Question

8
Determine if the ratios are in proportion.
a. 20 cm:4 m::40 cm:8 m​

Answer 1

Given:-

• Determine if the ratios are in proportion.20 cm:4 m::40 cm:8 m

To find:-

• The ratios are in proportion or not.

Solution:-

As we know that ratio or proportion must not include units so to remove units , they must contain same value such as if 1st term is in "cm" then second term also must be "cm".

So now as we know that higher units are converted to lower units here we will change "m" to "cm".

NOTE- M =Meter and Cm=Centi Meter

Now let's move on solving!

4m=400cm

8m=800cm

Now , As we know Product of means=Product of extremes

=>20×800=400×40

=>16000=16000

=>1=1

:.L.H.S.=R.H.S

Yes the ratios are in proportion as the product of both means and extremes is same.

Explanation:-

• Hey mate! overall we started from converting the units from m to cm in order to cancle the units out so that it could look alone a proper proportion.

• Now as we know that 1 m is equal to 100 cm so 4 m and 8 m were multiplied to 100 cm respectively and gave out 400 and 800 (cm) after when we got all units same we canceled them.

• Now moving on to clear whether the two ratios are in proportion of not we followed the rule "Product of means = Product of extremes"

Hey mate don't get much confused!

• Means is the 2nd and 3rd term and Extremes is the 1at and last term.

• Now according to the rule when 1st and 4th term gets multiplied they must have there products same as they of 3rd and 4th in order to prove them as proportion.

• So now 400 and 40 on multiplication gives 16000 and 800 and 20 on multiplication too gives 16000 as product

• Now when both have same products the given ratios are in proportion.

Additional Information:

What is a ratio?

• A ratio is the comparison of two or more quantities of the same kind using division.Then ratio of two quantities a and b of the same kind in the same units is written generally as a:b.

Hope it helped!

Answer 2

Yes the ratios are in proportion as Product of means= product of extremes.

hope it helped buddy!