Question

1. which numbers make this equation true?

$\frac{2}{4} \times ? = 1$
choose the three correct answers.
pick up to 6 answers.
a $\frac{2}{1}$
b $\frac{1}{2}$
c 2
d $\frac{2}{4}$
e $\frac{4}{2}$
f 1

Explanation:

Step1: Let the unknown number be \( x \), so the equation is \( \frac{2}{4} \times x = 1 \).

Step2: Solve for \( x \) by dividing both sides by \( \frac{2}{4} \), which is the same as multiplying by its reciprocal. The reciprocal of \( \frac{2}{4} \) is \( \frac{4}{2} \), so \( x = 1 \times \frac{4}{2}=\frac{4}{2} = 2=\frac{2}{1} \) (since \( \frac{4}{2}=2 \) and \( 2=\frac{2}{1} \)).

Now check each option:

• Option A: \( \frac{2}{1}=2 \), \( \frac{2}{4}\times\frac{2}{1}=\frac{4}{4} = 1 \), correct.
• Option B: \( \frac{1}{2} \), \( \frac{2}{4}\times\frac{1}{2}=\frac{2}{8}=\frac{1}{4}

eq1 \), incorrect.

• Option C: \( 2 \), \( \frac{2}{4}\times2=\frac{4}{4} = 1 \), correct.
• Option D: \( \frac{2}{4} \), \( \frac{2}{4}\times\frac{2}{4}=\frac{4}{16}=\frac{1}{4}

eq1 \), incorrect.

• Option E: \( \frac{4}{2}=2 \), \( \frac{2}{4}\times\frac{4}{2}=\frac{8}{8} = 1 \), correct.
• Option F: \( 1 \), \( \frac{2}{4}\times1=\frac{2}{4}=\frac{1}{2}

eq1 \), incorrect.

Answer:

A. \(\frac{2}{1}\), C. \(2\), E. \(\frac{4}{2}\)