Dividing Numbers that Result in a Decimal

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Student Summary

We can use long division to find quotients even when the numbers involved are not whole numbers. Here is the long-division calculation of 86÷486 \div 4, which results in a decimal quotient.

Long division calculation of 86 divided by 4. 
Long division calculation of 86 divided by 4. 8 rows. First row: 21 point 5, Second row: 4, long division symbol with 86 inside. Third row: minus 8. Horizontal line. Fourth row: 6. Fifth row: minus 4. Horizontal line. Sixth row: 2 point 0. Seventh row: minus 2 point 0. Horizontal line. Eighth row: 0. 

The calculation shows that, after removing 4 groups of 21, there are 2 ones remaining. We can continue dividing by writing a 0 to the right of the 2 and thinking of that remainder as 20 tenths, which can then be divided into 4 groups.

To show that the quotient we are working with now is in the tenths place, we put a decimal point to the right of the 1 (which is in the ones place) at the top. It may also be helpful to draw a vertical line to separate the ones and the tenths.

There are 4 groups of 5 tenths in 20 tenths, so we write 5 in the tenths place at the top. The calculation likewise shows 86÷4=21.586 \div 4 = 21.5.

Visual / Anchor Chart

Standards

Building On
5.NBT.7

5.NBT.B.7

Addressing
6.NS.2

6.NS.B.2

Building Toward
6.EE.A

6.EE.A