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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

a. Show that the ratios 10/20and 30/60 form a proportion by finding a common multiplier.
b.Show that the ratios in part (a) are equal by writing them in simplest form.

Respuesta :

sqdancefan

Answer:

  a) "common multiplier" is 3

  b) both reduce to 1/2

Step-by-step explanation:

a)

  [tex]\dfrac{30}{60}=\dfrac{3\cdot10}{3\cdot20}=\dfrac{3}{3}\cdot\dfrac{10}{20}=1\cdot\dfrac{10}{20}=\dfrac{10}{20}[/tex]

Perhaps your "common multiplier" is 3. It multiplies both numerator and denominator in 10/20 to give you 30/60.

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b)

  [tex]\dfrac{10}{20}=\dfrac{10}{10}\cdot\dfrac{1}{2}=\dfrac{1}{2}\\\\\dfrac{30}{60}=\dfrac{30}{30}\cdot\dfrac{1}{2}=\dfrac{1}{2}[/tex]

The simplest form of both fractions is 1/2.

RevyBreeze

Answer:

[tex]\left[A][/tex] The ratios [tex]\frac{10}{20}[/tex] form a proportion by common multiplier 3 to get [tex]\frac{30}{60}[/tex]

[tex]\left[B][/tex] Both ratio are equal to [tex]\frac{1}{2}[/tex] in simplest form

Step-by-step explanation:

[tex]\left[A][/tex] We need to show both fraction of same proportion.

Ratio 1:  [tex]\frac{10}{20}[/tex]

If we multiply by 3 at numerator and denominator

[tex]\frac{10*3}{20*3}[/tex]

[tex]\frac{30}{60}[/tex]

Therefore [tex]\frac{30}{60}[/tex] is equivalent ratio to second one 30/60

Hence, The ratio 10/20 form a proportion by common multiplier 3 to get 30/60

∴-----------------------------------------------------------------------------------------------------∴

[tex]\left[B][/tex] Now we simplify both ration into simplest form

→ [tex]\frac{10/10}{20/10} =\frac{1}{2}[/tex]

→ [tex]\frac{30/30}{60/30} =\frac{1}{2}[/tex]

→ [tex]\frac{1}{2} =\frac{1}{2}[/tex]

Hence, Both ratio are equal to [tex]\frac{1}{2}[/tex] in simplest form.

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