If your child writes that one half plus one third is two fifths, don’t say it’s wrong and don’t hand over the answer, which is 5/6. Ask whether two fifths is more or less than one half. It is less, and an addition never ends up below the number you started with. That one question lets your child find the slip, and it shows you what idea was behind it. Below are the most common wrong answers, with the question that helps in each case and a way to check the result. For printable materials, see creating fraction worksheets; this page stays with the conversation.
| Answer you see | Likely idea | Question you can ask | Check |
|---|---|---|---|
| Two fifths as the sum of one half and one third | Adds numerators and denominators separately | Is it more or less than one of the addends? | The correct result is greater than each addend |
| Three eighths when dividing three fourths by one half | Multiplies instead of using the reciprocal | How many halves fit in three fourths? | Quotient times divisor must give back 3/4 |
| Eight as three eighths of 24 counters | Divides by the numerator | What does the 8 on the bottom count? | Eight groups of 3 counters; three groups make 9 |
| 5/8 and 2/3 "are equal because both are above one half" | Treats a benchmark as if it settled everything | Can we write them with the same denominator? | 15/24 is less than 16/24 |
The table is a guide. A wrong answer can have another cause, and the question is there to find out. Once your child explains the step clearly, move on to the next one.
One hint per turn with one half plus one third
A worked conversation with 1/2 + 1/3
Your child wrote 2/5 and you want them to check it without being told.
- Ask for an estimate. Have them say whether the result can be less than one of the addends. Comparing, they see that something is off.
- Ask about the size of the parts. One half and one third are pieces of different sizes, so they can’t be counted together as they are.
- Give just one hint. Have them look for a number of equal parts that holds both halves and thirds. If they can’t find it, offer six.
- Let them fill it in. One half is 3/6 and one third is 2/6.
- Have them write the total. They write 3/6 + 2/6 = 5/6.
1/2 + 1/3 = 5/6
Check. Since 5/6 − 2/6 = 3/6, the first addend comes back, and the total is greater than one half, as the estimate required.
If they answer one thing, ask another
The conversation follows this tree. Start from what your child says and set aside what you already know.
- If they don’t know where to start, ask what is being looked for and what the whole is. In “3/8 of 24 counters,” the whole is the 24 counters.
- If they draw parts of different sizes, ask whether the parts are equal. A Spanish teacher-training institute suggests this same sequence in a GeoGebra activity: what the figure represents, how many parts it is divided into, whether they are equal, how many are shaded, and what fraction that is.
- If they calculate correctly but can’t explain it, ask them to tell it with a drawing.
- If a half-remembered rule leads them astray, look for the case where it does work. With the same denominator, 2/7 + 3/7 = 5/7, so the correct rule has a condition.
- If they get a step right, don’t repeat it. Ask what they need for the next one.
To test an attempt, the divide fractions calculator solves the division in the table, and compare fractions decides which of the two fractions in the last row is greater.
What to say when they get it wrong
Talk about the step and leave the person out of it. Say “this step changes the size of the parts” instead of “you don’t understand.” The same activity lists these as common mistakes: mixing up numerator and denominator, counting only the shaded parts, or not checking that the parts are equal. It treats them as a chance to learn (accessed October 16, 2026).
For more mistakes and their causes, read common fraction mistakes. If your child needs a picture, the fraction drawing tool makes one and the guide to drawing fractions explains how to read it.
- To understand why this topic is hard, read why fractions are hard to learn.
- Once a solution is written out, how to interpret the steps helps you go through it line by line.
- For practice with instant feedback, try checking answers.
- If you teach in a classroom, you will find that approach in the guide to teaching fractions.
What to share when you ask for help online
Share only the operation. The question “Why isn’t 5/6 − 1/4 equal to 4/2?” is enough to talk about the calculation, and the answer is 7/12. Leave out the name, the photo, the grade, and the school. UNICEF recommends explaining to children which information they should always be careful about sharing online, such as full name, birthday, address, phone number, or school name (UNICEF, online privacy, accessed October 16, 2026). If you use a screenshot, crop it first.
Sources
- UNICEF, online privacy, accessed October 16, 2026.