Back to Ganita Prakash: Class 7 Mathematics, Par...BackConcept

Sign Rules From Patterns

Continue a steady pattern of products below zero and see the four sign rules for multiplying integers appear.

7 micro-lessons

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Watch the Products Step Down

Multiplying by 3 while the multiplier drops: the product falls by 3 each time.

A pattern you know (Textbook p. 32)

$4 \times 3 = 12 \quad 3 \times 3 = 9 \quad 2 \times 3 = 6 \quad 1 \times 3 = 3 \quad 0 \times 3 = 0$

Each time the multiplier goes down by 1, the product goes down by 3, the multiplicand.

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Now the Products Climb

With −3 as the multiplicand, the product rises by 3 each step.

Now the multiplicand is −3 (Textbook pp. 32–33)

$4 \times (-3) = -12 \quad 3 \times (-3) = -9 \quad 2 \times (-3) = -6$
$1 \times (-3) = -3 \quad 0 \times (-3) = 0$

This time each unit decrease in the multiplier makes the product go up by 3. It is the opposite of the last pattern.

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Using the Pattern: (−3) × (−3)

Finding a negative times a negative by continuing the ladder.

Problem. Use the pattern to find $(-3) \times (-3)$ .

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Sign Rules Card

The four sign rules for multiplying integers.

Multiplying two integers

(+) \times (+) (-) \times (-) (+) \times (-) (-) \times (+) = (+) = (+) = (-) = (-)

What each part means

sign

— same signs give +, different signs give −

size

— multiply the sizes as usual

When it works

Works for any two integers. Find the sign first, then the size.

Example

(- 8) \times 4

: signs differ, so the answer is negative.

8 \times 4 = 32

, so the answer is

- 32

Continue the Ladder

Fill in the next products in the pattern for −5.

0 of 6 blanks filled

Continue the pattern with −5 as the multiplicand.

2 × (−5) =

1 × (−5) =

0 × (−5) =

(−1) × (−5) =

(−2) × (−5) =

Each time the multiplier goes down by 1, the product goes up by .

Find the Products

Figure it Out products with every sign combination.

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$4 \times (-3) = ?$

← previousSame Number, Different Tokens next →Brahmagupta's Rules: Fortune And Debt

Watch the Products Step Down

Multiplying by 3 while the multiplier drops: the product falls by 3 each time.

A pattern you know (Textbook p. 32)

$4 \times 3 = 12 \quad 3 \times 3 = 9 \quad 2 \times 3 = 6 \quad 1 \times 3 = 3 \quad 0 \times 3 = 0$

Each time the multiplier goes down by 1, the product goes down by 3, the multiplicand.

1 / 3

Now the Products Climb

With −3 as the multiplicand, the product rises by 3 each step.

Now the multiplicand is −3 (Textbook pp. 32–33)

$4 \times (-3) = -12 \quad 3 \times (-3) = -9 \quad 2 \times (-3) = -6$
$1 \times (-3) = -3 \quad 0 \times (-3) = 0$

This time each unit decrease in the multiplier makes the product go up by 3. It is the opposite of the last pattern.

1 / 3

Using the Pattern: (−3) × (−3)

Finding a negative times a negative by continuing the ladder.

Problem. Use the pattern to find $(-3) \times (-3)$ .

1 / 5

Find the Products

Figure it Out products with every sign combination.

1 / 6

$4 \times (-3) = ?$