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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.

time yourself

Costume 2 · sport + correctionsSun 4 October1 / 2

Batting averages, points per game　+　corrections

Both are "per one": per time at bat, per game

Name Date

Batting average in baseball

Batting average = hits ÷ times at bat (hits per time at bat)
Written to three decimal places (0.325). In Japan it is read with three old units: 0.1 = 1 wari, 0.01 = 1 bu, 0.001 = 1 rin → 0.325 = 3 wari 2 bu 5 rin (tenths, hundredths, thousandths).

1 · Batting average

1A player has 12 hits in 40 times at bat. Find the batting average as a decimal.

2Say 0.275 in wari, bu and rin. Then write 3 wari 1 bu 4 rin as a decimal.

3Find the average for 26 hits in 80 at bats, and say it in wari, bu and rin too.

4Find the average for 7 hits in 24 at bats, rounded to three decimal places.

Work to four decimal places, then round.

5Player A: 16 hits in 50 at bats. Player B: 18 hits in 60. B has more hits — but who has the higher average?

time yourself

Costume 2 · sport + correctionsSun 4 October2 / 2

Batting averages, points per game　+　corrections

Name Date

6A player batting 0.250 has had 120 at bats. How many hits is that?

2 · Points per game

7A football team scored 3, 1, 0, 2 and 4 goals in five games. How many goals a game on average?

average = total ÷ number of games. A game with 0 still counts as a game.

8A basketball team has averaged 64.5 points over 8 games. It wants an average of 65 after game 9. How many points does it need in game 9?

Find the 8-game total, and the total that 65 over 9 games needs.

3 · Corrections, and one puzzle problem

9From the corrections notebook, pick one you have not yet done a second time, and do it. September's fractions are fine.

10Chickens-and-rabbits — in a basketball game a player made 12 shots, some worth 2 points and some worth 3, scoring 29 points. How many 3-pointers?

First pretend all 12 were 2-pointers.

time yourself (optional)

Stretch (not recorded)From Sun 4 October, any time1 / 4

Stretch — "per one" from tables and graphs

Not recorded. Getting it wrong is fine. Some numbers in the sources are not needed

Name Date

1 · A night of heavy rain　[science: weather]

Source 1

On an evening when a typhoon was coming close, a (made-up) town measured the rain in each hour. The lowest air pressure that day was 972 hPa. On this sheet, 30 mm or more of rain in one hour is called "very heavy rain".

Source 2 — how deep the rain collected in a rain gauge in each hour. The numbers are made up.

1In which hour did the most rain fall, and how many mm was it?

2If the six hours of rain were "evened out" so that every hour had the same amount, how many mm would that be per hour?

Evening out = add everything, then divide by the number of hours. The same idea as Sunday's "points per game".

3Someone says: "Evened out, it is less than 30 mm an hour, so there was not a single hour of very heavy rain." Is that right? Explain with numbers from the graph.

time yourself (optional)

Stretch (not recorded)From Sun 4 October, any time2 / 4

Stretch — "per one" from tables and graphs

Name Date

2 · Water on a river bend　[science: running water]

Source 1

The day after the heavy rain, leaves were floated on the outside and the inside of a river bend, and the distance and time were measured (made up). The water was 18 °C.

where	distance	time taken
outside of the bend	12.6 m	4.2 s
inside of the bend	7.2 m	4.8 s

Source 2 — how far the leaves went (made up)

4How many metres per second did the water move on the outside, and on the inside?

Draw a double number line first, then write the calculation. Dividing by a decimal is still "per one".

5How many times as fast is the outside as the inside?

6After heavy rain, which bank is more easily worn away, the outside or the inside? Give a reason using your numbers from questions 4 and 5.

time yourself (optional)

Stretch (not recorded)From Sun 4 October, any time3 / 4

Stretch — "per one" from tables and graphs

Name Date

3 · What seeds need to sprout　[science: germination]

Source 1

Bean seeds were sown in four bags, and the sprouts were counted 7 days later (a made-up experiment).

bag	where	temperature	water	seeds sown	sprouted
A	bright window	about 25 °C	yes	40	34
B	inside a dark box	about 25 °C	yes	25	22
C	in the fridge	about 5 °C	yes	30	3
D	bright window	about 25 °C	no	20	0

Source 2 — results of a made-up experiment

7Which bag had the most sprouts?

8For A and B, work out "sprouted ÷ sown" as a decimal, and say which is larger.

The same calculation as a batting average (hits ÷ at-bats). You may also write fractions, simplify, and compare over a common denominator.

9"More seeds sprouted in A, so seeds need light to sprout." Is that right? Explain with numbers from the table.

time yourself (optional)

Stretch (not recorded)From Sun 4 October, any time4 / 4

Stretch — "per one" from tables and graphs

Name Date

4 · Two fishing boats　[social studies: fishing]

Source 1

One day's log for two fishing boats from a (made-up) harbour.

boat	hours fishing	fuel used	fish caught	crew
A	4.5 h	31.5 L	378 kg	3
B	3.5 h	17.5 L	280 kg	3

Source 2 — one day's log (made up)

10How many kg of fish did each boat catch per litre of fuel?

When you divide by a decimal, multiplying both numbers by 10 gives the same answer.

11How many kg of fish did each boat catch per hour?

12"Boat B fished better." Can you say that? Use your answers to questions 10 and 11 to give your view.

1 · Make the divisor a whole number

2 · Word problems — diagram first, then the calculation

1 · Batting average

2 · Points per game

3 · Corrections, and one puzzle problem

1 · A night of heavy rain [science: weather]

2 · Water on a river bend [science: running water]

3 · What seeds need to sprout [science: germination]

4 · Two fishing boats [social studies: fishing]

1 · A night of heavy rain　[science: weather]

2 · Water on a river bend　[science: running water]

3 · What seeds need to sprout　[science: germination]

4 · Two fishing boats　[social studies: fishing]