Grade 7 · lesson 4 of 4

Order Negative Fractions

For equal positive numerators, a smaller positive denominator creates a larger positive value.

About 20 minutes, plus any extended practice

Supplied materials

Paper or a browser scratch area; a calculator is optional unless rounding is requested.
Supplied teaching case: Using numerator 2, which comparison of the supplied negative fractions is true? Candidate answers: (A) Negative fractions cannot be ordered (B) −2/3 < −2/4 (C) −2/3 = −2/4 (D) −2/3 > −2/4.
Independent check inputs: Using numerator 3, which comparison of the supplied negative fractions is true? Candidate answers: (A) Negative fractions cannot be ordered (B) −3/3 < −3/4 (C) −3/3 = −3/4 (D) −3/3 > −3/4.

Learn the idea

Rational numbers can be represented as ratios of integers with nonzero denominator. Their decimal forms terminate or repeat, and negative quantities can be compared by their positions to the left of zero. For equal positive numerators, a smaller positive denominator creates a larger positive value. Negating both amounts reverses that ordering because the larger magnitude lies farther left of zero.

Here is the method on the supplied teaching case. 2/3>2/4 because thirds are larger than fourths for the same positive numerator. Negating reverses the order: −2/3 is farther left on the number line.

Do not apply a positive-number comparison unchanged to negatives. Sketch the locations or compare common-denominator signed numerators to confirm which negative value is actually smaller.

Write or sketch the supplied teaching case, labeling its quantities and restrictions.
Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
Solve the independent check with its changed inputs before revealing feedback.
Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Worked example

See the method in action

Teaching case: Using numerator 2, which comparison of the supplied negative fractions is true? Candidate answers: (A) Negative fractions cannot be ordered (B) −2/3 < −2/4 (C) −2/3 = −2/4 (D) −2/3 > −2/4. Solution: 2/3>2/4 because thirds are larger than fourths for the same positive numerator. Negating reverses the order: −2/3 is farther left on the number line. The final answer is −2/3 < −2/4. Do not apply a positive-number comparison unchanged to negatives. Sketch the locations or compare common-denominator signed numerators to confirm which negative value is actually smaller.

Your turn

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Helpful tips

For equal positive numerators, a smaller positive denominator creates a larger positive value.
Do not apply a positive-number comparison unchanged to negatives.

See the answer and explanation

−3/3 < −3/4

3/3>3/4 because thirds are larger than fourths for the same positive numerator. Negating reverses the order: −3/3 is farther left on the number line.

Take it further

Changed-input task: Using numerator 9, which comparison of the supplied negative fractions is true? Candidate answers: (A) Negative fractions cannot be ordered (B) −9/3 < −9/4 (C) −9/3 = −9/4 (D) −9/3 > −9/4. Show the mathematical reason, not only the selected answer. Expected result: −9/3 < −9/4. 9/3>9/4 because thirds are larger than fourths for the same positive numerator. Negating reverses the order: −9/3 is farther left on the number line.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

1. Using numerator 4, which comparison of the supplied negative fractions is true?−4/3 < −4/4−4/3 > −4/4−4/3 = −4/4Negative fractions cannot be ordered

Need a hint?

For equal positive numerators, a smaller positive denominator creates a larger positive value.
Do not apply a positive-number comparison unchanged to negatives.

2. Using numerator 5, which comparison of the supplied negative fractions is true?−5/3 > −5/4−5/3 < −5/4−5/3 = −5/4Negative fractions cannot be ordered

Need a hint?

For equal positive numerators, a smaller positive denominator creates a larger positive value.
Do not apply a positive-number comparison unchanged to negatives.

3. Using numerator 6, which comparison of the supplied negative fractions is true?−6/3 > −6/4−6/3 = −6/4−6/3 < −6/4Negative fractions cannot be ordered

Need a hint?

For equal positive numerators, a smaller positive denominator creates a larger positive value.
Do not apply a positive-number comparison unchanged to negatives.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.