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Year 7 Maths Integers

Integers on a Number Line

20 practice questions 2 video lessons Theory + worked examples

Integers on a Number Line uses a number line to picture positive and negative whole numbers in NSW Year 7 maths (NESA outcome MA4‑INT‑C‑01). Numbers to the right of zero are positive, numbers to the left are negative, and moving along the line shows how values change.

You will read and mark points on number lines with different scales, move a point left or right and say where it lands, find the distance between two points on opposite sides of zero, and match a jump to its number sentence. Board games and lifts that go down to underground car parks are everyday examples. It is part of Year 7 Integers.

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  • Integers on a Number Line - Video - Integers on a Number Line Watch
  • Integers on a Number Line - Video - Represents Integers on a Number Line and Recognise Ascending and Descending Order Watch
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Theory

A number line shows integers in order: positive integers are to the right of zero and negative integers are to the left. This Year 7 maths page shows how to read a point or a scale, how to move a point left or right past zero, and how to find the distance between two points and the point halfway between them.

Integers are the positive and negative whole numbers and zero. A number line shows the position and the order of numbers.

Moving right, numbers get larger. The arrow on the right end shows that numbers go on increasing forever. Moving left, numbers get smaller and become negative. The arrow on the left end shows that they go on decreasing forever.

Integers have size and direction. \(3\) (or \(+3\)) means \(3\) units in the positive direction (right), while \(-2\) means \(2\) units in the negative direction (left).

Not every gap on a number line is worth \(1\). The scale is the value of each gap: each gap \(=\) (difference between two labels) \(\div\) (number of gaps between them).

The distance between two points is the number of units between them. The halfway point (midpoint) is the smaller number plus half the distance.

Number line from minus 5 to 5 with points at minus 2 and 3 A number line from minus 5 to 5. Red dots mark minus 2 and 3. Numbers to the left are smaller and numbers to the right are larger. −5−4−3−2−1012345 −2 3
\(-2\) is \(2\) units left of zero; \(3\) is \(3\) units right of zero.
Moving 6 left from 2 A number line from minus 5 to 5. A blue dot at 2. An orange jump of 2 goes left to 0 and a red jump of 4 goes left to minus 4, where a red dot marks the end. −5−4−3−2−1012345 −2 −4
Start at \(2\) and move \(6\) left: \(2\) steps to \(0\), then \(4\) more. \(2 - 6 = -4\).
Number line with a scale of 5 A number line from minus 20 to 20 with ticks every 5. Only minus 20, 0 and 20 are labelled. A red arrow points to minus 15. −20020
\(4\) gaps from \(-20\) to \(0\), so each gap is \(20 \div 4 = 5\). The arrow is at \(-15\).
A lift as a vertical number line A vertical number line for lift levels from minus 4 to 4. Level 0 is the ground floor, shown dashed. A blue dot at 3 and a red dot at minus 2. −4 −3 −2 −1 0 1 2 3 4 start after 5 down
A lift is a number line standing up. From level \(3\), down \(5\) is \(3 - 5 = -2\).

Right is positive and left is negative:

\[ \text{move right} \Rightarrow \text{add}, \quad \text{move left} \Rightarrow \text{subtract} \]
move right add , move left subtract
\[ \text{gap} = \text{difference} \div \text{gaps} \]
gap = difference / gaps
\[ \text{distance from } {-6} \text{ to } 7 = 6 + 7 = 13 \]
distance from −6 to 7=6+7=13
\[ \text{halfway} = \text{smaller number} + \tfrac{1}{2} \times \text{distance} \]
halfway = smaller number +1/2 distance
Two directions. A point \(5\) units from \(-1\) can be on the right, at \(-1 + 5 = 4\), or on the left, at \(-1 - 5 = -6\).
Count gaps, not tick marks. From \(-2\) to \(3\) there are \(5\) gaps, even though you can see \(6\) tick marks.

How to read a point

  1. Find the scale: work out what each gap is worth.
  2. Count the gaps from \(0\) (or from the nearest label).
  3. Give the sign: left of \(0\) is negative, right of \(0\) is positive.

How to move a point

  1. Right means add; left means subtract.
  2. Crossing zero: jump to \(0\) first, then the rest.
  3. For two moves, do them one at a time.

