6th Grade Math Flashcards

Which two expressions, when applied to any variable value larger than zero, are equivalent?

Answer: b + b + 3c and 2b +3c

Equivalent expressions represent the same value regardless of the variable's input. In option A, 'b + b' simplifies to '2b'. Therefore, 'b + b + 3c' is equivalent to '2b + 3c' because the like terms are combined correctly. The other options involve incorrect simplification or distribution, making them not equivalent.

This equation is displayed below. 12 – 9 + c equals 12. For what value of c, the equation is true?

Answer: 9

To find the value of 'c' that makes the equation true, we first simplify the left side of the equation: '12 - 9' equals '3'. The equation then becomes '3 + c = 12'. To isolate 'c', subtract 3 from both sides of the equation, resulting in 'c = 12 - 3', which simplifies to 'c = 9'.

Which expressions are equivalent?

Answer: 4(3x + 4x) and 12x + 16x

Equivalent expressions have the same value for any variable. In option D, applying the distributive property to '4(3x + 4x)' gives '4 * 3x + 4 * 4x', which simplifies to '12x + 16x'. Alternatively, simplifying inside the parentheses first, '3x + 4x' equals '7x', so '4(7x)' is '28x'. Since '12x + 16x' also equals '28x', the expressions are equivalent.

Which of the following expressions represents 60 – 3y -9?

Answer: 3(17 – y)

To find the equivalent expression, first simplify the given expression '60 – 3y - 9' by combining the constant terms: '60 - 9' equals '51'. This simplifies the expression to '51 - 3y'. Now, check the options to see which one simplifies to '51 - 3y'. Option C, '3(17 – y)', uses the distributive property to become '3 * 17 - 3 * y', which is '51 - 3y', matching the simplified original expression.

The formula V = s3 can be used to find the volume, V, of any cube having a side length, s. What is the 2.3 centimeter side length's volume, measured in cubic centimeters?

Answer: 12.167

The problem provides the formula for the volume of a cube, V = s³, where 's' is the side length. To find the volume, substitute the given side length, 2.3 centimeters, into the formula. Calculating 2.3 × 2.3 × 2.3 results in 5.29 × 2.3, which equals 12.167. Therefore, the volume of the cube is 12.167 cubic centimeters.

Which values satisfy the inequality n ≥ – 5?

Answer: {- 5 , -4.5, – 3}

The inequality n ≥ – 5 means that 'n' must be a value greater than or equal to -5. We need to check which set of values satisfies this condition for all its members. Option D, {-5, -4.5, -3}, contains values where -5 is equal to -5, and both -4.5 and -3 are greater than -5. All other options contain at least one value that is less than -5, such as -6 or -7, making them incorrect.

It's Toni and Kent, crafting necklaces. 25 necklaces are made by Kent. Compared to Kent, Toni makes more necklaces. Which of the following sums up the number of necklaces that Toni and Kent have made?

Answer: 25 + (25 + m)

Kent makes 25 necklaces. Toni makes 'more' necklaces than Kent, which can be represented as 25 + m, where 'm' is the additional number of necklaces Toni makes. To find the total number of necklaces Toni and Kent made together, you add Kent's necklaces to Toni's necklaces. This results in the expression 25 + (25 + m), which represents the sum of their individual contributions.

Which of the following formulas sums up to n? Check all that are relevant.

Answer: n + 3

The question asks which formulas sum up to 'n', implying expressions that represent 'n' combined with another value through addition. Both 'n + 3' and '3 + n' represent the sum of 'n' and 3. Due to the commutative property of addition, n + 3 is equivalent to 3 + n. The other options represent multiplication (3n) or a sum of multiple 'n's (n + n + n = 3n), not just 'n' summed with a constant.

Which of the following best describes 2m + 7?

Answer: 7 more times than twice m

The expression 2m + 7 can be broken down into its components. '2m' means 'twice m' or 'm multiplied by 2'. The '+ 7' indicates '7 more than' the preceding term. Combining these, the expression describes '7 more than twice m'. Option C accurately reflects this interpretation, even with slightly awkward phrasing, as it is the closest and most mathematically sound description among the choices.

Which collection of values completely resolves the inequality 2x - 1 < 10?

Answer: {2, 3, 4}

To solve the inequality 2x - 1 < 10, first add 1 to both sides to get 2x < 11. Then, divide both sides by 2, which yields x < 5.5. This means any value of x in the solution set must be strictly less than 5.5. Option B, {2, 3, 4}, contains only values that are less than 5.5, making it the correct collection of values.

hich of the following phrases best describes it? 3 less than an amount, p.

Answer: p-3

The phrase '3 less than an amount, p' indicates subtraction. When you say 'less than', the number being subtracted comes after the 'less than' phrase, and the amount it is less than comes first. Therefore, '3 less than p' is correctly written as p - 3. Option A accurately represents this mathematical operation.