Question

Write in the simplest form
a) 6 days to 3 weeks b) 54cm to 2m​

Answer 1

a) Whenever we are representing numbers in ratio we must make sure to represent them once they both are in the same unit. So the first step would be to convert both the numbers or data to a common unit.

1 week = 7 days

3 weeks = 7 × 3 = 21 days

→ 6 days : 3 weeks

→ 6 days : 21 days

Now let's simplify the LHS and RHS.

→ 6 : 21

→ 2 : 7

∴ The simplest form of 6 days to 3 weeks is 2 : 7 days.

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b) Whenever we are representing numbers in ratio we must make sure to represent them once they both are in the same unit. So the first step would be to convert both the numbers or data to a common unit.

1 meter = 100 centimeter

2 meters = 100 × 2 = 200 centimeters

→ 54 cm : 2 m

→ 54 cm : 200 cm

Now let's simplify the LHS and RHS.

→ 54 : 200

→ 27 : 100

∴ The simplest form of 54 cm to 2 m is 27 : 100 cm.

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Answer 2

$\huge \rm \underline \color{blue}{required \: answer}$

a) 6 days to 3 weeks

As we know that 1 week = 7 days,

Likewise 3 weeks = 21 days (3×7)

Now,

6 days to 21 days

$\huge\rm \color{fuchsia} = \frac{6}{21}$

$\huge \rm \color{lime}{ = \frac{2}{7}}$

$\rm \color{blue} \therefore simplest \: form\:of \: 6 \: days \: to \: 3 \: weeks \: is \: 3:7$

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b) 54 cm to 2m

As we know that 1m = 100cm

Likewise 54m = 200cm

Now,

54 m to 200 cm

= 54/200

= 27:100

Therefore, simplest form of 54cm to 2m is 27:100

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☆Additional Points...

• Comparing two quantities are called ratio.

• we use symbol ':' to denote ratio.

While forming a ratio-

• The two quantities compared should be expressed in Same unit.

• The name or units of the two quantities should not be used in ratio.

• Ratio should always be expressed in the simplest form.

• The order of the term In a ratio is important.

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$\mathcal{BE \: BRAINLY}$