Division and remainders

What is a remainder in division?

The remainder is the amount left over after dividing. For example, 43 ÷ 5 = 8 with remainder 3, because 5 × 8 = 40 and 43 - 40 = 3.

In the division 43 ÷ 5, what is the quotient and what is the remainder?

The quotient is 8 and the remainder is 3. This is because 5 × 8 = 40 and 43 - 40 = 3.

What does the equation a = q × d + r mean in division?

It means: a is the number you divide (dividend), d is the number you divide by (divisor), q is the quotient, and r is the remainder. The remainder r is always less than the divisor d and not negative.

When you divide 37 by 6, what is the quotient and remainder?

37 ÷ 6 = 6 with remainder 1, because 6 × 6 = 36 and 37 - 36 = 1.

How do you check a division with a remainder using multiplication?

Multiply the quotient by the divisor, then add the remainder. You should get the dividend. For example, 8 × 5 + 3 = 43.

What is the rule for the remainder when dividing by a number?

The remainder must be less than the divisor and not negative. For example, when dividing by 7, the remainder can be 0, 1, 2, 3, 4, 5, or 6.

Divide 89 by 4. What is the quotient and remainder?

89 ÷ 4 = 22 with remainder 1, because 4 × 22 = 88 and 89 - 88 = 1.

What does 'division as sharing' mean?

Division as sharing means splitting a number into equal groups. For example, sharing 12 sweets among 3 friends gives each 4 sweets. If there is a remainder, some sweets are left over.

What does 'division as grouping' mean?

Division as grouping means finding how many groups of a certain size you can make. For example, how many groups of 5 are in 17? You get 3 groups and 2 left over.

In a real problem, when do you round a remainder up?

You round up when you need to have enough for everyone or everything. For example, if 23 children need seats and each bus holds 8, you need 3 buses because 2 buses hold 16 and 3 buses hold 24.

In a real problem, when do you round a remainder down?

You round down when you can only use full groups. For example, if you have 23 apples and each bag holds 8, you can fill 2 full bags and have 7 apples left over.

What is short division?

Short division is a quick way to divide by a one-digit number. You write the dividend and divisor, divide digit by digit, and carry remainders to the next digit. For example, 84 ÷ 3: 8 ÷ 3 = 2 remainder 2, then 24 ÷ 3 = 8, so the answer is 28.

Divide 72 by 5 using short division. What is the quotient and remainder?

72 ÷ 5 = 14 with remainder 2. Because 5 × 14 = 70 and 72 - 70 = 2.

What is a factor pair?

A factor pair is two numbers that multiply together to give a product. For example, 3 and 4 are a factor pair of 12 because 3 × 4 = 12.

List all factor pairs of 24.

The factor pairs of 24 are: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

What is a multiple of a number?

A multiple of a number is the result of multiplying that number by a whole number. For example, multiples of 4 are 4, 8, 12, 16, 20, ...

Is 36 a multiple of 9? How do you know?

Yes, 36 is a multiple of 9 because 9 × 4 = 36. So when you divide 36 by 9, the remainder is 0.

What is the remainder when you divide 100 by 7?

100 ÷ 7 = 14 with remainder 2, because 7 × 14 = 98 and 100 - 98 = 2.

What is the least positive remainder?

The least positive remainder is the smallest non-negative remainder you get when dividing. For example, 43 ÷ 5 gives remainder 3, which is the least positive remainder.

What is the least absolute remainder?

The least absolute remainder is the remainder closest to zero, which can be negative. For example, 43 ÷ 5 can also be written as 9 × 5 - 2, so the least absolute remainder is -2.

How do you find the remainder using long division?

In long division, you divide, multiply, subtract, and bring down digits. The final number left after all digits are used is the remainder. For example, 85 ÷ 4: 4 goes into 8 twice (2), multiply 2×4=8, subtract 8-8=0, bring down 5, 4 goes into 5 once (1), multiply 1×4=4, subtract 5-4=1, so remainder is 1.

What does the modulo operation do?

The modulo operation finds the remainder when you divide one number by another. For example, 17 mod 5 = 2, because 17 ÷ 5 = 3 with remainder 2.

If you have 50 pencils and you put them in packs of 6, how many full packs can you make and how many pencils are left?

You can make 8 full packs because 6 × 8 = 48, and 2 pencils are left over. So 50 ÷ 6 = 8 remainder 2.

A teacher has 35 stickers and wants to give each student 4 stickers. How many students can get stickers and how many stickers are left?

8 students can get 4 stickers each because 4 × 8 = 32, and 3 stickers are left. So 35 ÷ 4 = 8 remainder 3.