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Quotient: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">QuotientQuotient: Definition and ExampleTable of ContentsDefinition of Quotient

The quotient is the result we get when one number (dividend) is divided by another number (divisor). For instance, in the calculation 8÷4=28 \div 4 = 28÷4=2, the number 222 is the quotient, while 888 is the dividend and 444 is the divisor.

Quotients can take different forms depending on the division scenario. When a number is completely divisible by another (like 15÷3=515 \div 3 = 515÷3=5), the quotient is a whole number. However, if a number isn't completely divisible by another, the quotient can be expressed either as a decimal number (15÷2=7.515 \div 2 = 7.515÷2=7.5) or as a quotient with remainder (15÷2=715 \div 2 = 715÷2=7 R 111, where 777 is the quotient and 111 is the remainder).

Examples of Quotient Example 1: Finding a Quotient Using Repeated Subtraction Problem:

Find the quotient: 28÷328 \div 328÷3 using repeated subtraction.

Step-by-step solution: Step 1, understand that division can be viewed as repeated subtraction. We'll subtract the divisor (3) from the dividend (28) until we can't subtract anymore. Step 2, perform the repeated subtractions: 28−3=2528 - 3 = 2528−3=25 25−3=2225 - 3 = 2225−3=22 22−3=1922 - 3 = 1922−3=19 19−3=1619 - 3 = 1619−3=16 16−3=1316 - 3 = 1316−3=13 13−3=1013 - 3 = 1013−3=10 10−3=710 - 3 = 710−3=7 7−3=47 - 3 = 47−3=4 4−3=14 - 3 = 14−3=1 Step 3, observe that we can't subtract 3 from 1, so we stop here. Step 4, count how many times we subtracted 3: we did this 9 times. Step 5, therefore, the quotient of 28÷328 \div 328÷3 is 9 with a remainder of 1, which can be written as 999 R 111. Example 2: Finding a Quotient Using Long Division Problem:

Find the quotient 153÷7153 \div 7153÷7 using the long division method.

Step-by-step solution: Step 1, set up the long division format with 7 as the divisor and 153 as the dividend. Step 2, divide: Can 7 go into 1? No, so we look at the first two digits: Can 7 go into 15? Yes, 7 goes into 15 two times, so write 2 above the 5. 7×2=147 \times 2 = 147×2=14 Multiply: 7×2=147 \times 2 = 147×2=14 Subtract: 15−14=115 - 14 = 115−14=1 Bring down the next digit, which is 3: 1∣31|31∣3 Step 3, repeat the process: Can 7 go into 13? Yes, 7 goes into 13 one time, so write 1 above the 3. 7×1=77 \times 1 = 77×1=7 Multiply: 7×1=77 \times 1 = 77×1=7 Subtract: 13−7=613 - 7 = 613−7=6 Since there are no more digits to bring down, and 6 is less than 7, the division is complete. Step 4, therefore, the quotient of 153÷7153 \div 7153÷7 is 21 with a remainder of 6, which can be written as 212121 R 666. Example 3: Real-World Application of Quotient Problem:

Jack needs 2 mangoes to make a glass of mango juice. If he has 28 mangoes, how many glasses of mango juice can he make?

Step-by-step solution: Step 1, identify what we're being asked to find: the number of glasses of juice Jack can make. Step 2, determine the relationship between mangoes and glasses: 222 mangoes =1= 1=1 glass of juice. Step 3, set up the division problem: Number of glasses === Total mangoes ÷÷÷ Mangoes per glass Number of glasses =28÷2= 28 ÷ 2=28÷2 Step 4, perform the division: 28÷2=1428 \div 2 = 1428÷2=14 - Step 5, therefore, Jack can make 14 glasses of mango juice with his 28 mangoes. Comments(7)SSpanishTutorGusNovember 4, 2025I've been struggling to explain quotient to my students. This page's def and examples made it so much easier! Thanks!

MCMs. CarterSeptember 17, 2025I’ve used this glossary page to help my kids understand quotients during homework time. The examples are clear, and the step-by-step methods made division way easier for them to grasp!

MCMs. CarterSeptember 10, 2025I’ve been struggling to explain division to my kids, but this glossary page made it so simple! The examples, especially the repeated subtraction, really helped them grasp what a quotient is. Thanks for the clear explanation!

MCMs. CarterAugust 27, 2025I’ve been using this site to help my kids with their math homework, and the clear definition of 'quotient' made explaining division so much easier. The examples were super helpful too!

NNatureLover25August 20, 2025I’ve used this page to help my kids understand division better. The clear examples made it so easy for them to grasp what a quotient is. Thanks for breaking it down so well!

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