Quotient

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Quotient: meaning, method and solved example (6th Grade) – Maths PDF

In short: Quotient is the number you get when one number is divided by another, so in 91 divided by 7 the quotient is 13.

6th GradeNumbers and Operations6.NS.B.2

What is Quotient?

The quotient is the answer to a division. It tells how many equal groups or how big each group is when a total is split up. In \(91 \div 7 = 13\), the 91 is the dividend, the 7 is the divisor and 13 is the result.

Precisely, for a divisor \(d \neq 0\), the quotient of \(n\) and \(d\) is the number \(q\) with \(d \cdot q = n\). It can also be written \(\frac{n}{d}\), and when the split is uneven the leftover is called the remainder.

How to spot it

  • A problem shares a total equally among people, boxes or days and asks for one share.
  • A word problem asks “how many groups of” a certain size fit into a total.
  • The expression is written with a division sign, a fraction bar or a long division bracket.
  • You are asked for the result of dividing one number by another, and told to name each part.

The method

  1. Name the dividend (the total) and the divisor (the group size or count).
  2. Divide the dividend by the divisor, using a basic fact or long division.
  3. Write any remainder separately, or continue into decimals if the question calls for it.
  4. Check by multiplying: divisor times quotient, plus remainder, must equal the dividend.
91 stickers shared among 7 boxes1313131313131391 / 7 = 13 (dividend / divisor = quotient)
Each of the 7 boxes gets 13 stickers, so the quotient is 13.

Quotient: solved example

Problem

A ferry operator in Seattle must carry 275 bicycles in vans that each hold 12. Find the quotient and remainder, and say how many vans are needed.

Solution

Divide: \(275 \div 12\). Since \(12 \times 22 = 264\), the quotient is 22 and the remainder is \(275 – 264 = 11\).

Eleven bicycles still need a ride, so one more van is required: 23 vans.

Try it

Question 1

In \(144 \div 9\), which number is the dividend and what is the result?

Show the answer

The dividend is 144, and \(9 \times 16 = 144\), so the result is 16.

Question 2

Find the result of \(5.6 \div 0.8\).

Show the answer

Multiply both by 10: \(56 \div 8 = 7\).

Quotient vs. Long Division

The quotient is the number you end up with. Long division is one way to get there, a step-by-step layout that builds the number digit by digit. You can also reach it with a multiplication fact or a calculator.

Long Division

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