Concept 6 of 9
The Sorting Trays: Tackling Mixed Numbers
Today's big idea
Sort wholes into one tray and fractions into another, then glue the answers back.
3 1/5 + 2 2/5: wholes make 5, fractions make 3/5, glued as 5 3/5.
How it works
👀 What's going on?
A mixed number like 3 1/5 is really two numbers wearing one outfit, a whole and a fraction stuck side by side. Adding two of them at once is exactly where the muddle starts.
💡 Here's the trick
Look at the trays above. 3 1/5 + 2 2/5 gets sorted out. The wholes 3 and 2 go in one tray and make 5. The fractions 1/5 and 2/5 go in the other and make 3/5. Glue the trays back together and you have 5 3/5. Two easy jobs beat one confusing one.
🪄 How to do it
- 1.Sort the wholes into one tray and the fractions into the other, as the picture above does.
- 2.Add or subtract each tray on its own.
- 3.Glue the two results back into a single mixed number.
✍️ Try it
Work out 4 3/5 minus 1 1/5. Which tray gives which part of the answer?
The whole tray gives 4 minus 1 = 3. The fraction tray gives 3/5 minus 1/5 = 2/5. Glued back together that is 3 2/5. Subtraction sorts into trays in exactly the way adding does.
⚠️ Watch out
You might be thinking every subtraction sorts this neatly. Try 3 1/5 minus 1 2/5. The fraction tray now asks for 1/5 minus 2/5, which will not go. Break one whole into fifths first, the way the last concept did, and 3 1/5 becomes 2 6/5.
🌟 Why this matters
Recipes, timings and distances are nearly always written as mixed numbers, like 2 1/2 cups or 1 3/4 hours. Keeping the wholes and the parts apart is how people add them in their heads.
Exam tip: Write both trays down instead of doing them at once, because the mix-up is what the wrong options are built from.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“4 2/6 + 1 3/6 — add the mixed numbers.”
- 1
Sort into 2 trays
Wholes → 🔢 tray (4, 1). Fractions → 🍕 tray (2/6, 3/6).
- 2
Add the whole tray
4 + 1 = 5.
- 3
Add the fraction tray
2/6 + 3/6 = 5/6 (bottoms match).
- 4
Glue them back ✓
4 2/6 + 1 3/6 = 5 5/6
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Add mixed numbers by SORTING: send every whole to the wholes tray and every fraction to the fractions tray, then combine.
ADD THE MIXED NUMBERS
2 1/4 + 1 2/4
2 1/4
1 2/4
🔢 WHOLES TRAY
0
🍕 FRACTIONS TRAY
0/4
Send all 4 pieces to their trays…
Quick check
✅ VERIFICATION
Work out 5 2/7 minus 2 1/7.
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Block Smasher
Break a fraction into unit pieces like lego.