7th Grade Section
WME@Kimpton Middle

Dividing Integers

Two Rows of 5 Blue ChipsTo ask What is 10 divided by 2? is the same as asking What times 2 equals 10?. We know

10 ÷ 2 = 5 because 5 × 2 = 10

In other words

15 ÷ 5 = ? really asks ? × 5 = 15

When we divide a number by another, the answer is called the quotient of the two numbers.

Based on this understanding, do these problems.

14 ÷ 2 =   

-14 ÷ 2 =   

18 ÷ -2 =   

-18 ÷ -2 =   

Division is the inverse operation of multiplication because if you divide by a number then multiply by that number you have done nothing.

(10 ÷ 2) × 2 = 10

(10 × 2) ÷ 2 = 10

You can also think of 21 ÷ 7 as asking How many 7's are there in 21?.

Integer Division with RemainderSometimes an integer does not divide another evenly. 19 ÷ 7 is an example. We can fit 2 7's in 19 easily, but we can't fit 3 7's. In this case we say the quotient is 2 with a remainder of 5.

19 ÷ 7 = (14 + 5) ÷ 7 = 14 ÷ 7 + 5 ÷ 7 = 2 + 5/7

In general we have

integer division formula

Keep in mind that the remainder must be smaller than the divisor in absolute values. If the remainder is zero, then the divisor is a factor of the dividend.

Do these problems.

16 ÷ 5 gives quotient    and remainder  

-17 ÷ 3 gives quotient    and remainder   

Here is the method to perform long division

long multiplication



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