1fully worked

Work out $\dfrac{1}{2}+\dfrac{1}{3}$.

1common denominator $=6$Find a common denominator

2$\dfrac{1}{2}=\dfrac{3}{6},\;\; \dfrac{1}{3}=\dfrac{2}{6}$Rewrite each fraction over it

3$\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}$Add the numerators

4$\dfrac{5}{6}$ is already in its lowest termsSimplify if you can

Check - Why can we not just add the numerators of $\tfrac{1}{2}+\tfrac{1}{3}$ to get $\tfrac{2}{5}$?

A the pieces are different sizes until the denominators matchB because $2$ and $3$ are not equal numbersC you must always add the denominators tooD adding fractions is not allowed

2you finish it

Work out $\dfrac{2}{3}+\dfrac{1}{4}$.

1common denominator $=12$Find a common denominator

2$\dfrac{2}{3}=\dfrac{8}{12},\;\; \dfrac{1}{4}=\dfrac{3}{12}$Rewrite each fraction over it

3$\dfrac{8}{12}+\dfrac{3}{12}=\dfrac{11}{12}$Add the numerators

4Simplify if you can

Check - A student used $7$ as the common denominator of $\tfrac{2}{3}$ and $\tfrac{1}{4}$. What did they do wrong?

A they should multiply the two fractions insteadB nothing – $7$ is correctC you use a common multiple of $3$ and $4$ (which is $12$), not $3+4$D they should have used $3$

3you finish it

Work out $\dfrac{3}{4}+\dfrac{1}{6}$.

1common denominator $=12$Find a common denominator

2$\dfrac{3}{4}=\dfrac{9}{12},\;\; \dfrac{1}{6}=\dfrac{2}{12}$Rewrite each fraction over it

3Add the numerators

4Simplify if you can

Check - What is the lowest common denominator of $4$ and $6$?

A $24$B $12$C $10$D $2$

4you do it all

Work out $\dfrac{1}{6}+\dfrac{3}{8}$.

1Find a common denominator

2Rewrite each fraction over it

3Add the numerators

4Simplify if you can

Check - How can you tell that $\tfrac{13}{24}$ cannot be simplified?

A $24$ is even, so it never simplifiesB $13$ is prime and is not a factor of $24$, so they share no common factorC a fraction with $24$ on the bottom can never simplifyD it can – it equals $\tfrac{1}{2}$