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Side by Side

Let’s compare the two strategies side by side.

Goal:

Goal:

Young woman comparing with two things.

The best way to decide which strategy you prefer to use is to try out both methods. Work through each of the problems below using the two strategies: partial quotients and long division. After you have worked through each problem--with both strategies--compare the solutions. When ready, click the division expression to reveal the answers.

Let’s compare the two methods side by side.

Partial Quotient Long Division
Six hundred forty five minus nine hundred equals one hundred forty five minus one hundred twenty five equals twenty. Arrows pointing to twenty groups and five groups. You can not make any more groups of twenty five. What is left will become your remainder.

Add the parts of your quotient: 20 + 5 = 25.

Your final quotient is 25 R20.

 Six hundred forty five divided by twenty five minus fifty equals one hundred forty five minus one hundred twenty five equals twenty; twenty five remainder twenty is in the quotient.

Again, your final quotient is 25 R20.
Partial Quotient Long Division
Three thousand sixteen minus one thousand seven hundred equals one thousand three hundred sixteen minus one thousand one hundred and ninety equals one hundred twenty six minus one hundred nineteen equals seven. Arrows pointing to one hundred groups, seventy groups, and seven groups.

Add the parts of your quotient: 100 + 70 + 7 = 177.

Your final quotient is 177 R7.

 Three thousand sixteen divided by seventeen minus seventeen equals one hundred thirty one minus one hundred nineteen equals one hundred twenty six minus one hundred nineteen equals seven; one hundred seventy seven remainder seven is in the quotient.

Again, your final quotient is 177 R7.
Partial Quotient Long Division
Nine thousand one hundred minus six thousand five hundred equals two thousand six hundred minus two thousand six hundred equals zero. Arrows pointing to one hundred groups and forty groups.

Add the parts of your quotient: 100 + 40 = 140

Your final quotient is 140.

 Nine thousand one hundred divided by sixty five minus sixty five equals two hundred sixty minus two hundred sixty equals zero zero minus zero equals zero; one hundred forty is in the quotient.

Again, your final quotient is 140.