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MATH · GRADE 7Number

Compare and Order Positive and Negative Rationals

Two markers on one line: the one further right is greater.

Grade 7
−10−3/4−0.7?further right…
In this lesson

One line, every rational

Every rational number (integer, fraction, decimal, signed or unsigned) has a single position on the number line. Type any rational below and the marker shows where it sits.

-2
-1.5
-1
-0.5
0
0.5
1
1.5
2

Fraction

38

Decimal

0.375

Equivalent fraction forms

All three forms name the same number on the line.

Interactive strip showing that negative three quarters, negative three over four, and three over negative four all name the same point on the number line.
−34-\dfrac{3}{4}

minus on the whole

−34\dfrac{\color{#92400E}-}{3}{4}

minus on the numerator

3−4\dfrac{3}{\color{#92400E}-4}

minus on the denominator

As a decimal

-0.75

Comparing two rationals

To compare two numbers, place both on the line. The one further right is greater.

One positive, one negative. The positive wins, always. Even

−1000<0.001-1000 < 0.001. Every negative sits left of zero, every positive sits right.

Different forms. Rewrite one so they match. To compare

−34-\tfrac{3}{4} and −0.6-0.6, turn the fraction into a decimal: −0.75 versus −0.6. Now the order is obvious: −0.75 is further left, so it's smaller.

Fraction ↔ decimal converter

Type a fraction or a decimal — see the other form.

Two-way converter for fractions and decimals, including negative values. Type a fraction such as negative two fifths or a decimal such as negative zero point seven five and compare the equivalent form.

As a fraction

−25-\dfrac{2}{5}

As a decimal

−0.4-0.4

Long division — divide the top by the bottom.

−25=−2÷5=−0.4-\dfrac{2}{5} = -2 \div 5 = -0.4

Both negative: the trap

When both numbers are negative, magnitude and order disagree. Compare −3/4 and −2/3:

  • |−3/4| = 0.75 and |−2/3| ≈ 0.667, so |−3/4| > |−2/3|.
  • But on the number line, −2/3 ≈ −0.667 sits closer to zero than −3/4 = −0.75, so −2/3 > −3/4.

The number with the larger magnitude is the smaller one when both are negative. Larger magnitude means further from zero; for negatives, further from zero means further left, which means smaller.

Ordering more than two

Same skill, repeated. Drag the cards into ascending order, smallest on the left.

Try it

Drag the cards in order — smallest on the left, largest on the right.

Drag with the mouse or finger, or focus a card and use ←/→.

Worksheet

These aren't graded. Convert to a common form when the numbers don't sit on the same scale.

Practice · Not graded

MA.7.NUM.1

Practice the idea

01 / 12

Convert 3/4 to a decimal.

Convert three quarters to a decimal.
Show common mistakes

Student says

“−0.5 < −0.75 because 0.5 < 0.75.”

What it reveals

Whole-number comparison logic without flipping for negatives.

Targeted response

Number Line: −0.75 sits to the LEFT of −0.5. Left = smaller. The minus sign reverses the comparison.

Student says

“To compare 7/10 and 0.65, I compared 7 and 65.”

What it reveals

Not yet integrating fraction notation as a single number.

Targeted response

Use the number line. Type 7/10, then 0.65. The marker shows 0.7 sits further right than 0.65.

Student says

“It's impossible to find a number between −2/3 and −1/2.”

What it reveals

Missing the density of rationals; thinking only of integers in the gap.

Targeted response

Number-line marker: drop a point between −0.667 and −0.5. Many points work: −0.6, −0.55, −7/12.

Going further

Density of rationals is the deeper idea: between any two distinct rationals, infinitely many others sit. There's no "next number" after −2/3 on the way to −1/2; you can always find one closer.

The next lesson (adding and subtracting integers) uses the same line, with arrows for the operations.