Question

rewrite each of the following division problems as a multiplication problem.
a. 75 ÷ x = 15
b. x ÷ 3 = 14

a. the related multiplication problem is \\(\square\\).
(type an equation using x as the variable.)

b. the related multiplication problem is \\(\square\\).
(type an equation using x as the variable.)

Explanation:

Part a:

Step 1: Recall division-multiplication relation

In a division equation \( a\div b = c \), the related multiplication is \( b\times c = a \) (or \( c\times b = a \)). Here, \( 75\div x = 15 \), so comparing to \( a\div b = c \), \( a = 75 \), \( b = x \), \( c = 15 \).

Step 2: Form the multiplication equation

Using the relation, we get \( x\times15 = 75 \) (or \( 15\times x = 75 \)).

Part b:

Step 1: Recall division-multiplication relation

For \( x\div 3 = 14 \), comparing to \( a\div b = c \), \( a = x \), \( b = 3 \), \( c = 14 \). The related multiplication is \( b\times c = a \).

Step 2: Form the multiplication equation

Substituting the values, we get \( 3\times14 = x \) (or \( 14\times3 = x \)).

Answer:

a. \( 15\times x = 75 \) (or \( x\times15 = 75 \))
b. \( 3\times14 = x \) (or \( 14\times3 = x \))