore in the morning. In the afternoon, he rows \(55 \) kilometers further into the lake. Write an algebraic expression for the total distance he has travelled for a day if he rows the boat only twice a day.
    🔗
    🔗
🔗
[Image of a fisherman with the d distance representation for the question]
🔗
🔗
🔗

Subsection 2.1.3 Formation of Algebraic Expressions from Simple Algebraic Statements involving Multiplication and Division

Example 2.1.6.

A carpenter cuts a wooden plank of length \(L \) metres into \(5 \) equal pieces. Write an algebraic expression for the length of each piece.
🔗
Solution.
Total length = \(L \) metres.
🔗
The plank is cut into \(5 \) equal pieces, therefore the length of each piece
🔗
\begin{equation*} = \frac {Length of the plank}{Number of pieces} \end{equation*}
🔗
\begin{equation*} = L ÷ 5 = \frac {L}{5} metres \end{equation*}
🔗
🔗
🔗

Example 2.1.7.

Mama Steve is a farmer. She has \(t \) cows. Each cow produces \(12 \) litres of milk per day.
🔗
Form an algebraic expression for the total amount of milk produced by all the cows in one day.
🔗
Solution.
Each cow produces \(12 \) litres of milk per day.
🔗
Number of cows = \(t \) cows
🔗
Therefore:
🔗
The total amount of milk produced is:
🔗
\begin{equation*} 12 \times t \end{equation*}
🔗
\begin{equation*} = 12 t litres \end{equation*}
🔗
🔗
🔗

Checkpoint 2.1.8.

  1. A trader sold \(n \) bags of maize in a given day, each weighing \(90 \) kg. Form an algebraic expression for the total weight of maize sold on that day.
    🔗
    🔗
  2. A bakery bakes \(x \) loaves of bread per day. Each loaf sells for \(p \) shillings. Form an algebraic expression for the total income from the loaves sold in two day, if the bakery sells all the bread baked everyday.
    🔗
    🔗
  3. Cate a tailor has a given number of pieces of a fabric. Each piece is \(4 \) meters long. By choosing any letter to represent the number of pieces of the fabric, form an algebraic expression for the total length of the fabric.
    🔗
    🔗
  4. \(Tony wa maji \) has \(k \) litres of water in his tank. He needs to distribute the water to \(y \) households in the neighbourhood. What is the expression that represents the amount of water that each household will receives?
    🔗
    🔗
  5. A construction worker mixes \(r \) wheelbarrows of sand with \(5 \) wheelbarrows of cement to make concrete. Write an algebraic expression for the total number of wheelbarrows for the mixture.
    🔗
    🔗
  6. A well has \(v \) litere of water. If a pump extracts \(q \) litres of water per minute from the well, write an expression for the amount of water left after \(t \) minutes of pumping.
    🔗
    🔗
  7. The diagram below represents a stack of \(6 \) books, with each book having a thickness of \(b \) cm.
    🔗
    [Image of the stack of books with distance d for one book]
    🔗
    Form an algebraic expression for the total thickness of the stack.
    🔗
    🔗
  8. The school buys \(t \) bundles of chalk, with each bundle containing 100 sticks of chalk. Form an algebraic expression for the total number of chalk sticks each teacher receives if the school has \(g \) number of teachers.
    🔗
    🔗
🔗
🔗
🔗

Subsection 2.1.4 Simplication of Algebraic Expression in Real Life Situations

Activity 2.1.3.

Group Activity:
🔗
A fruit vendor arranges oranges in crates. Each crate contains \(x \) oranges.
🔗
  • Form an algebraic expression for the total number of oranges in \(6 \) crates.
    🔗
    🔗
  • If a basket contains \(15 \) more oranges than a crate, form an algebraic expression for the number of oranges in a basket.
    🔗
    🔗
  • Form and simplify an algebraic expression for the total number of oranges in 4 crates and 5 baskets.
    🔗
    🔗
  • Discuss and compare your expressions with other groups.
    🔗
    🔗
🔗
🔗

Activity 2.1.4.

