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

Division Of Integers

Divide integers by turning each division into a multiplication question, and use the same sign rules as multiplication.

7 micro-lessons

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Division Is Hidden Multiplication

Turning (−100) ÷ 25 into '25 × ? = −100'.

Ask a multiplication question

We can turn any division into multiplication.

$(-100) \div 25$ means: what should be multiplied to 25 to get $-100$ ?

$25 \times ? = -100$

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Three Divisions, Step by Step

Worked divisions with every sign combination.

Problem. Find $(-100) \div 25$ , $(-100) \div (-4)$ and $50 \div (-25)$ . (Textbook p. 38)

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Division Sign Rules

The three division rules, written the book's way.

Dividing integers (Textbook p. 39)

a \div (- b) (- a) \div b (- a) \div (- b) = - (a \div b) = - (a \div b) = a \div b

What each part means

a, b

— positive integers

b \neq = 0

— we can never divide by zero

When it works

Same signs give a positive quotient; different signs give a negative quotient. These are the same as the multiplication rules, and the same as Brahmagupta's rule for quotients.

Example

(- 46) \div (- 23) = 46 \div 23 = 2

36 ÷ (−18) the Multiplication Way

Fill in the missing-factor steps.

0 of 3 blanks filled

Figure it Out, Textbook p. 39, Q1(c): find 36 ÷ (−18).

36 ÷ (−18) means: (−18) × ? = .

Since (−18) × (−2) = 36, the answer is .

Check the sign: positive ÷ negative gives a answer.

Multiply and Divide

Mixed products and quotients from the exercises.

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$14 \times (-15) = ?$

Fill the Missing Integer

Find the integer that makes each statement true.

0 of 6 blanks filled

Figure it Out, Textbook p. 39, Q4.

(a) (−3) × = 27

(b) 5 × = (−35)

(d) × (−12) = 132

(e) ÷ (−8) = 7

(f) ÷ 12 = −11

Brackets First, Then Divide

Work out products inside brackets, then divide.

Find the values

Figure it Out, Textbook p. 44, Q11.

(a) $(32 \times (-18)) \div (-36)$

(d) $(280 \times (-7)) \div ((-8) \times (-35))$

For (b) $32 \div ((-36) \times (-18))$ and (c) $(25 \times (-12)) \div (45 \times (-27))$ , these don't come out to whole numbers. Just say whether each answer is positive or negative, and why.

(a) Work out the bracket*

Multiply 32 × (−18).

(a) Divide and give the answer*

Sign first, then size.

(d) Work out both brackets*

Two products.

(d) Divide and give the answer*

Sign first, then size.

(b) and (c): sign of each answer*

Count the negatives.

← previousThe Magic Grid Of Integers next →Multiplying Three Or More Integers

Division Is Hidden Multiplication

Turning (−100) ÷ 25 into '25 × ? = −100'.

Ask a multiplication question

We can turn any division into multiplication.

$(-100) \div 25$ means: what should be multiplied to 25 to get $-100$ ?

$25 \times ? = -100$

1 / 3

Three Divisions, Step by Step

Worked divisions with every sign combination.

Problem. Find $(-100) \div 25$ , $(-100) \div (-4)$ and $50 \div (-25)$ . (Textbook p. 38)

1 / 5

Multiply and Divide

Mixed products and quotients from the exercises.

1 / 7

$14 \times (-15) = ?$

Brackets First, Then Divide

Work out products inside brackets, then divide.

Find the values

Figure it Out, Textbook p. 44, Q11.

(a) $(32 \times (-18)) \div (-36)$

(d) $(280 \times (-7)) \div ((-8) \times (-35))$

For (b) $32 \div ((-36) \times (-18))$ and (c) $(25 \times (-12)) \div (45 \times (-27))$ , these don't come out to whole numbers. Just say whether each answer is positive or negative, and why.

(a) Work out the bracket*

Multiply 32 × (−18).

(a) Divide and give the answer*

Sign first, then size.

(d) Work out both brackets*

Two products.

(d) Divide and give the answer*

Sign first, then size.

(b) and (c): sign of each answer*

Count the negatives.