Question

Q4 Find answers to the following. Write and indicate how you solved them . a) Is 5/9 equal to 4/5 ? b) is 9/16 equal to 5/9? C) is 4/5 equal to 16/20 ? d) Is 1/15 equal to 4/30 ?​

Answer 1

${\huge{\underline{\large{\mathbb{\green{VERIFIED \: ANSWER}}}}}}$

C)4/5 = 16/20

Step-by-step explanation:

a/b = c/d

if a * d = b * c

5/4 = 4/5

if 5 * 5 = 4 * 4

if 25 = 16

but 25 ≠ 16

Answer 2

$\begin{gathered}{\underline{\underline{\Huge{\dag{\textsf{\textbf{\red{Solution :}}}}}}}}\end{gathered}$

$\begin{gathered}{\underline{\underbrace{\large{\textsf{\textbf{\blue{Question:}}}}}}}\end{gathered}$

• Find answers to the following. Write and indicate how you solved them . a) Is 5/9 equal to 4/5 ? b) Is 9/16 equal to 5/9? C) Is 4/5 equal to 16/20 ? d) Is 1/15 equal to 4/30 ?

$\begin{gathered}{\underline{\underbrace{\large{\textsf{\textbf{\blue{Answer :}}}}}}}\end{gathered}$

• a) Not equal
• b) Not equal
• c) Equal
• d) Not equal

$\begin{gathered}{\underline{\underbrace{\large{\textsf{\textbf{\blue{Formula \: To \: Solve \: This :}}}}}}}\end{gathered}$

• Here in the question 2 fractions are given we have to determine whether they are equal or not.
• First of all as we are seeing in the question the denominator in both the fraction are different in every part of the question.
• To make them same we have to find the L.C.M of the denominators of both the fractions and we have to divide once the L.C.M with both the denominators.
• After it the quotient we got by dividing both of the denominators of the fractions by the L.C.M. We have to multiply it with both of the fractions means with their numerators and denominators.
• Now we have the denominators of both fractions same we can easily compare the numerators and can get easily that they are equal or not.
• At last we can write whether they are same or not .

$\begin{gathered}{\underline{\underbrace{\large{\textsf{\textbf{\blue{Explanation :}}}}}}}\end{gathered}$

$\sf\bold{a) \: Is \: \dfrac{5}{9} \: equal \: to \: \dfrac{4}{5}}$

$\sf\implies \bold\red{The \: L.C.M \: of \: 9 \: and \: 5 \: :- \: 45 }$

$\sf\red\bigstar{ \: Dividing \: the \: denominators \: from \: the \: L.C.M \: we \: get \: :}$

$\sf\leadsto\bold{ 45 \div \: 9 \: = \: 5}$

$\sf\leadsto\bold{ 45 \div \: 5 \: = \: 9}$

$\sf\red\bigstar{ \: Multiplying \: the \: quotient \: with \: fractions \: :}$

$\sf\leadsto\bold{\dfrac{5 \times 5}{9 \times 5} \: = \: \dfrac{25}{45}}$

$\sf\leadsto\bold{\dfrac{4 \times 5}{9 \times 9} \: = \: \dfrac{36}{45}}$

$\sf\leadsto \bold{\dfrac{25}{45} \: \neq \: \dfrac{36}{45}}$

$\sf\leadsto \bold\red{Hence, \: \dfrac{5}{9} \: \neq \: \dfrac{4}{5}}$

• The fractions 5/9 and 4/5 are not equal.

$\sf\bold{b) \: Is \: \dfrac{9}{16} \: equal \: to \: \dfrac{5}{9}}$

$\sf\implies \bold\red{The \: L.C.M \: of \: 16 \: and \: 9 \: :- \: 144 }$

$\sf\red\bigstar{ \: Dividing \: the \: denominators \: from \: the \: L.C.M \: we \: get \: :}$

$\sf\leadsto\bold{ 144 \div \: 16 \: = \: 9}$

$\sf\leadsto\bold{ 144 \div \: 9 \: = \: 16}$

$\sf\red\bigstar{ \: Multiplying \: the \: quotient \: with \: fractions \: :}$

$\sf\leadsto\bold{\dfrac{9 \times 9}{16 \times 9} \: = \: \dfrac{81}{144}}$

$\sf\leadsto\bold{\dfrac{5 \times 16}{9 \times 16} \: = \: \dfrac{80}{144}}$

$\sf\leadsto \bold{\dfrac{81}{144} \: \neq \: \dfrac{80}{144}}$

$\sf\leadsto \bold\red{Hence, \: \dfrac{9}{16} \: \neq \: \dfrac{5}{9}}$

• The fractions 9/16 and 5/9 are not equal.

$\sf\bold{c) \: Is \: \dfrac{4}{5} \: equal \: to \: \dfrac{16}{20}}$

$\sf\implies \bold\red{The \: L.C.M \: of \: 5 \: and \: 20 \: :- \: 20 }$

$\sf\red\bigstar{ \: Dividing \: the \: denominators \: from \: the \: L.C.M \: we \: get \: :}$

$\sf\leadsto\bold{ 20 \div \: 5 \: = \: 4}$

$\sf\leadsto\bold{ 20 \div \: 20 \: = \: 1}$

$\sf\red\bigstar{ \: Multiplying \: the \: quotient \: with \: fractions \: :}$

$\sf\leadsto\bold{\dfrac{4 \times 4}{5 \times 4} \: = \: \dfrac{16}{20}}$

$\sf\leadsto\bold{\dfrac{16 \times 1}{20 \times 1} \: = \: \dfrac{16}{20}}$

$\sf\leadsto \bold\red{\: \dfrac{16}{20} \: = \: \dfrac{16}{20}}$

$\sf\leadsto \bold\red{Hence, \: \dfrac{4}{5} \: = \: \dfrac{16}{20}}$

• The fractions 4/5 and 16/20 are equal.

$\sf\bold{c) \: Is \: \dfrac{1}{15} \: equal \: to \: \dfrac{4}{30}}$

$\sf\implies \bold\red{The \: L.C.M \: of \: 15 \: and \: 30 \: :- \: 30 }$

$\sf\red\bigstar{\: Dividing \: the \: denominators \: from \: the \: L.C.M \: we \: get \: :}$

$\sf\leadsto\bold{ 30 \div \: 15 \: = \: 2}$

$\sf\leadsto\bold{ 30 \div \: 30 \: = \: 1}$

$\sf\red\bigstar{\: Multiplying \: the \: quotient \: with \: fractions \: :}$

$\sf\leadsto\bold{\dfrac{1 \times 2}{15 \times 2} \: = \: \dfrac{2}{30}}$

$\sf\leadsto\bold{\dfrac{4 \times 1}{30 \times 1} \: = \: \dfrac{4}{30}}$

$\sf\leadsto \bold\red{ \: \dfrac{2}{30} \: \neq \: \dfrac{4}{30}}$

$\sf\leadsto \bold\red{Hence, \: \dfrac{1}{15} \: \neq \: \dfrac{4}{30}}$

• The fractions 1/15 and 4/30 are not equal.

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