Answer:
[tex]\boxed{\boxed{\sf \frac{5}{4} \:\: or\:\: 1.25}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{10}{14}\div \cfrac{4}{7}[/tex]
Apply fraction rule:
[tex]\boxed{\sf \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}}[/tex]
[tex]\longmapsto\sf \cfrac{10}{14}\times \cfrac{7}{4}[/tex]
[tex]\longmapsto\sf \cfrac{10}{14}[/tex]
Factor numbers:
[tex]\longmapsto\sf \cfrac{2\cdot \:5}{2\cdot \:7}[/tex]
Cancel comment factor: 2
[tex]\longmapsto\sf \cfrac{5}{4}[/tex]
____________
[tex]\longmapsto\sf \cfrac{5}{7}\times \cfrac{7}{4}[/tex]
Cross:
Cancel 7:
[tex]\longmapsto\sf \cfrac{5}{4}[/tex]
or
[tex]\longmapsto\sf 1.25[/tex]
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