Question

What are equivalent ratios \[7\] to\[10\]?

Answer 1

Hint: A ratio is a comparison of two quantities by division. Ratios describe a part-to-part comparison or a part-to-whole comparison. Ratios are written in three ways: as a fraction, with a colon, and with the word “to.”

Complete step-by-step solution:
Ratios are the simplest Mathematical expressions that reveal the significant relationship between the values. In other words, a ratio is defined as the relationship between two numbers that indicate how many times the first number contains the second number. The ratios are expressed using the notation “:” or “/” or “to”.
The standard form of the ratio is given below:
Ratio \[ = \dfrac{a}{b} = \dfrac{\text{numerator}}{\text{denominator}}\]
Or
Ratio \[ = a:b = \text{Numerator}: \text{denominator}\]
Or
Ratio \[ = a\] to \[b\] \[ = \text{Numerator}\] to \[\text{denominator}\]
Equivalent ratios: A ratio obtained by multiplying or dividing the numerator and denominator of a given ratio by the same number is called an equivalent-ratios.in other words, If two ratios have the same value when simplified, then they are called Equivalent Ratios.
Now \[\dfrac{7}{{10}}\] is in its simplest form.
This means that no other number apart from \[1\] will divide into \[7\] and \[10\].
In this case we can choose any number to multiply the numerator and denominator to create equivalent ratios.
Choosing \[2\] we get
\[\dfrac{{7*2}}{{10*2}} = \dfrac{{14}}{{20}}\] (Equivalent ratio)
Choosing \[3\]we get
\[\dfrac{{7*3}}{{10*3}} = \dfrac{{21}}{{30}}\] (Equivalent ratio)
Therefore \[\dfrac{{14}}{{20}}\] and \[\dfrac{{21}}{{30}}\] are the required equivalent ratios.

Note: Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent, even though they may look very different. Equivalent ratios are obtained by multiplying or dividing the numerator and denominator of a given ratio by the same number.