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 (word problems · applications)Fri 16 October1 / 4

Dividing by decimals: word problems, applied

In every problem the diagram comes first, the calculation after. Find the "per one" first

Name Date

An answer with no diagram does not get a tickDraw a double number line or an area diagram before the calculation. It need not be neat.

Two steps, same picture: build the 1 first, then travel to the length you want. The numbers are made up.

Worked example: two steps

A ribbon costs 138 yen for 0.6 m. What do 0.9 m cost?
1. Draw it. 0.9 lies between 0.6 and 1 → the answer lies between 138 and "the price of 1 m"
2. Make it 1 m　138 ÷ 0.6 = 1380 ÷ 6 = 230 (yen)
3. For 0.9 m　230 × 0.9 = 207 → 138 < 207 < 230 ✓　Answer 207 yen
First "per one", then "that many".

1 · Find the "per one"

1Cloth costs 270 yen for 1.5 m. What does 1 m cost? Draw the double number line before you write the calculation.

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Maths B (word problems · applications)Fri 16 October2 / 4

Dividing by decimals: word problems, applied

Name Date

2Meat costs 1,080 yen for 1.2 kg. What do 0.75 kg cost?

Two steps, as in the example.

3An iron chain of 5.2 m weighs 7.9 kg. How much does 1 m weigh? Round to two decimal places.

Work to three decimal places, then round.

4There are 15.8 L of water, to be poured into bottles that hold 2.5 L.
(1) How many bottles are filled with 2.5 L, and how many litres are left over?
(2) How many bottles are needed to hold all the water?

The remainder's decimal point lines up with the one in 15.8.

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Maths B (word problems · applications)Fri 16 October3 / 4

Dividing by decimals: word problems, applied

Name Date

2 · How many times

5String A is 2.4 m, string B is 1.5 m.
(1) A is how many times B?
(2) B is how many times A?
Draw a diagram, and write what is taken as 1.

The answer to (2) is less than 1.

6This year my brother is 1.32 m tall, which is 1.1 times last year's height. How tall was he last year? Draw a diagram and write an equation with □ before solving it.

□ × 1.1 = 1.32.

3 · Together with averages

7A home's water use over five days was 118.4, 124.6, 109.2, 131.8 and 116.0 L.
(1) What is the average use per day, in L?
(2) The average daily amount fills how many 1.5 L bottles?

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Maths B (word problems · applications)Fri 16 October4 / 4

Dividing by decimals: word problems, applied

Name Date

8A car goes 45 km on 3.6 L. If it uses 2.4 L of petrol a day on average, how many km does it go in 5 days? Draw it and go step by step: per litre → per day → 5 days.

4 · Comparing, and working backwards

9Shop A sells mandarins at 94 yen for 0.4 kg, shop B at 84 yen for 0.35 kg. Which is cheaper per kg? By how many yen per kg?

10A piece of timber 0.75 m long weighs 1.8 kg. For the same timber weighing 6 kg, how long is it?

Treat "the weight of 1 m" like a unit price. length = weight ÷ (weight of 1 m).