**How to find the square of a fraction ?**

Here we are going to see how to find the square of fraction.

To obtain the square of a fraction, we have to take squares for both numerator and denominator.

For example,

**(a / b) ^{2} = a^{2} / b^{2}**

We should not take squares for the terms which are added or subtracted.

After converting two or more rational numbers as one rational number, we may take squares for both numerator and denominator separately.

Fro example,

[ (1/2) + (1/4) ]^{2} = ( (2 + 1)/4 )^{2}

= (3/4)^{2}

= 3^{2} / 4^{2}

= 9 / 16

Let us look into some more examples based on the concept given above.

**Example 1 :**

Find the square of 7/10

**Solution :**

Square of 7/10 = (7/10)^{2}

= 7^{2} / 10^{2}

= (7 ⋅ 7) / (10 ⋅ 10)

= 49/10

**Example 2 :**

Find the square of (1/12) + (1/3)

**Solution :**

Square of (1/12) + (1/3) = [(1/12) + (1/3)]^{2}

Since we have square for two rational number which are added, we have to convert it into one rational number by taking L.C.M.

= [(1/12) + (1/3) ⋅ (4/4)]

= [(1/12) + (4/12)]

= (1 + 4) / 12

= 5/12

[(1/12) + (1/3)]^{2} = (5/12)^{2}

= 5^{2} / 12^{2}

= 25/144

**Example 3 :**

Find the square of (4/15) ⋅ (3/20)

**Solution :**

Square of (4/15) ⋅ (3/20) = [(4/15) ⋅ (3/20)]^{2}

Since we have square for two rational number which are multiplied, we may simplify the rational numbers and take squares.

= [(4/15) ⋅ (3/20)]^{2}

= [(4 ⋅ 3) / (15 ⋅ 20)]^{2}

= [ (1 ⋅ 1) / (5 ⋅ 4) ]^{2}

= (1 / 20)^{2}

= 1^{2} / 20^{2}

= 1 / 400

**Example 4 :**

Find the square of (-3/4)

**Solution :**

Square of negative is positive.

square of (-3/4) = (-3/4)^{2}

= (-3)^{2} / 4^{2}

= 9/16

To find the square of the algebraic expression, we have to compare the given algebraic expression with one of the following algebraic identities given below and expand.

(a + b)^{2} = a^{2} + 2ab + b^{2}

(a - b)^{2} = a^{2} - 2ab + b^{2}

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca

To see more example please visit "Algebraic identities"

After having gone through the stuff given above, we hope that the students would have understood "How to find the square of a fraction"

Apart from the stuff given above, if you want to know more about "How to find the square of a fraction", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**