The image you've uploaded contains a set of algebraic expressions and identities, grouped into two columns. These are
basic algebraic rules involving variables and operations like multiplication, division, and addition. Let's go through each one, explain what it means, and verify if they are correct.
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✔ Left Column:
1.
`2 × a = 2a`
- This is correct. Multiplying a number by a variable is written as a coefficient in front of the variable.
- So, `2 × a = 2a`.
2.
`3 × q = 3q`
- Same logic as above. The number 3 multiplied by variable `q` becomes `3q`.
- Correct.
3.
`2a × 3 = 6a`
- Here, `2a` means `2 × a`, so:
```
(2 × a) × 3 = 2 × 3 × a = 6a
```
- Correct.
4.
`a × b = ab`
- When two variables are multiplied, we write them next to each other: `a × b = ab`.
- Correct.
---
✔ Right Column:
5.
`2a × 3b = 6ab`
- Break it down:
```
2a × 3b = (2 × a) × (3 × b) = (2 × 3) × (a × b) = 6ab
```
- Correct.
6.
`a ÷ 2 = a/2`
- Dividing a variable by a number is written as a fraction: `a ÷ 2 = a/2`.
- Correct.
7.
`a + a = 2a`
- Adding the same variable: `a + a = 2a` (like terms combine).
- Correct.
8.
`a × a = a²`
- Multiplying a variable by itself gives its square: `a × a = a²`.
- Correct.
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✔ Summary:
All the expressions shown in the image are
correct and represent
fundamental algebraic rules. They demonstrate:
-
Multiplication of numbers and variables
-
Combining like terms
-
Exponent notation for repeated multiplication
-
Division of variables by numbers
These are essential building blocks for algebra and are used frequently in simplifying expressions, solving equations, and more.
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🎯 Final Answer:
✔ All the given algebraic expressions are
correct and follow standard algebraic rules. No errors present.
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions 7th grade.
