Join and remove like parts

Keep the size of a part

A paper strip is one whole. It has eight equal parts. Mark three parts, then mark two more that do not overlap the first three.

There are now five marked eighths:

The denominator stays eight because the whole has not been cut into a new kind of part. We add the number of eighths, not the sizes written underneath.

Writing 3/8 + 2/8 = 5/16 would count sixteenths, which are smaller pieces. That does not match the strip.

Take away some of the same parts

If seven eighths are marked and three eighths are erased, four eighths remain:

Check by joining the remaining and erased parts: 4/8 + 3/8 = 7/8.

The answer 4/8 still means four eighth-pieces. It is also one half of the strip. Either 4/8 or 1/2 describes the amount left; these questions do not require you to change to the smallest possible numbers.

Check your understanding 1 Find the missing amount

A ribbon is split into ten equal lengths. Four tenths are used and three tenths are saved. What fraction is used or saved? What fraction is neither used nor saved?

Your answer or drawing on paper

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Used or saved is 4/10 + 3/10 = 7/10. The whole has ten tenths, so 10/10-7/10 = 3/10 is neither. The three groups together make the whole.

All parts make the whole

One whole is 6/6 when you work in sixths. If five sixths of a strip are coloured, one sixth is not coloured: 6/6-5/6 = 1/6.

Adding all the missing parts can give one whole: 3/8 + 5/8 = 8/8 = 1. Removing every marked part gives zero: 4/8-4/8 = 0. A zero answer does not mean that you may use zero as a denominator; the denominator still describes the equal parts of the whole.

Before calculating, check that the parts refer to the same whole and are the same size. These calculations use like denominators no greater than 12, with the result staying within one whole.

Check your understanding 2 Explain the wrong denominator

Jo writes 2/12 + 5/12 = 7/24. Draw a strip split into twelve equal parts to show what the answer should be.

Your answer or drawing on paper

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Mark two twelfths and five more twelfths. Seven of the twelve parts are marked, so the answer is 7/12. There are still twelve parts in the original whole; no extra cut made twenty-fourths.

Work without a prepared strip

Find 5/9-2/9. Draw your own whole to check the subtraction. Then add back what you removed.