Halves and thirds are different-size pieces. Rename both over a bottom they share first. 1/2 = 3/6 and 1/3 = 2/6, so 1/2 + 1/3 = 5/6.
Worked example
Add the two fractions: 12 + 712
Answer:1112
Different-size pieces can’t be counted together. halves and twelfths both fit into twelfths: 12 = 612 and 712 = 712. Now the pieces match, so add the tops: 6 + 7 = 13, which is 1312. That’s more than 1: 1112.
12=612
712
For grown-ups: Add/subtract unlike denominators via equivalent fractions, including mixed numbers. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
CCSS 5.NF.A.1–2
What this practises, for teachers
Practices add/subtract unlike denominators via equivalent fractions, including mixed numbers (5.NF.A.1–2). A printable sheet with its answer key, worked answers on the page, no accounts.
Different-size pieces can’t be counted together. tenths and fourths both fit into twentieths: 710 = 1420 and 14 = 520. Now the pieces match, so add the tops: 14 + 5 = 19, which is 1920.
710=1420
14=520
Add the two fractions: 1112 + 16
Show the answer and how
Answer:1112
Different-size pieces can’t be counted together. twelfths and sixths both fit into twelfths: 1112 = 1112 and 16 = 212. Now the pieces match, so add the tops: 11 + 2 = 13, which is 1312. That’s more than 1: 1112.
1112
16=212
Add the two fractions: 34 + 58
Show the answer and how
Answer:138
Different-size pieces can’t be counted together. fourths and eighths both fit into eighths: 34 = 68 and 58 = 58. Now the pieces match, so add the tops: 6 + 5 = 11, which is 118. That’s more than 1: 138.