Example 9 x 14 = (<10> * 14) - ([1] * 14) = 140 - 14 = 126
key: <> easier rounded number [] deal with rounding 'error'
The most important estimating still, after manipulation of sig figs is knowing which way to bend for the overall system. So say I'm tiling a kitchen floor or buying paver bricks for a modest sized patio. Well, some raw material is going to be too ugly to use and I'm going to screw up some of the trimming and cutting and I'm going to drop some, and the cost of the gasoline and time to drive out to the home center and buy one more (mismatched) tile or brick is very high, so in that scenario I'd buy the 10x15=150 tiles and hope thats enough (I'm feeling lucky today). On the other hand if I had 9 steel chains each rated (by whom? Static or dynamic loads? Point concentrations or perfectly (LOL) distributed?) to 1400 pounds each, I would round way down for safety's sake and not suspend more than 10 x 10 or 10000 pounds on that platform. Even if the chains are rated properly I only need to screw up or fail four of them and the thing crashes down.
Anyway for engineering purposes 9x14 is somewhere around 100 to 150.
But this is wildly off topic, and in reality I'd rather someone knew how to use their calculator or excel or Python to do this sum than know how to do this sum in their heads.
It's important they know the rough answer in terms of scale and shape, so that any mistype or error is quickly recognised, but I don't think it is important to actually know how to quickly do long multiplication in one's head.
Sure, but the interesting question is if they negatively impacted math skills.
I remember my classmate, 1st year at university, that passed one of his classes just because his calculator was capable of precise enough numeric integration.
Next semester he was required to construct proofs as well and he flunked the class.
The same can be said of general mathematics, and literary analysis, etc.
The main benefit is that knowing arithmetics well makes higher mathematics easier to learn. That's because one won't get distracted doing calculations. That's still true on the calculator era, just a bit less so, thus I do think it's important to learn arithmetics... It just the "it improves your brain" that I find highly suspect.
Math is a perishable skill. You get slow at it if you don't use it.
In general, that's the essence of learning. If we stop teaching that, then we're all in trouble ;)
9 x 10 = 90
9 x 4 = 36
90 + 36 = 126
14 x 10 = 140
140 - 14 = 126
Yep and that skill was rendered completely obsolete. Always remember being told "you won't always have a calculator with you!!" because I couldn't be bothered showing my working on my maths work.
How did that work out... oh everyone now always has calculators with them. Glad I didn't waste my time memorising multiplication tables.
The number of people that can't do 9x14 without reaching for a calculator is scary.