BananaLearnLearning LibraryGamesFind −5/6 + 1/4.
- Use denominator 12: −10/12 + 3/12.
- Add signed numerators: −10 + 3 = −7, so the result is −7/12.
- The positive amount is smaller than the negative magnitude, so a negative result makes sense.
Separate two jobs: the sign and the size of each part
In −3/4 + 1/2, the minus sign tells you where −3/4 lies relative to zero. The denominator tells you the size of the fractional unit. To combine quantities, use the same unit: one half is two quarters, so −3/4 + 2/4 = −1/4. You change the names of the parts, not their values.
Draw a number line with equal quarter steps. Start three steps left of zero, then move two steps right. The endpoint is one quarter left of zero. This makes the sign of the result visible before a written calculation is finished.
A denominator can be negative, but a positive one is easier to read
The fractions 3/−4 and −3/4 are equal: both name a negative number. The fraction −3/−4 is positive 3/4 because both signs change. Put the sign in the numerator or before the fraction, then work with positive denominators. Zero divided by a non-zero integer is rational; division by zero is not defined.
For −5/6 + 1/4, the smallest convenient common denominator is 12. Multiply both numerator and denominator in −5/6 by 2 and in 1/4 by 3. This gives −10/12 + 3/12, not −5/12 + 1/12. Changing only a denominator changes the value.
| Expression | Rewrite subtraction as addition | Result |
|---|---|---|
| 3/4 − 1/2 | 3/4 + (−2/4) | 1/4 |
| 3/4 − (−1/2) | 3/4 + 2/4 | 5/4 |
| −3/4 − 1/2 | −3/4 + (−2/4) | −5/4 |
| −3/4 − (−1/2) | −3/4 + 2/4 | −1/4 |
Use magnitude to predict the sign
When adding opposite signs, compare their distances from zero. For −7/10 + 2/5, two fifths is four tenths. Seven negative tenths outweigh four positive tenths, leaving three negative tenths. When both quantities are negative, their sum is farther left: −1/3 + (−1/6) = −1/2.
The rule about changing subtraction to addition applies to the entire number being subtracted. Brackets make that scope clear. A double minus does not mean every nearby minus symbol can be erased. First rewrite a − b as a + (−b), then combine matching fractional units.
Check with an inverse operation or a position
If −2/5 − 3/10 = −7/10, add 3/10 back: −7/10 + 3/10 = −4/10 = −2/5. The inverse check reconstructs the starting value. On a line, subtracting a positive amount should also move left, so an answer greater than −2/5 would be suspicious.
Improper fractions are valid answers unless the task requests mixed numbers. For negative mixed numbers, −1 1/4 means −(1 + 1/4) = −5/4. It does not mean −1 + 1/4. Use brackets or an improper fraction if the notation is confusing.
Worked examples: follow each decision
Find −2/5 − 3/10.
- Write −4/10 − 3/10.
- Both changes go in the negative direction: the result is −7/10.
- On the number line, move three tenths left from −4/10.
A diver is at −3/2 m relative to a marker and rises 5/6 m. Where is the diver now?
- Rewrite −3/2 as −9/6. Rising is a positive change.
- −9/6+5/6 = −4/6 = −2/3 m.
- The diver is still below the marker but closer to it. A positive final depth would contradict this calculation.
13 questions with explained answers
Attempt a short group of questions before opening the solutions. Use a drawing or written method where helpful. Explain the answer, then try a similar question with a detail changed.
−1/3 + 5/6
Show answer and reasoning
1/2
−2/6 + 5/6 = 3/6.
3/4 − (−1/8)
Show answer and reasoning
7/8
6/8 + 1/8 = 7/8.
−7/10 + 2/5
Show answer and reasoning
−3/10
−7/10 + 4/10 = −3/10.
−1/2 − (−3/4)
Show answer and reasoning
1/4
−2/4 + 3/4 = 1/4.
Does −2/3 + 2/3 equal −4/6?
Show answer and reasoning
No; it equals 0
A number and its opposite cancel.
−2/3 + 1/6
Show answer and reasoning
−1/2
−4/6+1/6=−3/6.
1/5 − 3/10
Show answer and reasoning
−1/10
2/10−3/10=−1/10.
−3/8 − (−1/4)
Show answer and reasoning
−1/8
−3/8+2/8=−1/8.
−4/9 + (−2/3)
Show answer and reasoning
−10/9
−4/9−6/9=−10/9.
5/12 − (−7/18)
Show answer and reasoning
29/36
15/36+14/36=29/36.
Find x: x + 2/5 = −1/10.
Show answer and reasoning
−1/2
Subtract 4/10 from both sides.
Which is larger: −2/3 or −3/4?
Show answer and reasoning
−2/3
−8/12 is to the right of −9/12.
Does 2/−5 + 2/5 equal zero?
Show answer and reasoning
Yes
2/−5 = −2/5; the two numbers are opposites.
Check what you can now explain
- Did you preserve the value when changing denominators?
- What does subtraction of this signed number mean?
- Does the result lie on the expected side of zero?
Keep these distinctions clear
- Keep the common denominator; do not add denominators.
- Compare magnitudes when adding opposite signs instead of assuming a negative input always gives a negative answer.
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Keep the ideas connected
- Negative numbers on a number line
- Adding fractions: match the parts first
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