Detailed Solutions to Questions on Maths Proportions
Detailed solutions the questions on proportions are presented with full explanations.

Find \( x \) if \( \dfrac{x}{2} = \dfrac{4}{8} \).
Solution
Multiply both terms of the proportion by the denominators 2 and 8.
\( \color{Red} {2\times8}\,\dfrac{x}{2}=\color{Red} {2\times 8}\,\dfrac{4}{8} \)
Simplify.
\( {\color{Red} {\cancel{2}\times8}}\,\dfrac{x}{\cancel{2}}={\color{Red} {2\times \cancel{8}}}\,\dfrac{4}{\cancel{8}} \)
Simplify.
\( 8x = 8 \)
Divide both sides of the equation by the factor of x and simplify.
\( \dfrac{8x}{8}= \dfrac{8}{8} \)
\( x = 1 \)

Find \( p \) if \( \dfrac{3}{p} = \dfrac{1}{5} \)
Solution
Multiply both terms of the proportion by the denominators p and 5.
\( \color{Red} {5\times p}\,\dfrac{3}{p}=\color{Red} {5\times p}\,\dfrac{1}{5} \)
Simplify.
\( {\color{Red} {5\times \cancel{p}}}\,\dfrac{3}{\cancel{p}}={\color{Red} {\cancel{5}\times p}\,\dfrac{1}{\cancel{5}} } \)
Simplify.
\( 15 = p \)

If \( \dfrac{31}{5} = \dfrac{w}{15}\), then what is the value of \( w \)?
Solution
Multiply both terms of the proportion by the denominators 5 and 15.
\( \color{Red} {5\times 15}\,\dfrac{31}{5}=\color{Red} {5\times 15}\,\dfrac{w}{15} \)
Simplify.
\( {\color{Red} {\cancel{5}\times 5}}\,\dfrac{31}{\cancel{5}}={\color{Red} {5\times \cancel{15}}\,\dfrac{w}{\cancel{15}} } \)
but do not multiply numbers.
\( 5 \times 31 = 5 \times w \)
Divide both sides by 5
\( \dfrac{5 \times 31}{5} = \dfrac{5 \times w}{5} \)
and simplify.
\( 31 = w \)

Find \( k \) if \( \dfrac{2k}{3} = \dfrac{20}{6} \).
Solution
Multiply both terms of the proportion by the denominators 3 and 6.
\( \color{Red} {3\times 6}\,\dfrac{2k}{3}=\color{Red} {3\times 6}\,\dfrac{20}{6} \)
Simplify.
\( \color{Red} {\cancel{3}\times 6}\,\dfrac{2k}{\cancel{3}}=\color{Red} {3\times \cancel{6}}\,\dfrac{20}{\cancel{6}} \)
Simplify.
\( 12k = 60 \)
Divide both sides by the factor of k (12).
\( \dfrac{12k}{12} = \dfrac{60}{12} \)
and simplify.
\( k = 5 \)

Solve the proportion \( \dfrac{3}{7} = \dfrac{y}{0} \) if possible.
Solution
No solution because the division by zero is not allowed in mathematics.

Solve the proportion \( \dfrac{1}{4} = \dfrac{0}{x} \) if possible.
Solution
The left side 1/4 is not equal to zero. The right side is either zero or undefined for x = 0. Hence the above proprotion does not have a solution.

If \( \dfrac{m}{4} = \dfrac{3}{12} \), then what is the value of m?.
Solution
Note here that the fraction on the right side 3 / 12 may be reduced to 1 / 4 by dividing both numerator and denominator by 3 as follows.
\( \dfrac{3}{12} = \dfrac{3 \div 3}{12\div 3} = \dfrac{1}{4} \)
Hence the given proportion may be written as.
\( \dfrac{m}{4} = \dfrac{1}{4} \)
The two fractions have the same denominator and therefore their numerators must be equal. Hence
\( m = 1 \)

Find \(t \) if \( \dfrac{6}{14} = \dfrac{2t}{14} \).
Solution
Note the two fractions making the proportion given above have equal denominator and therefore their numerator must be equal. Hence
\( 6 = 2 t \)
Divide by the coefficient of t (2)
\( 6 / 2 = 2 t / 2 \)
and simplify
\( 3 = t \)

More High School Maths (Grades 10, 11 and 12)  Free Questions and Problems With Answers
More Middle School Maths (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
More Primary Maths (Grades 4 and 5) with Free Questions and Problems With Answers
Home Page