The value of [tex]\dfrac{a}{b}[/tex] is required.
The required fraction is [tex]\dfrac{a}{b}=\dfrac{4}{7}[/tex]
Fractions
The given fraction is
[tex]\dfrac{a}{4}=\dfrac{b}{7}[/tex]
Multiplying by [tex]4[/tex] on both sides
[tex]a=\dfrac{4b}{7}[/tex]
Multiplying by [tex]7[/tex] on both sides
[tex]7a=4b[/tex]
Dividing by [tex]7[/tex] on both sides
[tex]a=\dfrac{4}{7}b[/tex]
Dividing by [tex]b[/tex] on both sides
[tex]\dfrac{a}{b}=\dfrac{4}{7}[/tex]
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