Question

question
what could you divide and then multiply by to go from the first number to the second?
first number: 27
second number: 72
answer attempt 1 out of 2
to get to 1, divide 27 by
. from 1, multiply by
to get to 72.
or, in a single step, multiply 27 by
to get to 72.
submit answer

Explanation:

Step1: Find the number to divide 27 by to get 1

Let the number be \( x \). We have the equation \( \frac{27}{x}=1 \). Solving for \( x \), we multiply both sides by \( x \) to get \( 27 = x\times1 \), so \( x = 27 \).

Step2: Find the number to multiply 1 by to get 72

Let the number be \( y \). We have the equation \( 1\times y=72 \), so \( y = 72 \). But wait, actually, we want to go from 27 to 72. First, we divided 27 by 27 to get 1, now we need to multiply 1 by \( \frac{72}{1}=72 \)? Wait, no, let's re - evaluate. The ratio of 72 to 27 is \( \frac{72}{27}=\frac{8}{3}\approx2.666... \). Wait, maybe a better way: To go from 27 to 72, if we first divide 27 by 27 to get 1, then multiply 1 by 72? No, that's not right. Wait, the first part: to get from 27 to 1, we divide by 27, because \( 27\div27 = 1 \). Then, to get from 1 to 72, we multiply by 72? No, that can't be. Wait, no, the correct approach is: The factor to go from 27 to 72 is \( \frac{72}{27}=\frac{8}{3} \). But the problem says "divide and then multiply". So first, divide 27 by \( a \) to get 1, then multiply 1 by \( b \) to get 72. So \( 27\div a = 1\implies a = 27 \), and \( 1\times b=72\implies b = 72 \). But also, in a single step, multiply 27 by \( \frac{72}{27}=\frac{8}{3} \)? Wait, no, the problem's "OR" part: multiply 27 by \( \frac{72}{27}=\frac{8}{3} \)? Wait, no, let's check again.

Wait, the first blank (divide 27 by _ to get 1): \( 27\div27 = 1 \), so the first blank is 27.

The second blank (multiply 1 by _ to get 72): \( 1\times72 = 72 \), so the second blank is 72.

The third blank (multiply 27 by _ to get 72): Let the number be \( z \), then \( 27\times z=72\implies z=\frac{72}{27}=\frac{8}{3}\approx2.666... \), but \( \frac{72}{27}=\frac{8}{3} \). Wait, but maybe the problem has a typo or I misread. Wait, no, let's do it step by step.

First, to get from 27 to 1: divide by 27 (since \( 27\div27 = 1 \)).

Then, to get from 1 to 72: multiply by 72 (since \( 1\times72 = 72 \)).

Or, in a single step, multiply 27 by \( \frac{72}{27}=\frac{8}{3} \) (because \( 27\times\frac{8}{3}=72 \)).

Answer:

First blank (divide 27 by): 27; Second blank (multiply 1 by): 72; Third blank (multiply 27 by): \( \frac{8}{3} \) (or 24/9, 8/3 is simplified)