Locate signed fractions and decimals

A unit from zero to one has five equally spaced tick marks, including both ends. What value does each interval represent?

A whole unit can be divided into equal parts

A number line increases from left to right. Consecutive integers are one unit apart

Four equal intervals in one unit are quarters. Three of those intervals from zero reach three quarters

The denominator describes the number of equal intervals in one whole unit, not the total number of tick marks in the picture

First read two labelled integers to establish the unit. Then count the intervals within that unit

A fraction and an equivalent decimal occupy the same position

Read a positive fraction

Write the value of P as a fraction in simplest form

The labelled integers increase from 0 to 1 as you move right

There are 4 equal intervals in each unit, so each small interval represents one quarter of a unit

Count intervals, not tick marks: P is 3 intervals to the right of 0

P lies between the consecutive integers 0 and 1

Relative to zero, P is 0 whole units and 3 of these small intervals to the right

Keep the sign and simplify the fraction without changing the position

Read a fifth-unit scale

Negative fractions lie left of zero

A negative fraction represents a position to the left of zero. Its magnitude is the distance from zero

Start at zero and move three quarter-unit intervals left. This is the opposite position to positive three quarters

Starting at negative one instead, moving one quarter-unit interval right reaches the same point

Moving right always increases the value, even when the positions are negative. A negative fraction closer to zero is greater

Read a negative quarter-unit position

Write the value of P as a fraction in simplest form

The labelled integers increase from -1 to 0 as you move right

There are 4 equal intervals in each unit, so each small interval represents one quarter of a unit

Count intervals, not tick marks: P is 1 interval to the right of -1

P lies between the consecutive integers -1 and 0

Relative to zero, P is 0 whole units and 3 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Keep the sign and simplify the fraction without changing the position

Keep the negative sign

Zero does not have to be in the picture

A number-line window may show only positive numbers or only negative numbers. Its ends need not be opposites

For example, the window from negative four to negative two is two units wide, even though zero is not visible

Read the labelled integers instead of treating the centre of the picture as zero

If each unit has six equal intervals, the whole two-unit window has twelve intervals

The denominator is still six because six intervals make one unit. It is not twelve just because the picture shows two units

Place a given negative fraction

Use a number line from -1 to 1, with 4 equal intervals in each unit

Locate the given number on a number line with 4 equal intervals in each unit

The labelled integers increase from -1 to 1 as you move right

There are 4 equal intervals in each unit, so each small interval represents one quarter of a unit

Count intervals, not tick marks: P is 3 intervals to the right of -1

P lies between the consecutive integers -1 and 0

Relative to zero, P is 0 whole units and 1 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Keep the sign and simplify the fraction without changing the position

Match a fraction to its point

A negative mixed number has one overall sign

A mixed number combines a whole-number distance and a proper fractional distance from zero

A negative sign before a mixed number applies to the whole amount

From zero, move two whole units left, then another third of a unit left. The point is between negative three and negative two

Do not read a negative mixed number as a negative whole number plus a positive fraction

That last expression is a different position, to the right of negative two

Number

\(\displaystyle -2\frac13\)

Which description places the given mixed number correctly?

Read a mixed number beyond one

Write the value of P as a mixed number

The labelled integers increase from 2 to 3 as you move right

There are 4 equal intervals in each unit, so each small interval represents one quarter of a unit

Count intervals, not tick marks: P is 3 intervals to the right of 2

P lies between the consecutive integers 2 and 3

Relative to zero, P is 2 whole units and 3 of these small intervals to the right

Write the whole-number distance and the proper fractional part, keeping the sign in front of the whole mixed number

Read a negative mixed position

Write the value of P as a mixed number

The labelled integers increase from -3 to -2 as you move right

There are 5 equal intervals in each unit, so each small interval represents one fifth of a unit

Count intervals, not tick marks: P is 3 intervals to the right of -3

P lies between the consecutive integers -3 and -2

Relative to zero, P is 2 whole units and 2 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Write the whole-number distance and the proper fractional part, keeping the sign in front of the whole mixed number

Write the whole signed mixed number

Locate a negative mixed number

Use decimal place value to read the scale

Ten equal intervals in one unit are tenths. Four equal intervals are quarters, each worth zero point two five

Keep the position sign when changing between a fraction and a decimal

Negative zero point six lies six tenth-unit intervals left of zero

Adding a trailing decimal zero does not move the point

The slider counts quarter-unit steps from zero. The labelled ticks are one unit apart. Compare the settings negative three and positive three, then move through the other settings

What is true at the settings negative three and positive three?

