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Alice and Will are measuring a liquid solution using graduated cylinders. Alice uses 6.5liters of the liquid solution, and Will uses 4,750milliliters of the liquid solution. What is the ratio of Alice's measurements to Will's measurements? Simplify your answer.

Respuesta :

calculista

Answer:

The ratio is 26/19

Step-by-step explanation:

step 1

Remember that

1 liter=1,000 milliliters

so

we know that

Alice uses 6.5 liters of the liquid solution

Will uses 4,750 milliliters of the liquid solution

Convert milliliters to liters

4,750 ml=4,750/1,000=4.75 l

step 2

Find the ratio of Alice's measurements to Will's measurements

Let

x ----> Alice's measurements

y ----> Will's measurements

To find the ratio divide x by y

x=6.5 l

Convert to mixed number

6.5=6 1/2 l

Convert to an improper fraction

6 1/2=(6*2+1)/2=13/2 l

y=4.75 l

Convert to mixed number

4.75=4 3/4 l

Convert to an improper fraction

4 3/4=(4*4+3)/4=19/4 l

Find the ratio

(13/2)/(19/4)=26/19

Ratio of two quantities is the simplified fraction usually. The ratio of Alice's measurements to Will's measurements is 26:19

What is ratio of two quantities?

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b)

[tex]a : b[/tex]

or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

For the given case, we've got:

Alice's measurement = 6.5 liters = 6500 millilitres (since 1 liter = 1000 millilitres so we multiplied 6.5 with 1000)

(we converted it to millilitres so that both Alice's measurement and Will's measurement get converted in same unit 'millilitre'. One more fact we used that quantities in liter are being expressed in decimal points which is not what we usually use in ratio, so converting to millilitre gave us integers )

Will's measurement = 4,750 millilitres

Thus, ratio of Alice's measurements to Will's measurements is:

[tex]\dfrac{\text{Alice's measurement}}{\text{Will's measurement}} = \dfrac{6500}{4750} = \dfrac{50 \times 130}{50 \times 95} = \dfrac{130}{95} = \dfrac{5 \times 26}{5 \times 19} = \dfrac{26}{19}[/tex]

Thus, ratio of Alice's measurements to Will's measurements is 26:19

Ratio tells us that for how much of something is there going to be another thing. For this case, 26:19 is telling that if Will got 19 quantity of that solution, then Alice would have got 26 of it. Its a comparison thing, and useful for getting some rough picture of how their measurement compares. (ratios have other uses too though).

Thus, The ratio of Alice's measurements to Will's measurements is 26:19

Learn more about ratio here:

https://brainly.com/question/12106245

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