Question

James added 3 and two-thirds plus 4 and one-eighth. His work is shown here. What did James do right? What did he do wrong? What should he have done?

three and two-thirds plus 4 and one-eighth equals 7 and three-elevenths

Answer 1

He went wrong by adding the two denominators. You don't add or subtract denominators.

He also needed to find a common denominator for fractions 2/3 + 1/8. To add or subtract fractions, you need a common denominator.

The easiest way to find a common denominator is to simply multiply the denominators.
So for fractions 2/3 + 1/8, you would multiply 3 times 8 to get a common denominator of 24.

He also needed to rewrite the two fractions 2/3 + 1/8 as equivalent fractions ( nicknames so to speak) using 24 as the new common denominator.

To do, that he would give each fraction a new nickname (equivalent fraction). So for faction 2/3, he would multiply the top and bottom of the fraction by 8. So that fraction's new nickname is 16/24. For fraction 1/8, he would multiply the top and bottom of the fraction by 3. So that's fraction's new nickname is 3/24.

So adding the two fraction with their new nicknames we get 16/24 + 3/24 = 19/24.

He did correctly add the two whole numbers( 3+4) and got 7. He also knew that he had to add the two numerators. He just forgot to change the fractions to equivalent fractions first.