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2 years ago

Put these fractions in order from least to greatest. 3/12 1/6 2/3

Mathematics

2 answers:

Kisachek [45]2 years ago

7 0

Answer:

The answer is 3/12 1/6 2/3

Step-by-step explanation:

The reason why is because the denominator is larger than the rest. The larger the denominator the smaller the number. For example: 2/13 is less than 4/6 because the denominator is bigger. Now if it were 6/12 and 1/2 it would be equal since 6 is half of 12. Hope this helped!

Shtirlitz [24]2 years ago

3 0

Answer:1

1/6 3/12 2/3

Step-by-step explanation:

3/12 = 2/6

2/3 = 4/6

1/6<2/6<2/3

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If Q is the midpoint of PR, and PQ = 2x + 3 and QR = 3x– 2, find x, PQ, QR, and PR.

leva [86]

Since they tell us that Q is the midpoint you now understand that the line is split evenly.
PQ=QR
2x+3=3x-2
2x+5=3x
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8 0

2 years ago

When you write a two column proof, the first thing in the reason column is always.....

Artemon [7]

The first thing in the reason column of a two colum proof is always GIVEN as it always coincide with an established fact which has been stated in the question to be worked on.

Two colum proofs involves using a tabulated format in establishing a conjecture.

Statements or facts are written on one side and the reason why the statement is true is stated in the reason column which is on the opposite side.

Starting a two column proof usually involve stating the the assumptions which are given about the shape or geometry.

Since each statement made requires a reason, then the reason behind the first statement which is based on what is stated in the question is written as GIVEN.

THEREFORE, after the statement given in the question has been established, then other reasons such as distributive, Commutative and other reasons may be used to proof one's solution statement.

Learn more :brainly.com/question/22172471

6 0

1 year ago

John, Joe, and James go fishing. At the end of the day, John comes to collect his third of the fish. However, there is one too m

Dmitry [639]

Answer:

The minimum possible initial amount of fish: $52$

Step-by-step explanation:

Let's start by saying that

$x$ = is the initial number of fishes

John:

When John arrives:

he throws away one fish from the bunch

$x-1$

divides the remaining fish into three.

$\dfrac{x-1}{3} + \dfrac{x-1}{3} + \dfrac{x-1}{3}$

takes a third for himself.

$\dfrac{x-1}{3} + \dfrac{x-1}{3}$

the remaining fish are expressed by the above expression. Let's call it John

$\text{John}=\dfrac{x-1}{3} + \dfrac{x-1}{3}$

and simplify it!

$\text{John}=\dfrac{2x}{3} - \dfrac{2}{3}$

When Joe arrives:

he throws away one fish from the remaining bunch

$\text{John} -1$

divides the remaining fish into three

$\dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3}$

takes a third for himself.

$\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}$

the remaining fish are expressed by the above expression. Let's call it Joe

$\text{Joe}=\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}$

and simiplify it

$\text{Joe}=\dfrac{2}{3}(\text{John}-1)$

since we've already expressed John in terms of x, we express the above expression in terms of x as well.

$\text{Joe}=\dfrac{2}{3}\left(\dfrac{2x}{3} - \dfrac{2}{3}-1\right)$

$\text{Joe}=\dfrac{4x}{9} - \dfrac{10}{9}$

When James arrives:

We're gonna do this one quickly, since its the same process all over again

$\text{James}=\dfrac{\text{Joe} -1}{3}+ \dfrac{\text{Joe} -1}{3}$

$\text{James}=\dfrac{2}{3}\left(\dfrac{4x}{9} - \dfrac{10}{9}-1\right)$

$\text{James}=\dfrac{8x}{27} - \dfrac{38}{27}$

This is the last remaining pile of fish.

We know that no fish was divided, so the remaining number cannot be a decimal number. <u>We also know that this last pile was a multiple of 3 before a third was taken away by James</u>.

Whatever the last remaining pile was (let's say $n$ ), a third is taken away by James. the remaining bunch would be $\frac{n}{3}+\frac{n}{3}$

hence we've expressed the last pile in terms of n as well. Since the above 'James' equation and this 'n' equation represent the same thing, we can equate them:

$\dfrac{n}{3}+\dfrac{n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}$

$\dfrac{2n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}$

L.H.S must be a Whole Number value and this can be found through trial and error. (Just check at which value of n does 2n/3 give a non-decimal value) (We've also established from before that n is a multiple a of 3, so only use values that are in the table of 3, e.g 3,6,9,12,..

at n = 21, we'll see that 2n/3 is a whole number = 14. (and since this is the value of n to give a whole number answer of 2n/3 we can safely say this is the least possible amount remaining in the pile)

$14=\dfrac{8x}{27} - \dfrac{38}{27}$