For a parent. These are the answers (4 A4 sheets). They are in nothing the child is given.

Answer key (for a parent)Week 02 · younger son1 / 4

Answers and reasoning

Look at the method, not only the answer. Question 1 is handed over already worked

Tue 8 Sept — hundred-millions

(printed as a worked example) 58 | 000 | 000 → 58 million

34 | 000 | 000 → 34 million

3 | 400 | 000 | 000 → 3.4 billion

720,000,000

26 billion (26,000,000,000). One place left.

8 billion. One place right.

480,000,000

2,000,000,000,000

500 million. Every digit moves one place right.

300 million. That is 300,000,000 against 290,000,000.

a hundred million

90 million + 20 million = 110 million

one trillion > 700 million > 90 million — 13 digits, 9 digits, 8 digits

extra 1

One trillion

extra 2

100 million has 9 digits, 1 million has 7 → two places → 100 times

Answer key (for a parent)Week 02 · younger son2 / 4

Answers and reasoning

Wed 9 Sept — costume 1

1-1

1 | 250 | 000 → 1.25 million

1-2

1,250,000 ÷ 5 ＝ 250,000

1-3

1,250,000 ÷ 10 ＝ 125,000. Twice as many sharing means half as much each.

1-4

1,250,000 ÷ 25 = 50,000

1-5

1,250,000 ÷ 125,000 = 10

1-6

2,500,000 ÷ 1,250,000 = 2 times

2-1

9300 ÷ 30 ＝ 310 yen

2-2

310 x 7 ＝ 2170 yen

2-3

9300 x 12 ＝ 111,600 yen

2-4

10,850 − 9,300 = 1,550 yen

2-5

310 x 30 = 9,300 yen — yes, the same. A check that multiplying undoes the division.

2-6

50 x 30 = 1,500 yen

Answer key (for a parent)Week 02 · younger son3 / 4

Answers and reasoning

Fri 11 Sept — short division and missing numbers

(printed as a worked example) 96 ÷ 4 ＝ 24

84 ÷ 3 ＝ 28

175 ÷ 5 ＝ 35

238 ÷ 7 ＝ 34

342 ÷ 6 ＝ 57

145 ÷ 6 ＝ 24 remainder 1 → 24 children, 1 sweet left

486 ÷ 6 = 81

523 ÷ 4 = 130 remainder 3 (4 x 130 + 3 = 523 ✓). Do not skip the 0 that belongs in the ones place.

700 ÷ 8 = 87 remainder 4 (8 x 87 + 4 = 700 ✓)

46 x 9 = 414

7 x 31 + 5 = 222. Forgetting the remainder, and answering 217, is the commonest slip.

222 ÷ 7 = 31 remainder 5 — back where we started, so it is right

160 ÷ 7 = 22 people, 6 stickers left over

extra 1

divisor x quotient ＋ remainder ＝ the number you divided. e.g. 6 x 24 ＋ 1 ＝ 145

extra 2

27 x 8 ＝ 216

Answer key (for a parent)Week 02 · younger son4 / 4

Answers and reasoning

Sun 13 Sept — costume 2, corrections, sum and difference

1-1

14 ÷ 2.1 ＝ 6.6… → about 7 times

1-2

14 − 2.1 ＝ about 11.9 million

1-3

14 million + 2.1 million = 16.1 million

2-1

95 ÷ 5 ＝ 19 points

2-2

95 ＋ 25 ＝ 120 points

2-3

120 ÷ 6 = 20 points

20 − 4 ＝ 16, 16 ÷ 2 ＝ 8 → younger 8, elder 8 ＋ 4 ＝ 12. Check: 8 ＋ 12 ＝ 20 ✓　12 − 8 ＝ 4 ✓

30 − 6 = 24, 24 ÷ 2 = 12 → 12 and 18

Call the younger 1 and the elder 4, making 5 parts. 20 ÷ 5 = 4, so the younger has 4 and the elder 16.

Question 5 gives a difference (4) and question 7 a ratio (4 times). A difference is subtract-then-halve; a ratio is split into five parts.

Same total, different second clue, different method — that is the whole point of these classic problems.

30 − 8 = 22, 22 ÷ 2 = 11 → 11 cm and 19 cm