How to find the distance and the halfway point

  1. Same side of zero: subtract the sizes. Across zero: add the sizes.
  2. Halve the distance and add it to the smaller number.
Example 1 — Reading points
On a number line, A is \(5\) steps left of \(0\) and B is \(3\) steps right of \(0\).
(i) Write the integers A and B.
(ii) Point C is the opposite of A. Which integer is C?
Points A and B on a number line A number line from minus 6 to 6 with point A at minus 5 and point B at 3. −6−5−4−3−2−10123456 A B
Solution

(i) A \(= -5\), B \(= 3\)
(ii) The opposite is the same distance on the other side, so C \(= 5\).

Example 2 — Moving right then left
The dot is at \(-2\). Where will it be if it moves
(i) \(3\) places to the right?
(ii) \(2\) places to the left?
Solution
\(-2 + 3\)\(=\)\(1\)
\(-2 - 2\)\(=\)\(-4\)
−2+3=1,−2−2=−4

(i) \(1\)
(ii) \(-4\)

Example 3 — Reading a scale
On a number line \(0\) and \(24\) are labelled, with \(4\) gaps between them. An arrow points \(2\) gaps left of \(0\). What integer is it?
Solution
\(24 \div 4\)\(=\)\(6\)
\(0 - 2 \times 6\)\(=\)\(-12\)
24÷4=6,0−2×6=−12

Each gap is \(6\), so the arrow points to \(-12\).

Example 4 — Two moves
Point \(P\) is at \(-6\). It moves \(9\) units right, then \(5\) units left. Where is \(P\) now?
Two moves from minus 6 A number line from minus 7 to 4. A jump of 9 to the right goes from minus 6 to 3, then a jump of 5 to the left goes from 3 to minus 2. −7−6−5−4−3−2−101234 +9 −5
Solution
\(-6 + 9\)\(=\)\(3\)
\(3 - 5\)\(=\)\(-2\)
−6+9=3,3−5=−2

\(P\) ends at \(-2\).

Example 5 — Distance and halfway
A is at \(-8\). The point halfway between A and B is \(-1\).
(i) Where is B?
(ii) How many units apart are A and B?
Solution
\(-1 + 7\)\(=\)\(6\)
\(8 + 6\)\(=\)\(14\)
−1+7=6,8+6=14

(i) A to the halfway point is \(7\) steps right, so B is another \(7\) steps right: B \(= 6\).
(ii) Across zero: \(14\) units. Check: half of \(14\) is \(7\), and \(-8 + 7 = -1\).

Example 6 — Two possible answers
Point M is at \(2\). Point N is \(9\) units away from M.
(i) N is to the right of M. Which integer is N?
(ii) N is to the left of M. Which integer is N?
Solution
\(2 + 9\)\(=\)\(11\)
\(2 - 9\)\(=\)\(-7\)
2+9=11,2−9=−7

(i) \(11\)
(ii) \(-7\)

Example 7 — A lift
A lift is on level \(4\). The car park levels are \(-1\), \(-2\), \(-3\), and so on. It goes down \(7\) levels and then up \(2\). Which level is it on now?
Solution
\(4 - 7\)\(=\)\(-3\)
\(-3 + 2\)\(=\)\(-1\)
4−7=−3,−3+2=−1

The lift is on level \(-1\).

Common pitfalls

Not checking the scale. If the labels are \(0\), \(6\), \(12\) with \(3\) gaps between each pair, each gap is \(2\), not \(1\).
Counting tick marks instead of gaps. From \(-2\) to \(3\) is \(5\) units, not \(6\).
Moving left from a negative. Left of a negative is more negative: \(6\) left from \(-2\) is \(-8\), not \(4\).
Subtracting sizes across zero. From \(-6\) to \(7\) is \(6 + 7 = 13\) units, not \(1\).

Frequently asked questions

Which way is positive on a number line?

Right is positive and left is negative. On a vertical number line, up is positive.

How do you find the scale of a number line?

Divide the difference between two labels by the number of gaps between them. \(20 \div 4 = 5\).

How do you move past zero?

Jump to zero first, then the rest. \(2 - 6 = 2 - 2 - 4 = -4\).

How do you find the distance between two integers?

On the same side of zero subtract the sizes; across zero add them. From \(-8\) to \(6\) is \(14\).

How do you find the halfway point?

Add half the distance to the smaller number. Halfway between \(-8\) and \(6\) is \(-8 + 7 = -1\).

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