Whether the given ratios are equivalent ratios or not. Given: The given

Julia White 2021-12-30 Answered
Whether the given ratios are equivalent ratios or not.
Given:
The given ratios are:
\(\displaystyle{\frac{{{3}}}{{{7}}}}\ {\quad\text{and}\quad}\ {\frac{{{18}}}{{{42}}}}\)

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Expert Answer

kalupunangh
Answered 2021-12-31 Author has 374 answers
Calculation:
Equivalent ratios are two ratios which have same relationship between the numbers.
The given ratios can be simplified further by cross multiplying as:
\(\displaystyle{\frac{{{3}}}{{{7}}}}={\frac{{{18}}}{{{42}}}}\)
\(\displaystyle{3}{\left({42}\right)}={18}{\left({7}\right)}\)
\(\displaystyle{126}={126}\)
As, both the results are equal. The given ratios are equivalent.
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braodagxj
Answered 2022-01-01 Author has 1151 answers
Step 1
Find the least common denominator or LCM of the two denominators:
LCM of 42 and 7 is 42
Next, find the equivalent fraction of both fractional numbers with denominator 42
For the 1st fraction, since \(\displaystyle{42}\times{1}={42}\)
\(\displaystyle{\frac{{{18}}}{{{42}}}}={\frac{{{18}\times{1}}}{{{42}\times{1}}}}={\frac{{{18}}}{{{42}}}}\)
Likewise, for the 2nd fraction, since \(\displaystyle{7}\times{6}={42}\)
\(\displaystyle{\frac{{{3}}}{{{7}}}}={\frac{{{3}\times{6}}}{{{7}\times{6}}}}={\frac{{{18}}}{{{42}}}}\)
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
\(\displaystyle{\frac{{{18}}}{{{42}}}}={\frac{{{18}}}{{{42}}}}\ {\quad\text{or}\quad}\ {\frac{{{18}}}{{{42}}}}={\frac{{{3}}}{{{7}}}}\)
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karton
Answered 2022-01-04 Author has 8454 answers

\(\frac{18}{42}=\frac{6\times3}{6\times7}=\frac{3}{7}\)
Conclude: \(\frac{3}{7}=\frac{18}{42}\)
the two ratios are equivalent. If you multiply both the numerator and the denominator by 6, you will get \(\frac{18}{42}.\)

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