Printing: use your browser's print (Ctrl+P / ⌘P). It comes out as exactly 4 A4 sheets (2 pieces of paper double-sided). No answers in here.

time yourself

Maths B (new unit · word problems)Fri 2 October1 / 4

Dividing by a decimal, in words

Always draw the diagram. This month is still "how much for one?"

Name Date

Today's idea

Division has two meanings, and both still work when the divisor is a decimal.
① How many fit　2.4 ÷ 0.4 asks how many 0.4s fit into 2.4 → 6
② How much for one　if 0.4 m costs 96 yen, what does 1 m cost? → 96 ÷ 0.4

How to calculate　Multiplying both numbers by the same thing does not change the answer.
2.4 ÷ 0.4 = 24 ÷ 4 = 6　(both times 10)　not 2.4 ÷ 4 (only the divisor times 10)
Make the divisor a whole number, and it is a division you already know.

The top and bottom scales always move in step. Draw it, and you know whether to multiply or divide before you write anything.

Worked example

A ribbon costs 96 yen for 0.4 m. What does 1 m cost?

① Draw the diagram (above). 1 is to the right of 0.4 → the answer must be more than 96
② Calculation　96 ÷ 0.4
③ Both times 10　960 ÷ 4 = 240
④ Check　240 x 0.4 = 96 ✓　　Answer 240 yen

time yourself

Maths B (new unit · word problems)Fri 2 October2 / 4

Dividing by a decimal, in words

Name Date

First, the most common mistake

"Dividing always makes a number smaller."　Only when the divisor is bigger than 1.

8 ÷ 2 = 4 (smaller), 8 ÷ 1 = 8 (the same), 8 ÷ 0.5 = 16 (bigger).
Sixteen 0.5s fit into 8. Divide by a number less than 1 and the answer is bigger than the number you started with.

1 · Make the divisor a whole number

13.6 ÷ 0.4

27.2 ÷ 1.2

34.5 ÷ 0.05

What must you multiply by to make the divisor whole?

46 ÷ 0.8

Keep going until it divides exactly.

52.1 ÷ 0.35

time yourself

Maths B (new unit · word problems)Fri 2 October3 / 4

Dividing by a decimal, in words

Name Date

6Answer without calculating. Which of these give an answer bigger than 8? Choose all of them.
　A 8 ÷ 0.5　　B 8 ÷ 1.2　　C 8 ÷ 1　　D 8 ÷ 0.99

Look only at whether the divisor is more or less than 1.

2 · Word problems — diagram first, then the calculation

7Cloth costs 150 yen for 0.6 m. What does 1 m cost? Draw the double number line before you write the calculation.

8There are 2.8 L of juice. Poured out 0.4 L to a cup, how many cups is that?

This is the "how many fit" kind.

9A 0.8 m iron bar weighs 2.4 kg. How much does 1 m of this bar weigh?

10A 5.3 m ribbon is cut into 0.7 m pieces. How many pieces, and how much is left over?

The remainder's decimal point lines up with the one in the original 5.3.

time yourself

Maths B (new unit · word problems)Fri 2 October4 / 4

Dividing by a decimal, in words

Name Date

11A rectangular flower bed has an area of 7.2 m². It is 2.4 m wide. How long is it?

12Write only the calculation (and the answer if you can). Decide between x and ÷ by drawing the diagram.
　(1) Cloth is 180 yen a metre. What do 0.6 m cost?
　(2) Cloth costs 108 yen for 0.6 m. What does 1 m cost?

The important question today. Same numbers, but what counts as "one" changes the calculation.

13A car goes 42 km on 3.5 L of petrol. How many km does it go per litre? Driving the same way, how many litres does it need for 60 km?

Extra · you may skip this

What is 1 ÷ 0.25? Think of sharing 100 yen out 25 yen at a time, and write in one line why that is the answer.