What value of c makes this multiplication sentence true? Hint: Use properties of multiplication. (649 · 439) · 422 = 649 · (439 · c) c = _____

Identify Property: Identify the property of multiplication used in the equation: Using the associative property of multiplication, we can rearrange the parentheses without changing the product. (649 · 439) · 422 = 649 · (439 · c)Calculate Left Side: Calculate the product on the left side of the equation: 649 * 439 = 285071 285071 * 422 = 120309962Set Up Equation: Set up the equation with the calculated product: 120309962 = 649 * (439 * c)Simplify Right Side: Simplify the right side of the equation: First, calculate 439 * c: Let's denote this as x, so x = 439 * c Now, substitute back into the equation: 120309962 = 649 * xSolve for x: Solve for x: x = 120309962 / 649 = 185377Solve for c: Now, solve for c: c = 185377 / 439 c = 422

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What value of $c$ makes this multiplication sentence true? $\newline$ Hint: Use properties of multiplication. $\newline$ $(649 \cdot 439) \cdot 422 = 649 \cdot (439 \cdot c)$ $\newline$ $c =$ _____

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Math Problems

Grade 6

Solve for a variable using properties of multiplication

Full solution

Q. What value of

c

makes this multiplication sentence true?

\newline

Hint: Use properties of multiplication.

\newline

(649 \cdot 439) \cdot 422 = 649 \cdot (439 \cdot c)

\newline

c =

_____

Identify Property: Identify the property of multiplication used in the equation: $\newline$ Using the associative property of multiplication, we can rearrange the parentheses without changing the product. $\newline$ $(649 \cdot 439) \cdot 422 = 649 \cdot (439 \cdot c)$
Calculate Left Side: Calculate the product on the left side of the equation: $\newline$ $649 \times 439 = 285071$ $\newline$ $285071 \times 422 = 120309962$
Set Up Equation: Set up the equation with the calculated product: $120309962 = 649 \times (439 \times c)$
Simplify Right Side: Simplify the right side of the equation: $\newline$ First, calculate $439 \times c$ : $\newline$ Let's denote this as $x$ , so $x = 439 \times c$ $\newline$ Now, substitute back into the equation: $\newline$ $120309962 = 649 \times x$
Solve for x: Solve for x: $\newline$ $x = \frac{120309962}{649} = 185377$
Solve for c: Now, solve for c: $\newline$ $c = \frac{185377}{439}$ $\newline$ $c = 422$