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1/0.3 - 1/0.2

I was revising for an up and coming exam and faced with this question ( I am not allowed to use a calculator

I had to find n in n=1/0.3 - 1/0.2

The solution in the answer booklet gave the answer as 0.1/0.06

I am completely confused

that would mean the denominators have been multiplied together and 1-1 is not 0.1.

Please may someone explain this
Hello.

Remember that when you add or subtract fractions, you need to multiply the WHOLE fractions by some numbers to get the same denominators. This means you also multiply the numerator by whatever you multiplied the denominator. This is to make sure that you don't actually change the value of the fraction. For example, 12=48=0.5 \frac{1}{2} = \frac {4}{8} = 0.5 but if you just multiply the denominator: 18=0.125 \frac{1}{8} = 0.125 .

This is a completely different number to the original number, so if you only multiply the denominators, you would then be performing an operation with different numbers. Hence, you must multiply both the numerator and denominator in each fraction by a number, in order to get equal denominators, and then perform the desired operation on the new numerators.

Say you have 23−34 \frac{2}{3} - \frac{3}{4} .

You need to have equal denominators to perform the subtraction, so you need to multiply the whole fractions by some numbers such that both their denominators become equal. In this case:

(2×4)(3×4)−(3×3)(4×3)=812−912=−112 \dfrac{(2 \times 4)}{(3 \times 4)} - \dfrac{(3 \times 3)}{(4 \times 3)} = \dfrac{8}{12} - \dfrac{9}{12} = \dfrac{-1}{12}

Try the same with your question.
(edited 7 years ago)
Original post by chemhelp2000
I was revising for an up and coming exam and faced with this question ( I am not allowed to use a calculator

I had to find n in n=1/0.3 - 1/0.2

The solution in the answer booklet gave the answer as 0.1/0.06

I am completely confused

that would mean the denominators have been multiplied together and 1-1 is not 0.1.

Please may someone explain this


You've confused me too

You can do it if you remember that 0.3 = 3/10, 1/any fraction is that fraction with the numerator and denominator swapped, that when subtracting fractions you should use identical denominators and that any fraction a/b is equivalent to ka/kb for any real k

I left an answer in the spoiler but I have no idea why it gives it in a decimal fraction form though, that's stupid

Spoiler

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