Common Core Math Worksheets Grade 6

Are you a teacher or parent in search of high-quality, comprehensive Common Core math worksheets for your sixth-grade students? Look no further! Our collection of grade 6 math worksheets is designed to help students master essential math concepts and skills aligned with the Common Core standards. Whether you need worksheets to reinforce specific topics or to provide extra practice, you can find a wide range of engaging worksheets that cater to various learning needs in our carefully curated collection.

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  8th Grade Writing Prompts

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  Negative Fractions On Number Line Worksheets

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What is the value of the variable in the equation 4x - 8 = 12?

The value of the variable in the equation 4x - 8 = 12 is x = 5. This can be found by first adding 8 to both sides of the equation to isolate the variable term, resulting in 4x = 20. Then, divide both sides by 4 to solve for x, giving x = 5.

Solve the expression: 2/3 * (3/5 + 1/2).

To solve the expression 2/3 * (3/5 + 1/2), first simplify the parentheses by finding a common denominator for 5 and 2, which is 10. Therefore, (3/5 + 1/2) becomes (6/10 + 5/10) which is equal to 11/10. Next, multiply 11/10 by 2/3 to get 22/30 which simplifies to 11/15. Therefore, the solution to the expression 2/3 * (3/5 + 1/2) is 11/15.

Find the area of a rectangle with length 10 cm and width 5 cm.

To find the area of a rectangle, you simply multiply the length by the width. In this case, the length is 10 cm and the width is 5 cm. Therefore, the area of the rectangle is 10 cm * 5 cm = 50 square cm.

Simplify the expression: 3(2x + 5) - 4(3x - 2).

To simplify the expression 3(2x + 5) - 4(3x - 2), distribute the coefficients inside the parentheses: 6x + 15 - 12x + 8. Combine like terms by adding the coefficients of x together and the constants together: 6x - 12x + 15 + 8 = -6x + 23. So, the simplified expression is -6x + 23.

Solve the equation: 2/3(x - 4) = 10.

To solve the equation 2/3(x - 4) = 10, first multiply both sides by 3 to get rid of the fraction, giving you 2(x - 4) = 30. Next, distribute the 2 on the left side to get 2x - 8 = 30. Add 8 to both sides to isolate x, which gives you 2x = 38. Finally, divide by 2 to find that x = 19. So, the solution to the equation is x = 19.

What is the perimeter of a square with a side length of 8 inches?

The perimeter of a square with a side length of 8 inches is 32 inches, calculated by multiplying the side length by 4 since all sides of a square are equal in length.

Simplify the expression: 5 + 3(2x - 7) - 2(x + 4).

The simplified expression is 5 + 6x - 21 - 2x - 8, which simplifies further to 4x - 24.

Solve the equation: 4x + 6 = 18 - 2x.

By simplifying both sides of the equation, we get: 4x + 6 = 18 - 2x. Bringing all variables to one side, we have 4x + 2x = 18 - 6. Combining like terms gives us 6x = 12. Dividing both sides by 6, we find x = 2. Therefore, the solution to the equation is x = 2.

Find the volume of a rectangular prism with length 12 cm, width 6 cm, and height 4 cm.

To find the volume of a rectangular prism, you multiply the length, width, and height. In this case, the volume of the rectangular prism with a length of 12 cm, width of 6 cm, and height of 4 cm would be 288 cubic centimeters (12 cm x 6 cm x 4 cm).

Simplify the expression: 7(a + b) - 3c + 2(a - b + c).

To simplify the expression 7(a + b) - 3c + 2(a - b + c), first distribute the coefficients and then combine like terms. This gives us 7a + 7b - 3c + 2a - 2b + 2c. Combining like terms, we get 7a + 2a + 7b - 2b - 3c + 2c, which simplifies to 9a + 5b - c. Thus, the simplified expression is 9a + 5b - c.