Written Methods for the Four Operations

Add the ones first and carry any complete ten.

Exchange one hundred into tens, then one ten into ones.

Write 28.4 with two decimal places before lining up the columns.

Use 70.00 so you can subtract hundredths and tenths.

Multiply the ones, carry the tens, then multiply the tens.

Split 24 into 20 and 4.

1. 36\times20=720 and 36\times4=144.
2. 720+144=864.

First multiply 72 by 4. Think about how each original factor was scaled.

1. 72\times4=288.
2. Both original factors were multiplied by 10 to make 72 and 4. Their product was therefore multiplied by 100.
3. 7.2\times0.4=288\div100=2.88. This is less than 7.2 because 0.4 is less than 1.

Divide from the hundreds column and carry remainders into the next column.

1. 8\div6=1 remainder 2, so carry 2 hundreds into the tens.
2. 26\div6=4 remainder 2, so carry 2 tens into the ones.
3. 24\div6=4. The answer is 144.

Keep the decimal point aligned while dividing.

1. 9\div3=3, 3 tenths \div3=1 tenth, and 6 hundredths \div3=2 hundredths.
2. So 9.36\div3=3.12. Check: 3.12\times3=9.36.

Multiply both numbers by 10 before dividing.

1. 4.8\div0.6=48\div6=8.
2. Both amounts were scaled equally, so the number of groups is unchanged.

Subtraction undoes addition.

1. 1000-587=413.
2. Check: 587+413=1000.

Find the cost of all three tickets before subtracting from the amount paid.

1. 3\times8.75=26.25, so the tickets cost £26.25.
2. 30.00-26.25=3.75. Maya receives £3.75 change.

Find the total length cut off, then subtract it from the original length.

1. 7\times1.35=9.45 m is used.
2. 12.50-9.45=3.05 m is left.

Check whether the remainder still needs a coach.

1. 48\times5=240, leaving 275-240=35 passengers.
2. A sixth coach is needed for those passengers. 48\times6=288 seats is enough, so the answer is 6.

Work out how many whole packs are needed at each shop.

1. Shop A needs 30\div6=5 packs, costing 5\times4.20=21.00.
2. Shop B needs 30\div10=3 packs, costing 3\times6.50=19.50.
3. The difference is 21.00-19.50=1.50, so Shop B is £1.50 cheaper.

Calculate the two subtotals, then the total paid and the change.

1. Books cost 4\times3.75=15.00. Folders cost 3\times2.60=7.80.
2. Total cost: 15.00+7.80=22.80. Total paid: 20+10=30.
3. Change: 30.00-22.80=7.20, so Oliver receives £7.20.

Find the number of boxes before deciding how many trolley trips are needed.

1. Usable books: 960-24=936.
2. Number of boxes: 936\div18=52, since 18\times50=900 and the remaining 36 books fill another 2 boxes.
3. Eight trips can move 8\times6=48 boxes. That leaves 52-48=4 boxes, so one more trip is needed.
4. The fewest number of trips is 9.

Find the amount spent from the payment and change. The booking charge is paid only once.

1. The total spent is 60.00-6.40=53.60, or £53.60.
2. The tickets alone cost 53.60-5.20=48.40.
3. One ticket costs 48.40\div8=6.05, or £6.05.
4. Check: 8\times6.05+5.20+6.40=60.00.

Find the fewest whole cans first, then the total amount bought.

1. Eleven cans contain 11\times1.25=13.75 litres, which is not enough. Twelve contain 12\times1.25=15 litres.
2. She buys 12 cans. The amount left is 15.00-14.80=0.20 litres.

Find each ticket subtotal, then subtract the hall cost before sharing.

1. Adult tickets bring in 120\times7.50=900, or £900.
2. Child tickets bring in 80\times4.50=360, or £360.
3. Total income: 900+360=1260, or £1260.
4. After paying for the hall, 1260-450=810 pounds remain.
5. Each club receives 810\div3=270, or £270.