Dividend, divisor and quotient

When we divide two counting numbers, the quotient is always less than the dividend. For example 128 ÷ 4 = 32, and 32 is less than 128. That feels like what division does.

But divide 128 by 0.4 and you get 320 — a quotient GREATER than the dividend. Will that always happen when the divisor is a decimal? Try several divisors and see.

The reason is the one you met with fractions. Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 0.4 is 2.5, which is greater than 1, so the quotient grows. The reciprocal of 4 is 0.25, less than 1, so the quotient shrinks.

So the rule is about the DIVISOR, not about decimals as such. If the divisor is greater than 1, the quotient is less than the dividend. If the divisor is between 0 and 1, the quotient is greater than the dividend. Make a table of situations, as you did for multiplication.

Now use all of this on real quantities. A 4 m wooden block is cut into 5 equal pieces: each is 4 ÷ 5 = 0.8 m.

A regular polygon with 12 sides has perimeter 208.8 cm, so each side is 208.8 ÷ 12 = 17.4 cm. Three litres of watermelon juice shared among 8 friends gives 3 ÷ 8 = 0.375 litres each, which is 375 millilitres.

A car covers 234.45 km on 12.6 litres, so it does 234.45 ÷ 12.6 = 18.607… km per litre — here the divisor is a decimal, so scale both by 10 first. And 13.5 kg of flour shared among 15 students gives 13.5 ÷ 15 = 0.9 kg each.