{"id":10876,"date":"2026-11-02T02:02:53","date_gmt":"2026-11-02T02:02:53","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10876"},"modified":"2026-11-02T02:02:53","modified_gmt":"2026-11-02T02:02:53","slug":"types-mathematical-operations","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/types-mathematical-operations\/","title":{"rendered":"Types & Mathematical Operations"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit<\/strong>: Mensuration<\/h2>\n

Chapter<\/strong>: Types & Mathematical Operations<\/h3>\n

Reference<\/strong>: \u2013 Introduction to Mensuration, Types of Mensuration (1D, 2D, 3D), Perimeter and Area of 2D Shapes (Square, Rectangle, Triangle, Circle, Parallelogram, Rhombus, Trapezium), Surface Area and Volume of 3D Shapes (Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere), Mathematical Operations in Mensuration (Addition, Multiplication, Division, Using Formulas), Scaling Laws<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/p>\n

    \n
  • Introduction to Mensuration & Its Meaning<\/li>\n
  • Types of Mensuration (1D, 2D, 3D)<\/li>\n
  • Perimeter and Area of 2D Shapes<\/li>\n
  • Surface Area and Volume of 3D Shapes<\/li>\n
  • Mathematical Operations Used in Mensuration<\/li>\n
  • Scaling Laws (Length, Area, Volume)<\/li>\n<\/ul>\n

    \nAddition of Metric Measures<\/strong><\/p>\n

    Metric measures are added in the same way as we add whole numbers or decimals.<\/p>\n

    We arrange the digits in columns as per their unit and then add as required.<\/p>\n

    Let us consider an example.<\/strong><\/p>\n

    Example-<\/strong><\/p>\n

    Add 4 km 9 hm 3 m 5 cm, 3 km 8 dam 2 dm and 3 dam 7 m 3 cm.<\/p>\n

    \u00a0<\/p>\n

    Solution<\/strong>:<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    We place the digits in columns and add as usual.<\/p>\n

    Ans. = 8 km 2 dam 2 dm 8 cm<\/p>\n

    \u00a0<\/p>\n

    Example:\u00a0 <\/strong>A container had 3.96L of water in it. 4.87L of water was more added to it. What quantity of water does the container have now?<\/strong><\/p>\n

    Solution<\/strong>:<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    \u00a0<\/p>\n

    Subtraction of Metric Measures<\/strong><\/p>\n

    \u00a0<\/p>\n

    Metric measures are subtracted in the same way as we subtract whole numbers or decimals.<\/p>\n

    We arrange the digits in columns and then subtract as required.<\/p>\n

    \u00a0<\/p>\n

    Let us take a look at an example<\/strong>:<\/p>\n

    Subtract 8 kg 7 g 5 dg 8 mg from 13 kg 3 dag 5 g 1 cg 7 mg.<\/strong><\/p>\n

    \u00a0<\/p>\n

    Solution:<\/strong><\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    We place the digits in columns and then subtract as usual.<\/p>\n

    Ans. 5 kg 2 dag 7 g 5 dg 9 mg<\/p>\n

    \u00a0<\/p>\n

    Example: <\/strong><\/p>\n

    The length of a pipe is 96 m 75cm. If a piece of 41 m 39 cm length is cut, what length of the pipe is left?<\/strong><\/p>\n

    \u00a0<\/p>\n

    Solution:<\/strong><\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    Multiplication of Metric Measures<\/strong><\/p>\n

    \u00a0<\/p>\n

    Metric measures are multiplied in the same way as we multiply whole numbers.<\/p>\n

    We place the digits in columns and then multiply as usual.<\/p>\n

    \u00a0<\/p>\n

    Let us consider some examples-<\/strong><\/p>\n

    (a). Multiply:\u00a0 5 kg 7 hg 2 dag 6 g by 9<\/strong><\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    We place the digits in columns and then multiply as usual.<\/p>\n

    Ans. 51 kg 5 hg 3 dag 4 g<\/p>\n

    \u00a0<\/p>\n

    (b). Multiply: 3 kl 7 hl 5 dal 8 l by 26\u00a0<\/strong><\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    We place the digits in columns and then multiply as usual.<\/p>\n

    Ans. 97 kl 7 hl 8 l<\/p>\n

    \u00a0<\/p>\n

    (c). Multiply: 213.65 kg by 41<\/strong><\/p>\n

    \u00a0\u00a0 <\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    \u00a0<\/p>\n

    We place the digits in columns and then multiply as usual.<\/p>\n

    Ans. 8759.65 kg<\/p>\n

    \u00a0<\/p>\n

    (d). Multiply: 729.36 ltr by 37<\/strong><\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    We place the digits in columns and then multiply as usual.<\/p>\n

    Ans. 26986.32 ltr.<\/p>\n

    \u00a0<\/p>\n

    Examples:<\/strong><\/p>\n

    \u00a0<\/p>\n

    Example: – 8 sacks of rice are kept in a warehouse. Each bag weighs 103 kg 450 g. What is the total weight of all the sacks?<\/strong><\/p>\n

    \u00a0<\/p>\n

    Solution:<\/strong><\/p>\n

    Weight of one sack = 103 kg 450 g<\/p>\n

    Weight of 8 sacks = 103 kg 450 g \u00d7 8<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    Total weight of 8 sacks = 827 kg 600 g<\/p>\n

    \u00a0<\/p>\n

    Division of Metric Measures<\/strong><\/p>\n

    \u00a0<\/p>\n

    Metric measures are divided in the same way as we divide whole numbers.<\/p>\n

    We place the digits in columns as per their units and then divide as usual.<\/p>\n

    \u00a0<\/p>\n

    Let us consider some examples-<\/strong><\/p>\n

    \u00a0<\/p>\n

    Divide the following:<\/strong><\/p>\n

    \u00a0<\/p>\n

      \n
    • 7 km 9 hm 6 dam 2 m by 6<\/strong><\/li>\n<\/ul>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      Ans. 1 km 3 hm 2 dam 7 m<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

        \n
      • 9 kg 5 hg 5dag 6 g by 4<\/strong><\/li>\n<\/ul>\n

        \u00a0<\/p>\n

        \"\"<\/p>\n

        Source: Kapdec.com<\/p>\n<\/div>\n

        Ans. 1 kg 3 hg 4 dag 8 g<\/p>\n

        \u00a0<\/p>\n

          \n
        • The total length of 7 wires of equal length is 29 m 5 cm. What is the length of each wire?<\/strong><\/li>\n<\/ul>\n

          \u00a0<\/p>\n

          Solution:<\/strong><\/p>\n

          Total length of 7 wires = 29 m 5 cm<\/p>\n

          Length of each wire \u00a0 \u00a0 = 29 m 5 cm \u00f7 7<\/p>\n

          Ans: 4 m 15 cm<\/p>\n

          \"\"<\/p>\n

          Source: Kapdec.com<\/p>\n<\/div>\n

          \u00a0<\/p>\n

          <\/p>\n