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Divide decimals with mental math, part 2: divisor is a decimal

Dividing a decimal by a decimal can seem counter-intuitive to students. What can 0.6 divided by 0.2 signify?

To see that, we first take a look at FACT FAMILIES involving two multiplications & two divisions that use the same numbers.

For example, if 7 × 0.04 = 0.28, then 0.28 ÷ 0.04 must equal 7. The quotient is LARGER than either of the numbers in the division! This can seem baffling and confusing, but it is true.

The easy way to think about such divisions is to consider them as "measurement divisions": how many times does the DIVISOR (the 2nd number) FIT into the DIVIDEND (the 1st number).

For example, to solve 0.36 divided by 0.04, think how many times 4 hundredths "fits into" or goes into or divides into 36 hundredths.

That is the same number of times as 4 goes into 36, so the answer is plain 9 (the whole number 9; not any decimal).

We look at several such decimal divisions that can be solved with mental math, and lastly solve a word problem that applies this exact concept.

Check out also the first part of this lesson, where we look at SHARING divisions involving decimals; in other words, divisions where the divisor is a whole number.

See also

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