nalinnair wrote:
Of the following, which is least?
A. \(\frac{0.03}{0.00071}\)
B. \(\frac{0.03}{0.0071}\)
C. \(\frac{0.03}{0.071}\)
D. \(\frac{0.03}{0.71}\)
E. \(\frac{0.03}{7.1}\)
If students didn't see the fast answer (in my above post), here's another (slightly longer approach):
Let's create
equivalent fractions with the
same denominator.
Let's make each denominator 7.1
A. \(\frac{0.03}{0.00071}\)
To get a denominator of 7.1, we must take 0.00071 and move the decimal 4 places to the right.
So, we'll multiply numerator and denominator by 10,000
When we do this, we get:
\(\frac{300}{7.1}\) B. \(\frac{0.03}{0.0071}\)
To get a denominator of 7.1, we must take 0.0071 and move the decimal 3 places to the right.
So, we'll multiply numerator and denominator by 1,000
When we do this, we get:
\(\frac{30}{7.1}\) C. \(\frac{0.03}{0.071}\)
To get a denominator of 7.1, we must take 0.071 and move the decimal 2 places to the right.
So, we'll multiply numerator and denominator by 100
When we do this, we get:
\(\frac{3}{7.1}\) D. \(\frac{0.03}{0.71}\)
To get a denominator of 7.1, we must take 0.71 and move the decimal 1 place to the right.
So, we'll multiply numerator and denominator by 10
When we do this, we get:
\(\frac{0.3}{7.1}\) E.
\(\frac{0.03}{7.1}\)This already has a denominator of 7.1
Now that we have the same denominator, we can that
\(\frac{0.03}{7.1}\) is the smallest fraction.
Answer: E
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