Compare fractions using equal-size parts

For 3/8 and 1/4, does the larger denominator always mean less?

With the same denominator, compare parts taken. With different denominators, express both with a common part size.

Divide one whole into eighths. For 3/8 and 5/8 the parts have the same size, so five parts are more than three: 5/8 is greater.

If numerators match, compare 2/3 and 2/5 by piece size. Dividing the same whole into more parts makes each part smaller. Two thirds exceed two fifths because each third is larger than each fifth.

For 3/8 and 1/4, the numbers of parts taken also differ. The denominator alone cannot settle the comparison. Rewrite 1/4 as the equal amount 2/8 to compare matching parts.

3/8 is three eighth-pieces, while 1/4 is two eighth-pieces. Thus 3/8 is greater. A common denominator puts different descriptions into the same unit.

On the same number line, the number farther right is greater. Different unit lengths in separate diagrams can mislead, so keep the 0-to-1 intervals equal.

Listen one paragraph at a time

1 / 5

2 / 5

3 / 5

4 / 5

5 / 5

If you compared only denominators

Say the piece size and piece count separately. To compare one large piece with several smaller ones, change both to common-size pieces.

Now change it yourself

Choose two fractions and view a common partition. Compare shaded lengths and numerators on equal wholes.

Choose two fractions

3/8 = 3/8 · One outlined strip = one equal-size whole

1/4 = 2/8 · One outlined strip = one equal-size whole

Both strips use the same whole; one common piece is 1/8.

A larger denominator gives a smaller positive fraction only when the numerators match. If both change, compare the full values.

Try with paper and objects

Shade two fractions on identical rectangles and add shared subdivisions to compare.

Check your idea with another example

Check your idea 1

Of the same whole, which is greater: 2/7 or 2/5?

Check your idea 2

Express 5/6 and 3/4 in common parts.

Try a different setting

Identical tanks contain 4/5 and 7/10 of their capacities. Which has more?

Write an answer yourself

Return to the explanation

Compare with an explanation

2/3 · 2/3=8/12, which is greater than 7/12.

Does your explanation include these ideas?

Speak, point or draw on paper. Explain the reason, not just the numerical answer.

I kept the whole size the same.I considered numerator as well as denominator.I explained using common pieces or a number line.

Continue, or pause here

Add or subtract numerators when units match; first find common units when denominators differ.