Multiplying decimals and whole numbers: scaling
We're thinking of decimal multiplication conceptually in this video, just working towards the common shortcut (which I introduce in part 2 of this lesson.)
We start out with problems that have a decimal times a whole number. For example, we can see 0.4 × 20 as 4/10 of 20 — the multiplication here "translates" or corresponds to the word "of", or to the idea of taking a fractional part of the quantity. To figure that out, first find 1/10 of 20, which is 2. Then, 4/10 of 20 is four times that, or 8.After practicing with few decimal multiplication problems along those lines, we go on to seeing decimal multiplication as SCALING.
I use the visual model of a stick, which we "scale", or make longer or shorter, by using decimal multiplication. We still first find 1/10 of the quantity, and based on that, solve the multiplications, such as 0.7 × 20 or others. But soon it is time for the SHORTCUT.
See also
Math Mammoth Decimals 2 — downloadable worktext
Multiplying decimals by decimals: the shortcut — video lesson
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