Hello, young mathematicians! Today, we’re going to learn how to create algebraic expressions. An algebraic expression is a way to represent a situation using numbers, variables, and mathematical operations. Let’s explore this with some examples.
Example 1: Adding Beads to a Bag
Scenario: Alia has k beads in a bag. Write an expression for the total number of beads she has when:
a. She puts in two more beads.
Solution: To find the total number of beads when Alia adds 2 more beads to her bag, we write the expression:
k + 2
b. She takes out 5 beads.
Solution: To find the total number of beads when Alia takes out 5 beads from her bag, we write the expression:
k−5k – 5
Example 2: Doubling the Temperature
Scenario: The temperature on Friday was t°C. Write an expression for the temperature when it is twice as warm as it was on Friday.
Solution: “Twice” means we multiply by 2. The expression for the temperature when it is twice as warm is:
2 × t = 2t°C
Example 3: Adding Paperclips
Scenario: There are two envelopes on the table. Each envelope has x paperclips. Sania puts 4 more paperclips on the table. How many paperclips are there altogether?
Solution: Each envelope has x paperclips. So, the total paperclips in two envelopes are:
x + x = 2x
Adding the 4 paperclips that Sania puts on the table:
2x + 4
Example 4: Counting Counters in Jars
Scenario: There are 3 jars. Each jar has p counters. 5 counters are placed beside these jars. How many counters are there altogether?
Solution: Each jar has p counters, so the total counters in the jars are:
p + p + p = 3p
Adding the 5 counters placed beside the jars:
3p + 5
Example 5: Multiplying and Subtracting
Scenario: Write an expression following these steps:
- Start with p
- Multiply it by 3
- Then subtract 5
Solution: First, multiply p by 3:
3p
Next, subtract 5 from 3p:
3p – 5
Example 6: Subtracting from a Number
Scenario: Write an expression following these steps:
- Start with q
- Multiply it by 2
- Then subtract the result from 24
Solution: First, multiply q by 2:
2q
Next, subtract 2q from 24:
24 – 2q
Summary
Constructing expressions in algebra involves translating a situation into a mathematical statement using numbers, variables, and operations. By following the steps carefully, you can create accurate expressions to represent different scenarios. Keep practicing, and soon you’ll be able to write any algebraic expression with ease!
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