SME
Grade 4 Math · Problem type
Interpret remainders
Use this for “Each van holds 7 students. How many vans do 45 students need?”
Diagram
6 full vans and 2 students left over: 7 vans needed.
Full groups: 6
This is an example. Type your own values to start a new problem.
Total
÷
In each group
=
Full groups
remainder
Left over
In the full groups
worked out (not typed)
Groups needed
calculated
Formulas
6 × 8 = 48
Full groups × in each group = in the full groups
48 + 2 = 50
In the full groups + left over = total
50 ÷ 8 → 6 full groups
Total ÷ in each group = full groups, with some left over
6 full groups and 2 left over: 7 groups needed
Full groups, and 1 more when any are left over = groups needed
Assumptions
•
Divide, then decide what the remainder means in the story.
•
Buses or boxes needed: any left over need one more, so round the quotient up.
•
Full teams or full boxes: drop the remainder. “How many are left?”: the remainder is the answer.
•
Numbers to 999, divisors to 9.
Step-by-step
WE KNOW
Total: 50
In each group: 8
FIND
full groups, in the full groups, left over, groups needed
Step 1 · Find full groups
50 ÷ 8 → ? full groups
Total ÷ in each group = full groups, with some left over
Divide. The whole-number part of the answer is the full groups.
6
8
)
5
0
−
4
8
2
6 × 8 = 48
7 × 8 = 56 is too many
Full groups = 6
Step 2 · Find in the full groups
6 × 8 = ?
Full groups × in each group = in the full groups
The full groups times the size of each: how many are in them.
In the full groups = 48
Step 3 · Find left over
48 + ? = 50
In the full groups + left over = total
The leftover is what is not in a full group.
Left over = 50 − 48
Left over = 2
Step 4 · Find groups needed
6 full groups and 2 left over: ? groups needed
Full groups, and 1 more when any are left over = groups needed
Everyone needs a group. Any left over need one more group.
Groups needed = 6 + 1
Full groups only: 6. Left over: 2.
Groups needed = 7 (2 left over can’t be left behind, so round up)
Check
Put the numbers back in. Both sides should match.
6 × 8 = 48 ✓
48 + 2 = 50 ✓
50 ÷ 8 = 6 remainder 2 ✓
6 full groups and 1 more for the 2 left: 7 ✓
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Divide multi-digit numbers by one-digit numbers
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Fraction equivalence and comparison
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