 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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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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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
$$\displaystyle{\frac{{{18}}}{{{42}}}}={\frac{{{18}}}{{{42}}}}\ {\quad\text{or}\quad}\ {\frac{{{18}}}{{{42}}}}={\frac{{{3}}}{{{7}}}}$$ karton

$$\frac{18}{42}=\frac{6\times3}{6\times7}=\frac{3}{7}$$
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 $$\frac{18}{42}.$$