Insight
🔗
Simplifying algebraic expressions helps in solving real-world problems efficiently.
🔗
Combining like terms makes algebraic expressions easier to work with.
🔗
🔗

Example 2.1.9.

A cyclist starts with \(d \) kilometres to travel. He covers \(8 \) km in the first hour. His friend has three times the remaining distance to cover.
🔗
Form an algebraic expression for the total distance they both have left to travel.
🔗
Solution.
The cyclist had travelled \(d \) km
🔗
Therefore he had \((d - 8)\) left
🔗
His friend has \(3(d - 8) \) km left
🔗
\begin{equation*} = 3d - 24 \end{equation*}
🔗
The total distance left:
🔗
\begin{equation*} (d - 8) (3d - 24) \end{equation*}
🔗
\begin{equation*} = 4d -32 \end{equation*}
🔗
🔗
🔗

Example 2.1.10.

A trader bought x bags of rice at KSh 4,200 per bag. He also bought sacks of beans, which were y fewer than the number of rice bags, at KSh 3,800 per sack.
🔗
Form an algebraic expression for the total amount of money the trader spent on the food supplies.
🔗
Solution.
The amount spent on x bags of rice:
🔗
\begin{equation*} x \times 4200 \end{equation*}
🔗
\begin{equation*} = 4200 x \end{equation*}
🔗
The number of sacks of beans:
🔗
\begin{equation*} = x - y \end{equation*}
🔗
The amount spent on beans:
🔗
\begin{equation*} 3800 (x - y) \end{equation*}
🔗
Total amount spent:
🔗
\begin{equation*} 4200 x + 3800 (x - y) \end{equation*}
🔗
\begin{equation*} 4200 x + 3800 x - 3800 y \end{equation*}
🔗
\begin{equation*} = 8000 x - 3800y \end{equation*}
🔗
🔗
🔗

Checkpoint 2.1.11.

  1. Kim has maize and bananas in his farm. After harvesting, he sells a bunch of bananas for \(1,500 \) shillings. The price of a sack of maize is \(x \) shillings more than the price of the bananas.
    🔗
    Form an algebraic expression for the total cost of \(4 \) bunches of bananas and \(3 \) sacks of maize.
    🔗
    🔗
  2. Joseph a farmer has \(t \) sacks of maize. He sells \(4 \) sacks and later harvests twice the amount he originally had. Write and simplify an algebraic expression for the total number of sacks he now has
    🔗
    🔗
  3. A matatu driver covers \(y \) kilometres daily. If he increases his distance by \(30 \% \) on weekends, form an algebraic expression for the total distance covered in a week.
    🔗
    🔗
  4. A shopkeeper had \(m \) kilograms of sugar. He sold \(\frac{1}{3} \) of it in the morning and \(5 \) kg in the afternoon.
    🔗
    1. Write an algebraic expression for the remaining amount of sugar.
      🔗
      🔗
    2. One day, the shopkeeper bought \(t \) kilograms of sugar. He repackaged it into \(2 \) kg and \(5 \) kg packs. If the number of \(2 \) kg packs is \(4 \) more than twice the number of \(5 \) kg packs, form an algebraic expression for the total number of packs.
      🔗
      🔗
    🔗
    🔗
  5. In a school library, there are \(n \) shelves of books. Each shelf contains \(5 \) fewer books than the previous one. If the first shelf has \(60 \) books, form an algebraic expression for the number of books on the third shelf.
    🔗
    🔗
  6. A notebook costs \(m \) shillings, while a mathematical set costs \(8 \) shillings more than the notebook.
    🔗
    Form an algebraic expression for the cost of:
    🔗
    1. A mathematical set
      🔗
      🔗
    2. \(3 \) notebooks and \(2 \) mathematical sets
      🔗
      🔗
    🔗
    🔗
🔗
🔗
🔗
🔗
PrevTopNext