When Division Makes Numbers Bigger

Predict whether a quotient is bigger or smaller than the dividend by comparing the divisor with 1, and order expressions without calculating.

5 micro-lessons

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Dividing by Less Than 1

Dividing by 0.4 asks 'how many 0.4s fit?', and lots do.

With counting numbers the quotient is always less than the dividend: $128 \div 4 = 32$ .

But $128 \div 0.4 = 320$ . The quotient is bigger than the dividend.

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Compare the divisor with 1 to predict the quotient.

Problem. Describe how the dividend, divisor and quotient are related. Make a table, as we did for multiplication. (Textbook p. 86)

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Compare the divisor with 1.

How big is the quotient?

Divisor greater than 1 → quotient smaller than the dividend.

Divisor equal to 1 → quotient equal to the dividend.

Divisor between 0 and 1 → quotient bigger than the dividend.

Mirror image of multiplication: × a number below 1 shrinks; ÷ a number below 1 grows.

Put six expressions in increasing order.

Figure it Out, Textbook p. 95, Q11: drag the expressions into increasing order, smallest at the top. Try it without calculating.

Drag to reorder

Predict the size of quotients.

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Is $45 \div 0.9$ bigger than 45?

Dividing by 0.4 asks 'how many 0.4s fit?', and lots do.

With counting numbers the quotient is always less than the dividend: $128 \div 4 = 32$ .

But $128 \div 0.4 = 320$ . The quotient is bigger than the dividend.

1 / 3

Predict the size of quotients.

1 / 4

Is $45 \div 0.9$ bigger than 45?