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Which is more : sum of 3/4 , 2 1/5 or 1/3 of (5/6 divided by 5/36)
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Show your step by step working for this question and i am warning: Only @mathdude500 or @QιиAι will answer
Which is more : sum of 3/4 , 2 1/5 or 1/3 of (5/6 divided by 5/36)
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Answer:
[tex]\qquad\qquad\boxed{ \sf{ \: \bf \:\dfrac{3}{4} + 2\dfrac{1}{5} \: > \: \dfrac{1}{3} \: of \: \bigg(\dfrac{5}{6} \div \dfrac{5}{36} \bigg) \: }}\\ \\ [/tex]
Step-by-step explanation:
Consider,
[tex]\qquad\sf \: \dfrac{3}{4} + 2\dfrac{1}{5} \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{3}{4} + \dfrac{5 \times 2 + 1}{5} \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{3}{4} + \dfrac{10 + 1}{5} \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{3}{4} + \dfrac{11}{5} \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{15 + 44}{20} \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{59}{20} \\ \\ [/tex]
[tex]\qquad\sf \: = \: 2\dfrac{19}{20} \\ \\ [/tex]
Hence,
[tex]\qquad\sf\implies \sf \: \dfrac{3}{4} + 2\dfrac{1}{5} = 2\dfrac{19}{20} - - - (1) \\ \\ \\ [/tex]
Now, Consider
[tex]\qquad\sf \: \dfrac{1}{3} \: of \: \bigg(\dfrac{5}{6} \div \dfrac{5}{36} \bigg) \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{1}{3} \: \times \: \bigg(\dfrac{5}{6} \times \dfrac{36}{5} \bigg) \\ \\ [/tex]
[tex]\qquad\sf \: = \: \dfrac{1}{3} \: \times \: \bigg(6 \bigg) \\ \\ [/tex]
[tex]\qquad\sf \: = \: 2\\ \\ [/tex]
Hence,
[tex]\qquad\sf\implies \sf \: \dfrac{1}{3} \: of \: \bigg(\dfrac{5}{6} \div \dfrac{5}{36} \bigg) = 2 - - - (2)\\ \\ [/tex]
Thus, from equation (1) and (2), we concluded that
[tex]\qquad\sf\implies \bf \:\dfrac{3}{4} + 2\dfrac{1}{5} \: > \: \dfrac{1}{3} \: of \: \bigg(\dfrac{5}{6} \div \dfrac{5}{36} \bigg)\\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
1. Commutative Property of Addition.
[tex]\sf \: \boxed{ \sf{ \:a + b = b + a \: }} \\ \\ [/tex]
2. Associative Property of Addition
[tex]\sf \: \boxed{ \sf{ \:(a + b) + c = a + (b + c) \: }} \\ \\[/tex]
3. Additive Identity
[tex]\sf \: \boxed{ \sf{ \:x + 0 = 0 + x = x \: }} \\ \\ [/tex]
4. Commutative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:a \times b = b \times a \: }} \\ \\ [/tex]
5. Associative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:(a \times b) \times c = a \times (b \times c) \: }} \\ \\[/tex]
6. Multiplicative Identity
[tex]\sf \: \boxed{ \sf{ \:x \times 1 = 1 \times x = x \: }} \\ \\ [/tex]
Solution:
To solve this question, we will take the L.C.M of denominator or convert the given fractions into like fractions.
(i) 5/4 + (-11/4)
= 5/4 -11/4
= (5 - 11)/4
= - 6/4
= - 3/2
(ii) 5/3 + 3/5
Taking L.C.M of 3 and 5 , we get 15
5/3 + 3/5
= (5 × 5)/(3 × 5) + (3 × 3)/(5 × 3)
= 25/15 + 9/15
= (25 + 9)/15
= 34/15
(iii) -9/10 + 22/15
Taking L.C.M of 10 and 15 , we get 30
-9/10 + 22/15
= (- 9 × 3)/30 + (22 × 2)/30
= -27/30 + 44/30
= 17/30
(iv) -3/(-11)+ 5/9
Taking L.C.M of 11 and 9 , we get 99
-3/(-11)+ 5/9
= (-3 × 9)/(-99) + (5 × 11)/99
= 27/99 + 55/99
= 82/99
(v) - 8/19 + ( -2)/57
Taking L.C.M of 19 and 57, we get 57
-8/19 + ( -2)/57
= (-8 × 3)/(19 × 3) + (-2 × 1)/(57 × 1)
= -24/57 + (-2/ 57)
= (-24 - 2)/57
= -26/57
(vi) -2/3 + 0
Taking L.C.M of 3 and 1, we get 3
-2/3 + 0
= (-2 × 1)/3 + (0 × 3)/3
= -2/3 + 0/3
= (-2 + 0)/3
= -2/3