How to multiply decimal with wholenumber?

How Can I multiply

x = (0.35)(80)

x = 28
steps by step fastest way

I am not going to lie, but it is time for me to take a test without using a calculator. Schools have made me worse by giving us a calculator in exam. now in GRE exam I can't use it.

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$9\times 0.35\neq 20$ – user39572 Oct 17 '12 at 14:03
@J.G. sorry fixed, I am working on so many problems. – Mowgli Oct 17 '12 at 14:04

$$9 \times 0.35 = 9 \times \frac{35}{100} = \frac{315}{100} = 3.15$$

This reduces it to just calculating $9 \times 35$.

IMHO if you are taking the GRE, it is better to convert the decimal to the form $\frac{x}{100}$ and reduce the problem to simple multiplication of the first term and the numerator. Then, dividing by $100$ is easy.

I took the GRE general test recently.

Edit

$$80 \times 0.35 = 80 \times \frac{35}{100} = 8 \times \frac{35}{10} = \frac{280}{10}$$

Once again, you can simplify the problem to multiplication by the first term and the numerator.

IMHO this is the simplest, least error-prone, and fastest way for GRE questions involving decimals.

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Thanks alot that is what I needed – Mowgli Oct 17 '12 at 14:33
@Mogli don't forget to accept a response you feel has answered your question :) – jsj Oct 17 '12 at 14:37
I am glad you satisfied the questioner, however I don't really see why, because 35 * 8 is exactly the same problem as 0.35 * 8 :D – jsj Oct 17 '12 at 14:43
@trideceth12 - Usually GRE takers trip over multiplying by decimals, and GRE questions take advantage of that. My approach actually turns many of those questions trivial. Of course, this advice is specific to the GRE test. I would strongly advise GRE takers not to use the methods in the other answers because the questions are counting on confusing test takers trying to juggle fractions or decimals. – Legendre Oct 18 '12 at 5:48

You could for example do $10 \times 0.35$ then subtract $0.35$. That would be my favourite option. However, it would not give you $20$!$$9 \times 0.35=10 \times 0.35 - 0.35= 3.5-0.35 =3.15$$

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I made a big mistake, it was 80 * .35 = 28 – Mowgli Oct 17 '12 at 14:17

9 x 0.35 is only four steps:

1. 9 x 5 carrying the four,

2. 9 x 3 + 4 (add the carried four +1 step)

3. 0 + 3

Where did you get 20 steps from!

EDIT:

80 x 0.35 is actually easier as there is no carrying.. I recommend you watch the Khan Academy video.

Three Steps:

1. 8x5
2. 8x3
3. 4+4
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I made a big mistake, it was 80 * .35 = 28 – Mowgli Oct 17 '12 at 14:19
@Mogli 80 x .35 is also four steps – jsj Oct 17 '12 at 14:24

Multiplying and dividing by 10 is easy: shifting to the right or to the left the digits for instance $.35\times 10=3.5$ and $.35/10=.035$.

Can you add decimal fractions? Then $9\times\,.35 = (10-1)\times\,.35 =3.5 -.35 = 3.50 - 0.35 = 3.15$

Or, you can just multiply it, digit by digit from right to left: $5\times 9=45$, so last digit will be $5$ and carry on $4$ for adding to the next digit. $3\times 9=27$ then add the carried $4$, it is $31$, so this digit is $1$ and $3$ is carried to the next digit to the left, yielding indeed $3.15$: $$.35\times 9 = \frac{35}{100}\times 9 =\frac{35\times 9}{100} = \frac{315}{100}$$

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$$0.35=0.25+0.1=\frac{1}{4}+\frac{1}{10}=\frac{7}{20}$$

$$9\times \frac{7}{20}=\frac{63}{20}=\frac{60}{20}+\frac{3}{20}=3+\frac{3}{20}=3+3\times\frac{1}{20}= 3+3\times 0.05=3.15$$

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I would just set it up like a regular multiplication, then apply the two decimals at the end. $$\ \ \ 35 \\ \underline{\times \ 80} \\ 2800$$ Now apply the two decimals to get $28.00$

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