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Helpful Examples

Let’s practice using partial quotients with remainders.

Goal:

Goal:

Elementary school girl writing in a notebook.

The example problems below demonstrate the steps to solve division expressions using partial quotients with remainders. Work through each problem, using partial quotients. Then, click each row to reveal the solution.

The powers of 10 when multiplied by your divisor of 16 are:
160 (16 x 10), 1,600 (16 x 100), and 16,000 (16 x 1,000)

Both 1,600 and 16,000 are too large to be used with a dividend of 657.
But, 160 is less than 657, so we can subtract groups of 160 to begin calculating for the partial quotient:

Compare your solution to the one below.

Six hundred fifty seven minus one hundred sixty equals four hundred ninety seven minus one hundred sixty equals three hundred thirty seven minus one hundred sixty equals one hundred seventy seven minus one hundred sixty equals seventeen minus sixteen equals one. Arrows pointing to ten groups and one group. You can not make anymore groups of sixteen. What is left becomes your remainder.

So, what is the final quotient?

The powers of 10, when multiplied by the divisor of 14 are:
140 (14 x 10), 1,400 (14 x 100), and 14,000 (14 x 1,000)

Both 1,400 and 14,000 are too large to be used with a dividend of 961.
However, 140 is less than 961, so we can begin by subtracting groups of 140 to start calculating for the partial quotients.

Compare your solution to the one below.

Nine hundred sixty one minus one hundred forty equals eight hundred twenty one minus one hundred forty equals six hundred eighty one minus one hundred forty equals five hundred forty one minus one hundred forty equals four hundred one minus one hundred forty equals one hundred twenty one minus one hundred twelve equals nine. Arrows pointing to ten groups and eight groups. You can not make anymore groups of fourteen. What is left becomes your remainder.

What is your final quotient?

The powers of 10 when multiplied by your divisor of 37 are:
370 (37 x 10), 3,700 (37 x 100), and 37,000 (37 x 1,000)

Both 3,700 and 37,000 are too large to be used with the dividend of 1,949.
However, 370 is less than 1,949, so we can begin by subtracting groups of 370 to start calculating for the partial quotient.

Compare your solution to the one below.

One thousand nine hundred forty nine minus three hundred seventy equals one thousand five hundred seventy nine minus three hundred seventy equals one thousand two hundred nine minus three hundred seventy equals eight hundred thirty nine minus three hundred seventy equals four hundred sixty nine minus three hundred seventy equals ninety nine minus seventy four equals twenty five. Arrows pointing to ten groups and two groups. You can not make anymore groups of thirty seven. What is left is your remainder.

What is your final quotient?

The powers of 10 when multiplied by your divisor of 87 are:
870 (87 x 10), 8,700 (87 x 100), and 87,000 (87 x 1,000)

87,000 is too large to be used with the dividend of 9,605.
However, 8,700 is less than 9,605, so we can subtract groups of 8,700 to start calculating for the partial quotients.

Compare your solution to the one below.

Nine thousand six hundred five minus eight thousand seven hundred equals nine hundred five minus eight hundred seventy equals thirty five. Arrows pointing to hundreds groups and ten groups. You can not make anymore groups of eighty seven. What is left is your remainder.

What is your final quotient?