To determine which equations represent the statement "63 is how many times as much as 9," we need to find an equation that shows 63 is a multiple of 9.
We know that [tex]\( n \times 9 = 63 \)[/tex]. Solving for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{63}{9}
\][/tex]
[tex]\[
n = 7
\][/tex]
Thus, 63 is 7 times as much as 9. Let's evaluate each equation option:
A. [tex]\( 63 = \qquad \div 9 \)[/tex] is incorrect because it does not define the relationship.
B. [tex]\( 63 \times \qquad = 9 \)[/tex] is also incorrect because 63 multiplied by any number does not equal 9.
C. [tex]\( \qquad \times 9 = 63 \)[/tex] is correct because [tex]\( 7 \times 9 = 63 \)[/tex].
D. [tex]\( \qquad \div 63 = 9 \)[/tex] is incorrect; dividing any number by 63 should not result in 9 here.
E. [tex]\( 63 \div 9 = \qquad \)[/tex] is correct because [tex]\( 63 \div 9 = 7 \)[/tex].
So, the correct equations are:
C) [tex]\( \qquad \times 9 = 63 \)[/tex]
E) [tex]\( 63 \div 9 = \qquad \)[/tex]
