Simplifying Algebraic Expressions Quiz For Grade 7
Reviewed by Janaisa Harris
Janaisa Harris, BA (Mathematics)|
High School Math Teacher
Review Board Member
Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.
, BA (Mathematics)
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Are you a student in grade 7th? How easily can you solve algebraic expressions with accuracy? Take this 'Simplifying algebraic expressions quiz' and check your logical and reasoning skills regarding it. An algebraic expression is made up of variables and consonants along with algebraic operations (addition, subtraction, multiplication, etc. ) In this quiz, you need to combine like terms and use the order of operations to simplify algebraic expressions. Do you think you can do so? Go ahead, then!
Questions and Answers
1.
3x + 1 + 8x + 9
A.
12x + 10
B.
5x + 8
C.
11x + 11
D.
11x + 10
Correct Answer
D. 11x + 10
Explanation The given expression is a sum of two terms: 3x + 1 and 8x + 9. To simplify the expression, we can combine the like terms by adding the coefficients of x and the constants separately. Adding 3x and 8x gives us 11x, and adding 1 and 9 gives us 10. Therefore, the simplified expression is 11x + 10.
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2.
2x + 5y - 7x + 8y
A.
9x + 13y
B.
5x + 3y
C.
-5x + 3y
D.
-5x + 13y
Correct Answer
D. -5x + 13y
Explanation The given expression involves adding and subtracting the terms involving x and y. To simplify the expression, we combine like terms by adding the coefficients of x and y separately. In this case, the x terms are 2x and -7x, which combine to give -5x. The y terms are 5y and 8y, which combine to give 13y. Therefore, the simplified expression is -5x + 13y.
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3.
4(x + 8) - 9
A.
4x + 32
B.
4x + 23
C.
12x - 9
D.
4x + 24
Correct Answer
B. 4x + 23
Explanation To solve the expression 4(x + 8) - 9, you can follow these steps:
Distribute the 4 to both terms inside the parentheses:
4(x + 8) = 4x + 32
Now, you have the expression: 4x + 32 - 9.
Subtract 9 from 32:
32 - 9 = 23
Now, you have the simplified expression: 4x + 23.
So, the solution is 4x + 23.
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4.
-3(x + y) + 5(x - y)
A.
2x - 8y
B.
-2x + 2y
C.
8x - 8y
D.
4x - 6y
Correct Answer
A. 2x - 8y
Explanation The given expression is -3(x + y) + 5(x - y). To simplify this expression, we can distribute the -3 and 5 to the terms inside the parentheses. Distributing -3 gives us -3x - 3y, and distributing 5 gives us 5x - 5y. Combining like terms, we have -3x + 5x - 3y - 5y, which simplifies to 2x - 8y. Therefore, the correct answer is 2x - 8y.
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5.
A + b = b + a is an example of the property called
A.
Commutative Property of Addition
B.
Associative Property of Addition
C.
Both A and B
D.
None of these
Correct Answer
A. Commutative Property of Addition
Explanation The given equation, a + b = b + a, demonstrates the commutative property of addition. This property states that the order of the numbers being added does not affect the sum. In other words, when adding two numbers, it does not matter which number is added first, the result will be the same. This property is applicable to addition but not to subtraction, multiplication, or division. Therefore, the correct answer is the Commutative Property of Addition.
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6.
What number is known as the multiplicative identity?
A.
1
B.
2
C.
-1
D.
0
Correct Answer
A. 1
Explanation The number 1 is known as the multiplicative identity because any number multiplied by 1 will result in the original number. In other words, 1 is the identity element for multiplication. When any number is multiplied by 1, it retains its value and does not change. This property is true for all numbers, making 1 the multiplicative identity.
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7.
3x - 5x
A.
2x
B.
-2x
C.
3x
D.
8x
Correct Answer
B. -2x
Explanation The given expression is 3x - 5x. To simplify this expression, we need to combine like terms. In this case, the like terms are the ones with the same variable, which is x. When we subtract 5x from 3x, we get -2x. Therefore, the correct answer is -2x.
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8.
3x + 2x -3x
A.
-2x
B.
2x
C.
-3x
D.
3x
Correct Answer
B. 2x
Explanation The given expression is a combination of like terms. The like terms in the expression are 3x and 2x, which can be combined to give 5x. However, there is also a -3x term in the expression. When we subtract 3x from 5x, we get 2x as the final answer.
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9.
3w - m + w + 6m
A.
3w + 5m
B.
3w + 7m
C.
4w + 7m
D.
4w + 5m
Correct Answer
D. 4w + 5m
Explanation The given expression involves adding and subtracting variables. To simplify it, we can combine like terms. The terms "3w" and "w" can be combined to give "4w", and the terms "-m" and "6m" can be combined to give "5m". Therefore, the simplified expression is "4w + 5m".
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10.
Ab(c) = (ab)c is an example of what property?
A.
Associative Property of Addition
B.
Associative Property of Multiplication
C.
Commutative Property of Multiplication
D.
None of these
Correct Answer
B. Associative Property of Multiplication
Explanation The given equation ab(c) = (ab)c represents the associative property of multiplication. This property states that the grouping of numbers being multiplied does not affect the final result. In this case, it means that multiplying a and b first and then multiplying the result by c will yield the same result as multiplying b and c first and then multiplying the result by a. This property holds true for multiplication, but not for addition or cumulative properties.
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Janaisa Harris |BA (Mathematics)|
High School Math Teacher
Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.
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