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

When The Multiplier Is Negative

A negative multiplier means taking tokens out of the bag. Use zero pairs to see why (−4) × (−2) = +8.

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A Negative Multiplier Means Remove

Why (−4) × 2 means taking 2 positives out of the bag 4 times.

Put in or take out

When the multiplier is positive, we place tokens into the bag.
When the multiplier is negative, we remove tokens from the bag.

So $(-4) \times 2$ means: remove 2 positives from the bag, 4 times.

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(−4) × 2 = −8

Removing 2 positives four times leaves 8 negatives.

Problem. Use tokens to find $(-4) \times 2$ . (Textbook p. 30)

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(−4) × (−2) = +8

Removing 2 negatives four times leaves 8 positives.

Problem. What happens when both numbers are negative? Find $(-4) \times (-2)$ . (Textbook p. 30)

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The Four Token Results

All four sign cases in one card.

Four products from the token bag

4 \times 2 4 \times (- 2) (- 4) \times 2 (- 4) \times (- 2) = 8 = - 8 = - 8 = 8

What each part means

4

— positive multiplier: put tokens in

- 4

— negative multiplier: take tokens out, after adding zero pairs

When it works

The multiplicand decides which tokens go in or come out.

Example

(- 4) \times (- 2)

: add 2 zero pairs and remove 2 negatives, 4 times. 8 positives are left.

Token Steps for (−5) × (−2)

Fill in each step of the removal method.

0 of 6 blanks filled

Figure it Out, Textbook p. 31, Q1(b): find (−5) × (−2).

The multiplier is negative, so we tokens.

Each time, we add zero pairs and remove negatives. We do this times.

Left in the bag: positives. So (−5) × (−2) = .

Token Products Practice Set

The book's token questions, one at a time.

1 / 4

$3 \times (-2) = ?$

Use 123 × 456 = 56088

Find signed products without multiplying again.

1 / 3

Given $123 \times 456 = 56088$ , what is $(-123) \times 456$ ?

← previousMultiplying With A Token Bag next →Same Number, Different Tokens

A Negative Multiplier Means Remove

Why (−4) × 2 means taking 2 positives out of the bag 4 times.

Put in or take out

When the multiplier is positive, we place tokens into the bag.
When the multiplier is negative, we remove tokens from the bag.

So $(-4) \times 2$ means: remove 2 positives from the bag, 4 times.

1 / 3

(−4) × 2 = −8

Removing 2 positives four times leaves 8 negatives.

Problem. Use tokens to find $(-4) \times 2$ . (Textbook p. 30)

1 / 5

(−4) × (−2) = +8

Removing 2 negatives four times leaves 8 positives.

Problem. What happens when both numbers are negative? Find $(-4) \times (-2)$ . (Textbook p. 30)

1 / 5

Token Products Practice Set

The book's token questions, one at a time.

1 / 4

$3 \times (-2) = ?$

Use 123 × 456 = 56088

Find signed products without multiplying again.

1 / 3

Given $123 \times 456 = 56088$ , what is $(-123) \times 456$ ?