Question

can some one help me​

Answer 1

Solution:-

(I) Convert the given fraction or decimal into percentage:-

 $\sf{1) \: \dfrac{1}{5}=\dfrac{1}{5} \times 100=20\%}$

$\sf{2) \: 0.62=\dfrac{62}{100} \times 100 = 62\%}$

(II) Express each of the following as fraction in their lowest terms:-

$\sf{1) \: 75\%=\dfrac{75}{100}=\dfrac{3}{4}}$

$\sf{2) \: 15 \dfrac{1}{2}\%=\dfrac{31}{2} /100=\dfrac{31}{2} \times \dfrac{1}{100}=\dfrac{31}{200}}$

(III) Use prime factor method to find the HCF(Highest common factor) of 18, 27 and 36:-

⇒ Refer the Attachment

(IV)  Express 36 hours as a percentage of 2 days:-

  First Convert 2 days in hours

       First day = 24 hours

       Second day = 48 hours

Then,

Let 36 hours be x percent of 2 days

So,

$\sf{(\dfrac{x}{100}) \times 48 =36}$

$\sf{x=\dfrac{3600}{48}}$

x = 75%

Therefore, 36 hours is 75% of 2 days

(V) The product of two numbers is 144. Their LCM is 36. Find their HCF?

 Product of two numbers = HCF x LCM

                                    36x = 144

                                         x = 144/36

                                         x = 4

⁂ Hence, the HCF of the two numbers is 4

Answer 2

Answer:

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$\Large \underline \frak \red{Question }$

❶ Convert the given fraction or decimal into percentage.

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$\Large \underline \frak \red{ Solution }$

1) 1/5

$: \implies \sf\dfrac{1}{5} \times 100$

$: \implies \sf\cancel\dfrac{100}{5}$

$: \implies \sf20\%$

$: \longmapsto\underline{\boxed {\sf{\red{20 \%}}}}$

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2) 0.62

$: \implies \sf \dfrac{62}{100} \times 100$

$: \implies \sf \cancel\dfrac{6200}{100}$

$:\implies \sf62 \%$

$: \longmapsto\underline{\boxed {\sf{\red{62\%}}}}$

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$\Large \underline \frak \red{Question }$

❷ Express each of the following as fraction in their lowest terms.

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$\Large \underline \frak \red{ Solution }$

1) 75%

$: \implies \sf75 \%$

$: \implies \sf \cancel\dfrac{75}{100}$

$: \implies \sf\dfrac{3}{4}$

$: \longmapsto \underline{\boxed{\sf {\red{Lowest \: term = \dfrac{3}{4} }}}}$

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2) 15½%

$: \implies \sf15 \dfrac{1}{2} \%$

$: \implies \sf \dfrac{31}{2} \%$

$: \implies \sf\dfrac{31}{2} \times \dfrac{1}{100}$

$: \implies \sf\dfrac{31}{200}$

$: \longmapsto \underline{\boxed{\sf {\red{Lowest \: term = \dfrac{31}{200} }}}}$

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$\Large \underline \frak \red{Question }$

❸ Use prime factor method to find the HCF of 18,27 and 36.

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$\Large \underline \frak \red{ Solution }$

18

• 2 | 18
• 3 | 9
• 3 | 3
• ⠀| 1

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27

• 3 | 27
• 3 | 9
• 3 | 3
• ⠀| 1

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36

• 2 | 36
• 2 | 18
• 3 | 9
• 3 | 3
• ⠀| 1

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$\Rightarrow \sf18 = 2 × \cancel{3} × \cancel{3}$

$\Rightarrow \sf27 = \cancel{3 }× \cancel{3}× 3$

$\Rightarrow \sf36 = 2 × 2 × \cancel{ 3} × \cancel{3}$

HCF = 3 × 3 = 9

$: \longmapsto\underline{\boxed {\sf{\red{HCF = 9}}}}$

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$\Large \underline \frak \red{Question }$

❹ Expree 36 hours as Percentage 2 day.

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$\Large \underline \frak \red{ Solution }$

As we know that

$: \implies \sf{1 \: day = 24 \: hours}$

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So,

$\implies \sf{2 \: days = 2×24 = 48 \: hours.}$

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Now,

$: \implies \sf\dfrac{x}{100} \times48= 36$

$: \implies \sf \dfrac{48x}{100} = 36$

$: \implies \sf{x = \dfrac{36 \times 100}{48} }$

$:\implies \sf {x = \cancel \dfrac{3600}{48} }$

$: \implies \sf{x =75 \%}$

$: \longmapsto \underline{ \boxed{\sf \red{Percentage = 75 \%}}}$

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$\Large \underline \frak \red{Question }$

❺ The product of two number is 144 and their LCM is 36.Find their HCF.

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$\Large \underline \frak \red{ Solution }$

As we know that

${\Rightarrow{\textsf{LCM × HCF = Product of the numbers. }}}$

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So,

Let the HCF be 'x'

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Now,

$: \implies \sf{36 \times x} = 144$

$: \implies \sf{36x = 144}$

$: \implies \sf{x = \cancel \dfrac{144}{36} }$

$: \implies \sf{x = 4}$

$: \longmapsto \underline{ \boxed{\sf \red{HCF = 4}}}$

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