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Integer Puzzles: Alien Coins And Expressions

Pay exact amounts with +13 and −9 coins, then use brackets and signs to make expressions as big or as small as possible.

9 micro-lessons

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Paying in Pibs

An alien shop with only +13 and −9 coins.

The pibs puzzle (Textbook p. 43, Q10)

An alien society uses a currency called pibs. There are only two coins: a $+13$ pibs coin and a $-9$ pibs coin. You have plenty of both. Can you buy an item that costs $+85$ pibs?

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The Pibs Coin Shop

Two alien coins: one worth +13 pibs, one worth −9 pibs.

$An alien shopkeeper at a market stall, with a pile of +13 pibs coins and a pile of −9 pibs coins on the counter.$

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Every payment is some +13 coins and some −9 coins. The total is what you pay.

Paying 85 Pibs

The book's answer: 10 coins of +13 and 5 coins of −9.

Problem. Pay exactly $+85$ pibs with $+13$ and $-9$ coins. (Textbook p. 44)

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Make +20 Pibs

Fill in the coin counts for a total of +20.

0 of 4 blanks filled

Textbook p. 44 (a): make a total of +20 pibs.

5 coins of +13 make pibs.

65 − 20 = , and 45 = coins of −9.

So 5 × 13 + 5 × (−9) = .

The Big Pibs Challenge

Make each total with +13 and −9 coins, then the big one.

Make each total

Textbook p. 44. Using $+13$ and $-9$ coins, make these totals. Write how many of each coin you use.

(b) $+40$ (c) $-50$ (d) $+8$ (e) $+10$ (f) $-2$ (g) $+1$

(h) Is it possible to buy an item that costs 1568 pibs?

(b) +40 and (c) −50*

Coins of each kind, and a check.

(d) +8 and (e) +10*

Coins of each kind, and a check.

(f) −2 and (g) +1*

Coins of each kind, and a check.

(h) 1568 pibs: yes or no, and how?*

Can you build on (g)?

Building Expressions with Integers

Brackets and signs can change an answer a lot.

Same numbers, different answers

With the same numbers and operations, moving the brackets can change the result a lot. $(3 + 5) \times -6 = -48$ , but $3 + 5 \times -6 = -27$ .

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Biggest and Smallest

Using 3, −2, 5, −6 with +, − and × once each.

Problem. Use the numbers $3, -2, 5, -6$ exactly once and the operations $+$ , $-$ and $\times$ exactly once, with brackets as needed. Make (a) the biggest result and (b) the smallest result. (Textbook p. 44, Q15)

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Paying in Pibs

An alien shop with only +13 and −9 coins.

The pibs puzzle (Textbook p. 43, Q10)

An alien society uses a currency called pibs. There are only two coins: a $+13$ pibs coin and a $-9$ pibs coin. You have plenty of both. Can you buy an item that costs $+85$ pibs?

1 / 3

Paying 85 Pibs

The book's answer: 10 coins of +13 and 5 coins of −9.

Problem. Pay exactly $+85$ pibs with $+13$ and $-9$ coins. (Textbook p. 44)

1 / 5

The Big Pibs Challenge

Make each total with +13 and −9 coins, then the big one.

Make each total

Textbook p. 44. Using $+13$ and $-9$ coins, make these totals. Write how many of each coin you use.

(b) $+40$ (c) $-50$ (d) $+8$ (e) $+10$ (f) $-2$ (g) $+1$

(h) Is it possible to buy an item that costs 1568 pibs?

(b) +40 and (c) −50*

Coins of each kind, and a check.

(d) +8 and (e) +10*

Coins of each kind, and a check.

(f) −2 and (g) +1*

Coins of each kind, and a check.

(h) 1568 pibs: yes or no, and how?*

Can you build on (g)?

Building Expressions with Integers

Brackets and signs can change an answer a lot.

Same numbers, different answers

With the same numbers and operations, moving the brackets can change the result a lot. $(3 + 5) \times -6 = -48$ , but $3 + 5 \times -6 = -27$ .

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Biggest and Smallest

Using 3, −2, 5, −6 with +, − and × once each.

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