{"id":4366,"date":"2020-12-22T10:46:50","date_gmt":"2020-12-22T05:16:50","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=4366"},"modified":"2020-12-22T16:38:57","modified_gmt":"2020-12-22T11:08:57","slug":"what-is-a-ratio-and-proportion","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/what-is-a-ratio-and-proportion\/","title":{"rendered":"What is a Ratio and Proportion"},"content":{"rendered":"

What is a Ratio and Proportion<\/strong><\/h2>\n

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\nRATIO<\/strong>
\nIn our day-to-day life, we compare one quantity with another quantity of the same kind by using the \u2018method of subtraction’ and \u2018method of division\u2019.
\nExample:<\/strong> The height of Seema is 1 m 67 cm and that of Reema is 1 m 62 cm. The difference in their heights is:
\n167 cm – 162 cm = 5 cm
\nThus, we say Seema is 5 cm taller than Reema.
\nSimilarly, suppose the weight of Seema is 60 kg and the weight of Reema is 50 kg. We can compare their weights by division, i.e.,
\n\\(\\frac{\\text{Weight of Seema}}{\\text{Weight of Reema}}=\\frac{\\text{50 kg}}{\\text{60 kg}}\\)
\n\\(=\\frac { 6 }{ 5 }\\)
\nSo, the weight of Seema is \\(\\frac { 6 }{ 5 }\\)\u00a0times the weight of Reema.
\nWhen we compare two similar quantities by division, the comparison is called the \u2018ratio\u2019<\/strong>. It is denoted by ‘:’<\/strong> and read as \u2018is to\u2019<\/strong>.
\nExample:<\/strong>\u00a0\\(\\frac { 5 }{ 8 }\\) = 5 : 8 (read as 5 is to 8).
\nAs shown in the above example a ratio is like a fraction or comparison of two numbers, where a numerator and a denominator is separated by a colon (:). The first term or the quantity (5), called\u00a0antecedent means \u2018that precedes\u2019 and the second term, called consequent means \u2018that follows\u2019.<\/p>\n

Read More:<\/strong>
\nRatio and Proportion Rs Aggarwal Class 7 Solutions<\/a>
\nRatio and Proportion Rs Aggarwal Class 6\u00a0Solutions<\/a><\/p>\n

Properties of Ratio<\/strong><\/h3>\n

When we compare two quantities, the following points must be taken care of:<\/p>\n

    \n
  1. A ratio is usually expressed in its simplest form.
    \nExample:\u00a0<\/strong>
    \n\\(\\frac{12}{36}=\\frac{1}{3}=1:3\\)<\/li>\n
  2. Both the quantities should be in the same unit. So, ratio is a number with no unit involved in it.
    \nExample:<\/strong> 200 g : 2 kg
    \n= 200 g : 2000 g
    \n\\(\\frac{200}{2000}=\\frac{1}{10}=1:10\\)<\/li>\n
  3. The order of the quantities of a ratio is very important.
    \nExample:<\/strong> 5 : 6 is different from 6 : 5.
    \nThey are not equal.
    \n5 : 6 \u2260 6 : 5<\/li>\n<\/ol>\n

    Equivalent Ratios<\/strong><\/h3>\n

    A ratio is similar to a fraction. So, if we divide or multiply the numerator (antecedent) and denominator (consequent) by the same number, we get an equivalent fraction (ratio).
    \nExample:<\/strong> 5 : 6 = \\(\\frac { 5 }{ 6 }\\)<\/p>\n

    Comparison of Ratios<\/strong><\/h3>\n

    To compare two ratios, we have to follow these\u00a0steps:
    \nStep 1:<\/strong> Convert each ratio into a fraction in its simplest form.
    \nStep 2:<\/strong> Find the LCM of denominators of the fractions obtained in step 1.
    \nStep 3:<\/strong> Convert the denominators equal to LCM obtained in step 2 in each fraction.
    \nStep 4:<\/strong> Now, compare the numerators of the fractions; the fraction with a greater numerator will be greater than the other.<\/p>\n