# The Number Line and Addition, Subtraction, Multiplication, and Division

The *number line* is just a line with numbers marked off at regular intervals. You probably saw your first number line when you were learning how to count to ten. You can use this trusty tool to perform the Big Four operations (adding, subtracting, multiplying, and dividing) on relatively small numbers.

The number line can be a useful tool for adding and subtracting small numbers:

When you add, move

*up*the number line, to the right.When you subtract, move

*down*the number line, to the left.

To multiply on the number line, start at 0 and count by the *first number* in the problem as many times as indicated by the *second number.*

To divide on the number line, first block off a segment of the number line from 0 to the *first number* in the problem. Then divide this segment evenly into the number of pieces indicated by the *second number.* The length of each piece is the answer to the division.

## Sample questions

Add 6 + 7 on the number line.

**13.**The expression 6 + 7 means*start at 6, up 7,*which brings you to 13.Subtract 12 – 4 on the number line.

**8.**The expression 12 – 4 means*start at 12, down 4,*which brings you to 8.Multiply 2 x 5 on the number line.

**10.**Starting at 0, count by twos a total of five times, which brings you to 10.Divide 12 / 3 on the number line.

**4.**Block off the segment of the number line from 0 to 12. Now divide this segment evenly into three smaller pieces. Each of these pieces has a length of 4, so this is the answer to the problem.

## Practice questions

Add the following numbers on the number line:

**a.**4 + 7 = ?**b.**9 + 8 = ?**c.**12 + 0 = ?**d.**4 + 6 + 1 + 5 = ?Subtract the following numbers on the number line:

**a.**10 – 6 = ?**b.**14 – 9 = ?**c.**18 – 18 = ?**d.**9 – 3 + 7 – 2 + 1 = ?Multiply the following numbers on the number line:

**a.**2 x 7 = ?**b.**7 x 2 = ?**c.**4 x 3 = ?**d.**6 x 1 = ?**e.**6 x 0 = ?**f.**0 x 10 = ?Divide the following numbers on the number line:

**a.**8 / 2 = ?**b.**15 / 5 = ?**c.**18 / 3 = ?**d.**10 / 10 = ?**e.**7 / 1 = ?**f.**0 / 2 = ?

The answers to the practice questions are as follows:

Add on the number line.

**a.**4 + 7 =**11****.**The expression 4 + 7 means*start at 4, up 7,*which brings you to 11.**b.**9 + 8 =**17****.**The expression 9 + 8 means*start at 9, up 8,*which brings you to 17.**c.**12 + 0 =**12****.**The expression 12 + 0 means*start at 12, up 0,*which brings you to 12.**d.**4 + 6 + 1 + 5 =**16****.**The expression 4 + 6 + 1 + 5 means*start at 4, up 6, up 1, up 5,*which brings you to 16.Subtract on the number line.

**a.**10 – 6 =**4****.**The expression 10 – 6 means*start at 10, down 6,*which brings you to 4.**b.**14 – 9 =**5****.**The expression 14 – 9 means*start at 14, down 9,*which brings you to 5.**c.**18 –18 =**0****.**The expression 18 – 18 means*start at 18, down 18,*which brings you to 0.**d.**9 – 3 + 7 – 2 + 1 =**12****.**The expression 9 – 3 + 7 – 2 + 1 means*start at 9, down 3, up 7, down 2, up 1,*which brings you to 12.Multiply on the number line.

**a.**2 x 7 =**14****.**Starting at 0, count by twos a total of seven times, which brings you to 14.**b.**7 x 2 =**14****.**Starting at 0, count by sevens a total of two times, which brings you to 14.**c.**4 x 3 =**12**. Starting at 0, count by fours a total of three times, which brings you to 12.**d.**6 x 1 =**6****.**Starting at 0, count by sixes one time, which brings you to 6.**e.**6 x 0 =**0****.**Starting at 0, count by sixes zero times, which brings you to 0.**f.**0 x 10 =**0****.**Starting at 0, count by zeros a total of ten times, which brings you to 0.Divide on the number line.

**a.**8 / 2 =**4****.**Block off a segment of the number line from 0 to 8. Now divide this segment evenly into two smaller pieces. Each of these pieces has a length of 4, so this is the answer to the problem.**b.**15 / 5 =**3****.**Block off a segment of the number line from 0 to 15. Divide this segment evenly into five smaller pieces. Each of these pieces has a length of 3, so this is the answer to the problem.**c.**18 / 3 =**6****.**Block off a segment of the number line from 0 to 18 and divide this segment evenly into three smaller pieces. Each piece has a length of 6, the answer to the problem.**d.**10 / 10 =**1****.**Block off a segment of the number line from 0 to 10 and divide this segment evenly into ten smaller pieces. Each of these pieces has a length of 1.**e.**7 / 1 =**7****.**Block off a segment of the number line from 0 to 7 and divide this segment evenly into 1 piece (that is, don’t divide it at all). This piece still has a length of 7.**f.**0 / 2 =**0****.**Block off a segment of the number line from 0 to 0. The length of this segment is 0, so it can’t get any smaller. This shows you that 0 divided by*any*number is 0.