CLASS-6
COMPARISON OF RATIO

COMPARISON OF RATIO :-

When comparing ratios, you are essentially examining the relationship between two or more quantities. There are several ways to compare ratios, depending on the specific context and what you want to determine. Here are some common methods for comparing ratios,

(1) Using the Colon (:) Notation:-

  • Ratios are often represented with a colon (:) between the numbers. For example, a ratio of 2:3 means that the first quantity is twice as large as the second quantity.
  • When comparing two ratios with the same denominator, you can simply compare the numerators. For example, if you have ratios 2:3 and 4:3, the second ratio (4:3) is larger because the numerator is greater.

(2) Using Fractions:-

  • Ratios can also be represented as fractions. For example, the ratio 2:3 is equivalent to the fraction 2/3.
  • When comparing ratios as fractions, you can use standard fraction comparison rules. For instance, you can find a common denominator and then compare the numerators.
  • We can compare two ratios to determine which one is greater or smaller. For instance, if you have the ratios 3:4 and 2:3, you can see that 3:4 is greater because the fraction 3/4 is larger than 2/3.

(3) Cross-Multiplication:-

  • In some cases, you may be asked to compare two ratios in the form of fractions. You can cross-multiply to compare them.
  • To compare two ratios more precisely, you can use cross-multiplication. Given ratios a:b and c:d, if ad is greater than bc, then a:b is greater than c:d. If ad is less than bc, then a:b is less than c:d. This method allows for a direct quantitative comparison.
  • For example, if you have ratios 2/3 and 4/5, you can cross-multiply to get 2 * 5 = 10 and 3 * 4 = 12. Since 10 is less than 12, the ratio 2/3 is smaller than 4/5.

(4) Percentages:-

  • You can convert ratios into percentages for easier comparison. To do this, multiply the ratio by 100 to get the percentage.
  • For example, if you have a ratio of 3:4, you can convert it to a percentage: (3/4) * 100 = 75%. Then, you can easily compare this percentage to others.
  • Ratios can be compared as percentages. You can convert ratios to percentages by multiplying by 100. For instance, the ratio 3:4 is equivalent to 75% (because 3/4 = 0.75 when expressed as a decimal).

(5) Equivalent Ratios:-

  • Sometimes, you may be given ratios that are not in their simplest form. You can simplify ratios by finding equivalent ratios with a common factor.
  • For example, if you have ratios 4:6 and 2:3, you can see that both represent the same relationship because they can be simplified to 2:3 by dividing both parts by a common factor of 2.
  • Two ratios are equal if the fractions they represent are equal. For example, if you have the ratios 2:3 and 4:6, they are equal because both simplify to 2/3.

(6) Proportions:-

  • When you have two ratios, you can set them up as a proportion to compare them. This involves setting the two ratios equal to each other and solving for an unknown.
  • Sometimes, you may want to determine if two ratios are in proportion or if they follow a proportional relationship. If two ratios are equal, they are in proportion. For example, 1:2 and 3:6 are in proportion because they are both equal to 1/2.
  • For example, if you want to compare 2:3 and 4:5, you can set up the proportion (2/3) = (4/5) and then solve for the missing value.

(7) Scaling Ratios:-

You can scale up or down ratios to compare quantities at different scales. For example, if you have the ratio 2:5, you can scale it up to 4:10 or down to 1:2. Scaling ratios can be useful in various real-world scenarios.