Adding and subtracting fractions

Ribbon A is three quarters of a metre long. Ribbon B is two fifths of a metre long. Find their total length. Try it first. Pause if you like. Quarters and fifths are different sizes. How can we measure both ribbons using equal-sized parts? Each reference strip represents one metre. The blue ribbon lengths are three quarters and two fifths of that same metre. The smallest common multiple of four and five is twenty. Split each quarter into five equal parts, and each fifth into four equal parts. The reference metre stays exactly the same length. Write total length as three quarters plus two fifths. Three quarters is fifteen twentieths. Two fifths is eight twentieths. Both now use the same-sized parts. Join the two ribbons end to end. No part changes size, and no part overlaps another. Fifteen twentieths plus eight twentieths equals twenty-three twentieths. Twenty of these parts make one whole metre. Three twentieths extend beyond it. Twenty-three twentieths equals one and three twentieths. The fraction part is in its simplest form. The total length of the two ribbons is one and three twentieths of a metre. Rename using equal parts of the same metre, add the parts, then write the improper fraction as a mixed number.

Hafiz had three litres of juice. He drank five sixths of a litre. How much juice was left? Try it first. Pause if you like. How can one of the three whole litres help us subtract five sixths of a litre? These three equal strips each represent one litre of juice. Write juice left as three minus five sixths. Keep two litres whole. Divide the third litre into six equal parts. Its amount stays the same. Three litres is two wholes and six sixths. So write two and six sixths minus five sixths. Five of those sixths are the juice Hafiz drank. Move them aside to keep track of that amount. Two whole litres and one sixth of a litre remain. The five sixths he drank are separate. Two and six sixths minus five sixths equals two and one sixth. Two and one sixth litres of juice was left. Rename one whole as equal parts before subtracting. Check that the answer gives the amount left.