First method
Put 1¾ as an improper fraction 7/4, then multiply by 3 to get 21/4.
21/4 converts back to a mixed number as 5¼.
[tex]1\frac{3}4=1+\frac{3}4=\frac{4}4+\frac{3}4=\frac{7}4\\\\\frac{7}4\times3=\frac{21}4=\frac{20}4+\frac{1}4=\boxed{5\frac{1}4}[/tex]
Second method
Think of 1¾ as an addition of 1 and ¾. Multiplying that by 3 works with the distributive property. 1×3 = 3. ¾×3 = 9/4 = 2¼. 3 + 2¼ = 5¼.
[tex]3\times1\frac{3}4=3\times(1+\frac{3}4)=1\times3+\frac{3}4\times3=3+\frac{9}4=3+2\frac{1}4=\boxed{5\frac{1}4}[/tex]
