Helping with Lesson 4 — Subtracting fractions

Helping someone learn · Fractions · Lesson 4

Helping fraction subtraction make sense

Subtraction is easiest when it is visible: start with an amount, physically remove some equal-sized pieces, and look at what remains. If the pieces are different sizes, rename them first.

Begin by taking pieces away

Start with fractions that already use the same denominator, such as 5/7 − 2/7. Build 5 seventh-pieces, remove 2, and count what remains.

Example:

Start with 5 sevenths. Take away 2 sevenths. Three seventh-pieces remain, so 5/7 − 2/7 = 3/7.

The denominator stays the same because the size of the pieces has not changed. We are only changing how many of those pieces remain.

Use objects that can actually be removed

MathLink cubes or LEGO

Build the starting amount as equal groups, then physically detach the groups being subtracted.

Sweets or counters

Take a known fraction of a collection, then remove some of those equal groups. This works especially well when the whole is a set rather than one shape.

Fraction strips

Lay out the starting length, then cover or remove pieces. The remaining length makes the result visible immediately.

Then introduce one familiar mismatch

A good next example is 3/4 − 1/2. The pieces do not match, so do not subtract yet.

Rebuild the half as two quarters. Now both amounts use quarter-sized pieces:

3/4 − 1/2 = 3/4 − 2/4 = 1/4.

This should feel like the same move as Lesson 3, only now pieces are being removed rather than joined.

Keep the story visible

Subtraction is easier to understand when the learner can say what is happening.

Start: “We have three quarters.”
Rename: “One half is the same as two quarters.”
Remove: “Take away two quarter-pieces.”
Remain: “One quarter is left.”

Common misconceptions to watch for

Subtracting denominators.

If the learner writes 5/7 − 2/7 = 3/0 or 3/7 by a memorised rule they cannot explain, return to the pieces. The seventh-sized pieces do not change size when some are removed.

Removing before matching piece sizes.

A half-piece cannot simply be “taken away” from three quarter-pieces without first expressing both amounts with the same-sized pieces.

Losing track of the original whole.

Keep the whole fixed. The meaning of one quarter depends on what the whole is.

Questions that reveal understanding

“What do we start with?”
“What are we removing?”
“Are the pieces the same size yet?”
“Can you rename the half using quarters?”
“How many pieces are left?”
“Can you check by putting the removed pieces back?”

Cross-topic links worth noticing

Time
Three quarters of an hour minus half an hour leaves one quarter of an hour.
Money
75p − 50p = 25p and 75¢ − 50¢ = 25¢ mirror 3/4 − 1/2 = 1/4 of £1 or $1. This is often a much friendlier route into the same subtraction than starting with symbols.
Measurement
Three quarters of a litre minus half a litre leaves one quarter litre.
Checking addition
If 3/4 − 1/2 = 1/4, then 1/4 + 1/2 should rebuild 3/4.

When to move on

The learner is ready when they can:

  • subtract fractions with the same denominator by physically removing equal-sized pieces;
  • explain why the denominator stays the same;
  • rename a familiar fraction such as one half as two quarters before subtracting;
  • describe what remains rather than relying only on a memorised rule;
  • check subtraction by rebuilding the original amount.

Use the learner lesson alongside this guide

The learner page follows the same progression: remove equal-sized pieces first, then handle familiar mismatches such as halves and quarters by renaming before subtracting.

Open Lesson 4: Subtracting fractions →