1.GUIDED
47 passengers are waiting for a train. Each car seats 6 people. How many cars are needed so that everybody gets a seat?
Divide: 47 ÷ 6 = remainder
The remainder means people still have no seat.
Can they be left at the station?
So how many cars?
Answer:
Did you know? A train wheel isn't flat — it's cone-shaped, which is what steers it around a curve without any steering at all.
2.
A station loads 62 crates onto carts. Each cart holds 8 crates. How many carts get completely full, and how many crates are left on the platform?
SHOW YOUR WORK
Answer:
Did you know? Freight trains can be over a mile long — some in Australia run to 4 miles.
3.
75 students are taking a train to a museum. Each car holds 9 students. Every student must have a seat. How many cars does the school need?
SHOW YOUR WORK
Answer:
Did you know? The world's busiest station is Shinjuku in Tokyo — about 3.5 million people pass through it every day.
4.
A conductor has 40 tickets to sort into books of 6. How many complete books can he make, and how many tickets are left over?
SHOW YOUR WORK
Answer:
Did you know? Conductors once punched each ticket with a uniquely shaped hole so no one could reuse it.
5.
53 suitcases must all be stored, and each luggage rack holds 7. How many racks are used, and how many suitcases are on the last rack?
SHOW YOUR WORK
Answer:
Did you know? The first luggage racks were nets, so passengers could see their bags from their seat.
1.GUIDED
Yusuf finishes 1/3 of a train journey before lunch and another 1/4 of it after lunch. What fraction of the journey has he travelled?
Common bottom number: 3 × 4 =
Rewrite: 1/3 = and 1/4 =
Add the tops, keep the bottom:
Answer:
Did you know? The fastest passenger train in service, the Shanghai Maglev, floats above the track on magnets at 267 mph.
2.
A train is 2/5 full when it leaves the first station. At the next stop, enough people board to fill another 1/3 of the train. What fraction of the train is now full?
SHOW YOUR WORK
Answer:
Did you know? Trains are so efficient that moving one ton of freight a mile by rail uses about a quarter of the fuel a truck would.
3.
A track crew lays 3/8 of a mile of rail on Monday and 1/2 a mile on Tuesday. How much track did they lay in total?
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Answer:
Did you know? Rails are laid with small gaps because steel expands in summer heat — that's the clackety-clack sound.
4.
A locomotive starts with 5/6 of a tank of fuel and burns 1/4 of a tank on the trip. What fraction of a tank is left?
SHOW YOUR WORK
Answer:
Did you know? A big diesel locomotive holds about 5,000 gallons of fuel — roughly 300 car fill-ups.
5.
Yusuf reads 2/3 of a book on the train and his brother reads a different 1/5 of it. What fraction of the book has been read between them?
SHOW YOUR WORK
Answer:
Did you know? Reading on a train makes some people queasy because the eyes say 'still' while the inner ear says 'moving'.
3rd Grade (remainders)
1. 8 cars.
47 ÷ 6 = 7 r 5. Seven full cars, 5 people still standing → round up to 8.
2. 7 full carts, 6 crates left.
62 ÷ 8 = 7 r 6. Asks for completely full → do not round up. 7 carts, 6 crates.
3. 9 cars.
75 ÷ 9 = 8 r 3. Everyone needs a seat → 9 cars, the last holding 3.
4. 6 books, 4 tickets left.
40 ÷ 6 = 6 r 4. Complete books only → 6, with 4 spare tickets.
5. 8 racks; 4 suitcases on the last one.
53 ÷ 7 = 7 r 4. All must be stored → 8 racks, last one holds 4.
4th Grade (unlike denominators)
1. 7/12 of the journey.
Common bottom 12. 1/3 = 4/12, 1/4 = 3/12. 4/12 + 3/12 = 7/12.
2. 11/15 full.
Common bottom 15. 2/5 = 6/15, 1/3 = 5/15. 6/15 + 5/15 = 11/15.
3. 7/8 of a mile.
8 already works. 1/2 = 4/8. 3/8 + 4/8 = 7/8. Good one for spotting you don't always multiply the bottoms.
4. 7/12 of a tank.
Common bottom 12. 5/6 = 10/12, 1/4 = 3/12. 10/12 − 3/12 = 7/12.
5. 13/15 of the book.
Common bottom 15. 2/3 = 10/15, 1/5 = 3/15. 10/15 + 3/15 = 13/15.