Read a negative decimal position

Write the value of P as a decimal

The labelled integers increase from -1 to 0 as you move right

There are 10 equal intervals in each unit, so each small interval represents one tenth of a unit

Count intervals, not tick marks: P is 4 intervals to the right of -1

P lies between the consecutive integers -1 and 0

Relative to zero, P is 0 whole units and 6 of these small intervals to the left

Divide the numerator and denominator by their common factor 2 to simplify

The negative sign applies to the entire distance from zero, not just its whole-number part

Convert the fractional distance exactly to decimal notation and keep the position sign

Read tenths on a two-unit window

Locate a decimal without showing zero

Use a number line from -3 to -1, with 5 equal intervals in each unit

Locate the given number on a number line with 5 equal intervals in each unit

The labelled integers increase from -3 to -1 as you move right

There are 5 equal intervals in each unit, so each small interval represents one fifth of a unit

Count intervals, not tick marks: P is 3 intervals to the right of -3

P lies between the consecutive integers -3 and -2

Relative to zero, P is 2 whole units and 2 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Convert the fractional distance exactly to decimal notation and keep the position sign

Use quarter-unit decimal positions

Read sixths on an all-negative window

Write the value of P as a fraction in simplest form

The labelled integers increase from -4 to -2 as you move right

There are 6 equal intervals in each unit, so each small interval represents one sixth of a unit

Count intervals, not tick marks: P is 7 intervals to the right of -4

P lies between the consecutive integers -3 and -2

Relative to zero, P is 2 whole units and 5 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Keep the sign and simplify the fraction without changing the position

Use the unit, not the whole window

Find the consecutive integers on either side

Consecutive integers differ by one. A non-integer rational number lies strictly between two consecutive integers

For a negative mixed number, the whole-number part is on its right, not its left

The lesser bounding integer is negative three. The greater bounding integer is negative two

Check that the bounds are one unit apart and that the target lies strictly inside them

Bound a negative mixed number

Use a number line from -4 to -2, with 3 equal intervals in each unit

Write the two consecutive integers immediately on either side of the given number, with the lesser integer first

The labelled integers increase from -4 to -2 as you move right

There are 3 equal intervals in each unit, so each small interval represents one third of a unit

Count intervals, not tick marks: P is 5 intervals to the right of -4

P lies between the consecutive integers -3 and -2

Relative to zero, P is 2 whole units and 1 of these small intervals to the left

The negative sign applies to the entire distance from zero, not just its whole-number part

Write the whole-number distance and the proper fractional part, keeping the sign in front of the whole mixed number

Write both neighbouring integers

Bound a negative decimal near zero

Interpret a height below a reference level

Zero represents sea level. Values below zero represent heights below sea level, measured in metres. Read the signed height of point P as a decimal

The labelled scale is in metres and each unit is divided into ten equal intervals

P is between negative two and negative one, thirteen tenths below the zero reference

Its signed height is negative one point three metres

The distance below sea level is positive one point three metres, but the requested signed height is negative

Report the signed height, not just the distance

Draw and label your own number line

Independent drawing task

Draw a horizontal line from negative two to positive two. Mark consecutive integers at equal distances, then divide every unit into four equal intervals

Without choosing from supplied diagrams, plot and label these four numbers

Write an equivalent fraction and decimal beside each point. Use the same point for equivalent values rather than drawing a new point for each notation

Explain the unit, interval size, direction from zero and neighbouring integers for each point before moving to the checking page

The online diagram choices check recognition of supplied positions. Your independent drawing and explanation are not automatically checked

Check the scale and all four positions

A four-unit window with four intervals in each unit has sixteen intervals. The endpoints and zero must stay on the same uniformly spaced scale

This point is five quarter-unit intervals left of zero, between negative two and negative one

This point is three quarter-unit intervals left of zero, between negative one and zero

This point is two quarter-unit intervals right of zero, between zero and one

This point is six quarter-unit intervals right of zero, between one and two

Read your labels from left to right and check this order. Equivalent fractions and decimals must share a point, and every quarter-unit interval must have the same drawn length

Read the scale, keep the sign

Establish one whole unit from the integer labels, then count equal intervals rather than tick marks

A fraction and its equivalent decimal occupy the same point. Positive values lie right of zero and negative values lie left

The minus sign before a mixed number applies to its entire distance from zero

A window need not include zero or have opposite endpoints. Use the scale labels, not the centre of the drawing

Check the consecutive integer bounds, especially for negative mixed numbers

In a context, distinguish a signed position from its non-negative distance to a reference level