Properties of division


Before giving practice in complex division problems I introduce following properties of division to the children.

  1. The right identity element for division: The reason for calling it the right identity element is obvious. 15 ÷ 1 = 15 is true as far as the 1 is placed to the right of the division symbol. This relation will not hold the moment 1 is placed to the left of the division symbol. 1 ÷ 15 ≠ 15.

    Children should be reminded the two ways of looking at this division. Suppose, if we have 15 lollipops and we distribute it to one child, how many lollipops the child would get? The answer is 15 lollipops! This is the partitive meaning of 15 ÷ 1

    The second situation would be: If we decide to give 1 lollipop to each child, to how many children we can distribute 15 lollipops? The answer is 15 children! This is the measurement meaning of 15 ÷ 1.

    Children understand this easily if this is related to the identity element for multiplication. They know that the sentence 15 x ? = 15 will be true only for 1. I remind them about the relationship between multiplication and division and explain the word identity. The word identity element is used as 1 does not change the number 15 when divided by 1. I also summarize the observation that a number divided by 1 is always equal to the number itself.

  2. Right distributive property of division over addition: Take the example solved by children earlier, i.e. 84 ÷ 2. While solving this example with the help of a drawing of beads, we had split the number 84. We used 8 tens and 4 ones instead of 84. We then divided the tens and ones separately and then added the results of the two divisions as follows: (80 + 4) ÷ 2 = (80 ÷ 2) + (4 ÷ 2) = 40 + 4 = 44.

    To carry out such divisions I encourage children to use buttons, counters, if required.

    Children discover this property on their own if following types of problems are set for them:

    • 60 ÷ 3 = (30 ÷ 3) + (30 ÷ 3) =?
    • 84 ÷ 4 = (40 ÷ 4) + (44 ÷ 4) =?
    • 28 ÷ 7 = (21 ÷ 7) + (7 ÷ 7) =?

    I also set following pairs of problems for children and ask to observe the pattern:

    • (15 + 20) ÷ 3 =? And (15 ÷ 3) + (20 ÷ 3) =?
    • The copyright of the article Properties of division in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Properties of division in print or online must be granted by the author in writing.

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