Is there a fast way to multiply these numbers mentally? Some examples:
- $0.85 \times 1.15$
- $0.5 \times 1.5$
- $0.2 \times 1.4$
Is there a fast way to multiply these numbers mentally? Some examples:
when the numbers are simple, for example your second and third example, you can multiply directly, but pay attention of the posion of the point. $$0.5*1.5=0.75\\0.2*1.4=0.28$$ when the numbers are not simple enough, you can use the formula for the difference of square: $(a+b)(a-b)=a^2-b^2$. for example, $$0.85*1.15=(1-0.15)*(1+0.15)=1-0.15^2=0.9775\\ 0.5*1.5=(1-0.5)*(1+0.5)=1-0.5^2=0.75\\ 0.2*1.4=(0.8-0.6)*(0.8+0.6)=0.8^2-0.6^2=0.28$$
I move the decimal points around as needed, then move them back. I also use fraction-decimal equivalents.
For example, for $0.5\times 1.5$ I think "half of 150 is 75," then put the decimal back: $0.75$.
For $0.2\times 1.4$, I think "a fifth of 140, which is a fifth of 100 plus a fifth of 40, or 20 + 8 = 28." Then put the decimal back: 0.28. Or just: $2\times 14 = 28$.
For $0.85\times 1.15$ I would estimate "very close to 1," because $(1-x)(1+x) \approx 1$ when $x$ is small.
(In the last case, I might next adjust the estimate by thinking "$15^2=225$, so come back 0.02" to give approximately 0.98.)
Well for 0.2 x 0.14 you can convert it to 2 x 14, but remember that there were 2 numbers after the decimal point (2 and 14). So when you multiply 2 by 14 you get 28. But wait! What about the 2 spaces after the decimal point? Well that's easy! If you want to make 28, two numbers after the decimal point just make it 0.8! Therefore 0.2 x 0.14 = 0.28 Hope this worked!!!