Question

simplify 5 1 /2 +[7 1/2 -{4+(5- 6 1/2 - 4 1/2 )}]​

Answer 1

★ How to do :-

Here, we are given with some fractions to simplify them. We are given with three different brackets in those. To find the answer in this question, we should make use of a concept called as BODMAS rule. This rule says that we should solve first division, multiplication, addition and finally the addition. In this question, first we should solve the smaller brackets. Then, we should solve the second or curly brackets. Finally, we can solve the numbers given in the square brackets. If any of the numbers are given on out of all the brackets, then that should be solved at last. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 5 \dfrac{1}{2} + \bigg[ 7 \dfrac{1}{2} - \bigg\{ 4 + \bigg( 5 - 6 \dfrac{1}{2} - 4 \dfrac{1}{2} \bigg) \bigg\} \bigg]}$

Convert all mixed fractions to improper fractions.

${\tt \leadsto \dfrac{11}{2} + \bigg[ \dfrac{15}{2} - \bigg\{ \dfrac{4}{1} + \bigg( \dfrac{5}{1} - \dfrac{13}{2} - \dfrac{9}{2} \bigg) \bigg\} \bigg]}$

First let's solve the smaller brackets.

${\tt \leadsto \dfrac{5}{1} - \dfrac{13}{2} - \dfrac{9}{2}}$

LCM of 1 and 2 is 2.

${\tt \leadsto \dfrac{5 \times 2}{1 \times 2} - \dfrac{13}{2} - \dfrac{9}{2}}$

Write all the numerators with a common denominator.

${\tt \leadsto \dfrac{10 - 13 - 9}{2} = \dfrac{(-12)}{2}}$

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Insert the obtained answer in it's place.

${\tt \leadsto \dfrac{11}{2} + \bigg[ \dfrac{15}{2} - \bigg\{ \dfrac{4}{1} + \dfrac{(-12)}{2} \bigg\} \bigg]}$

Now, let's solve the curly brackets.

${\tt \leadsto \dfrac{4}{1} + \dfrac{(-12)}{2}}$

LCM of 1 and 2 is 2.

${\tt \leadsto \dfrac{4 \times 2}{1 \times 2} + \dfrac{(-12)}{2}}$

Write both numerators with a common denominator.

${\tt \leadsto \dfrac{8 + (-12)}{2}}$

Write the second number in numerator with one sign

${\tt \leadsto \dfrac{8 - 12}{2} = \dfrac{(-4)}{2}}$

Insert the obtained answer in it's place.

${\tt \leadsto \dfrac{11}{2} + \bigg[ \dfrac{15}{2} - \dfrac{(-4)}{2} \bigg]}$

Now, let's solve the square brackets.

${\tt \leadsto \dfrac{15}{2} - \dfrac{(-4)}{2}}$

Write both numerators with a common denominator.

${\tt \leadsto \dfrac{15 - (-4)}{2}}$

Write the second number in numerator with one sign.

${\tt \leadsto \dfrac{15 + 4}{2} = \dfrac{19}{2}}$

Insert the obtained answer in it's place.

${\tt \leadsto \dfrac{11}{2} + \dfrac{19}{2}}$

Add those fractions now.

${\tt \leadsto \dfrac{11 + 19}{2} = \dfrac{30}{2}}$

Write the obtained answer in lowest form.

${\tt \leadsto \cancel \dfrac{30}{2} = 15}$

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${\red{\underline{\boxed{\bf So, \: the \: obtained \: answer \: is \: 15.}}}}$

Answer 2

Answer :-

• The required number is 15.

Solution :-

$\sf 5 \dfrac{1}{2} + \left[7 \dfrac{1}{2} - \left\{4 + \left(5 - 6 \dfrac{1}{2} - 4 \dfrac{1}{2}\right) \right\}\right]$

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Let's solve the round brackets first!

$\hookrightarrow\sf \left(5 - 6 \dfrac{1}{2} - 4 \dfrac{1}{2}\right)$

Converting the mixed fractions into improper fractions,

$\hookrightarrow\sf \left(5 - \dfrac{13}{2} - \dfrac{9}{2} \right)$

The LCM of 1, 2 and 2 is 2, so subtracting the fractions using their denominators,

$\hookrightarrow\sf \left(\dfrac{5 \times2 - 13 \times 1 - 9 \times 1}{2}\right)$

On simplifying,

$\hookrightarrow\sf \left(\dfrac{10 - 13 - 9}{2}\right)$

Subtracting the numbers,

$\hookrightarrow\left(\sf \dfrac{-12}{\:\:\:\:\:2}\right)$

Reducing the fraction to it's simplest form,

$\hookrightarrow\left(\sf \dfrac{-6}{\:\:\:\:1}\right)$

Removing the denominator,

$\hookrightarrow\sf \left(-6\right)$

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Let's solve the curly brackets now!

$\hookrightarrow\sf{\left\{4\:+\:(-6)\right\}}$

Adding -6 to 4,

$\hookrightarrow\sf \{(-2)\}$

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Next, let's solve the square brackets!

$\hookrightarrow\sf \left[7 \dfrac{1}{2} - (-2)\right]$

Converting the mixed fraction into improper fraction,

$\hookrightarrow\sf \left[\dfrac{15}{2} - (-2) \right]$

The LCM of 2 and 1 is 2, so subtracting the fractions using their denominators,

$\hookrightarrow\sf \left[\dfrac{15 \times 1 - (-2) \times 2}{2}\right]$

On simplifying,

$\hookrightarrow\sf \left[\dfrac{15 - (-4)}{2} \right]$

Subtracting -4 from 15,

$\hookrightarrow\sf \left[\dfrac{19}{2}\right]$

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Finally, let's add the result to 5 1/2 to get our answer!

$\hookrightarrow\sf 5 \dfrac{1}{2} + \dfrac{19}{2}$

Converting the mixed fraction into improper fraction,

$\hookrightarrow\sf \dfrac{11}{2} + \dfrac{19}{2}$

The denominators of the fractions are same, so we will add them like normal numbers,

$\hookrightarrow\sf \dfrac{11 + 19}{2}$

Adding the numbers,

$\hookrightarrow\sf \dfrac{30}{2}$

Reducing the fraction to it's simplest form,

$\hookrightarrow\sf \dfrac{15}{1}$

Removing the denominator,

$\hookrightarrow\underline{\boxed{\sf 15}}$

• Hence, the answer is 15.

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Know more :-

In the above question, we have used BODMAS.

BODMAS stands for :-

• B - Bracket
• O - Of
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

Order of Brackets :-

• Round brackets or first brackets :- ()
• Curly brackets or second brackets :- {}
• Square brackets or third brackets :- []