Lesson 6 of 10 · Grades 3 to 5
Subtract fractions with the same denominator
Subtracting fractions with the same denominator works like adding. The parts are all the same size, so you simply take some away. Subtract the second numerator from the first and keep the denominator.
Taking parts away
Subtracting fractions with the same denominator works exactly like adding them. All the parts are the same size, so you simply take some away and count what is left. Five sixths take away two sixths leaves three sixths. The size of the parts does not change, so the denominator does not change.
The rule is: subtract the second numerator from the first and keep the denominator. For 5/6 - 2/6, subtract 5 - 2 = 3 and keep the 6. The answer is 3/6.
Subtracting from a whole
If the first fraction is a whole, write the whole with the same denominator before you subtract. A whole bar cut into fifths is 5/5. So 5/5 - 2/5 = 3/5. The little trick of writing 1 as n/n, where n is the denominator, lets you subtract any same-denominator fraction from a whole.
Sometimes the two numerators are the same and nothing is left: 4/9 - 4/9 = 0. That makes sense. If you take away every part, no parts remain. Anything minus itself is zero, and fractions behave the same way.
Tidying the answer
After subtracting, check whether the answer can be simplified. 4/8 can be divided top and bottom by 4 to make 1/2, and 5/10 becomes 1/2 by dividing both numbers by 5. Simplifying does not change the amount, but it makes the answer easier to read. If no number except 1 divides both parts, the fraction is already in its simplest form.
Worked example
Work out 8/10 - 3/10. Step 1: the denominators match, so the parts are tenths. Step 2: subtract the numerators: 8 - 3 = 5. Step 3: keep the denominator: the answer is 5/10. Step 4: simplify. Both 5 and 10 divide by 5, so 5/10 becomes 1/2. The answer is 1/2.
Now a word problem. A ribbon is 7/8 of a metre long. You cut off 3/8 of a metre. How much ribbon is left? The parts are both eighths, so subtract 7 - 3 = 4 and keep 8. The answer is 4/8 of a metre, which simplifies to 1/2 of a metre.
Watch out for this
Do not subtract the denominators. 5/6 - 2/6 is 3/6, not 3/0 and not 3/6 with a changed denominator. The denominator is the name of the part, and taking parts away does not rename them. Also make sure you subtract the smaller numerator from the larger one, so the answer is not negative.
Remember
- Same denominator: subtract the numerators and keep the denominator.
- Write a whole as a fraction with the same denominator, like 5/5.
- Equal fractions take away to 0.
- Simplify the answer when you can.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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5/6 - 2/6 = ?
Show answer
3/6, which simplifies to 1/2.
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7/8 - 3/8 = ?
Show answer
4/8, which simplifies to 1/2.
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9/10 - 4/10 = ?
Show answer
5/10, which simplifies to 1/2.
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4/5 - 1/5 = ?
Show answer
3/5.
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A ribbon is 5/8 of a metre long. You cut off 1/8 of a metre. How much ribbon is left?
Show answer
4/8 of a metre, which simplifies to 1/2 of a metre.
Puzzle · Juice jug
Puzzle time
A full jug of juice is 12/12. Mia pours 5/12 into her cup. Then Leo pours some into his cup. Now 4/12 is left in the jug. How much did Leo pour?
Show a hint
Start with 12/12 and take away Mia's 5/12. How much is in the jug just before Leo pours?
Show the answer
Answer: 3/12. Before Leo pours, the jug holds 12/12 - 5/12 = 7/12. After he pours, 4/12 is left, so he poured 7/12 - 4/12 = 3/12. Check: 5/12 + 3/12 + 4/12 = 12/12.