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Grade 7 · unit review

Review: Rational Numbers as Fractions, Decimals, and Locations

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.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Write 7/8 as an exact decimal.
Need a hint?
  • A denominator built from factors two and five can be renamed as a power of ten.
  • A decimal with three displayed places need not be approximate.
2. Convert 0.666… (the digit 6 repeats forever) to a fraction.
Need a hint?
  • A repeating decimal can be converted using two equations whose repeating tails match.
  • The dots mean the specified pattern repeats forever.
3. Compute −7/3 + 8/4 exactly.
Need a hint?
  • Equivalent fractions put both quantities into the same-size parts.
  • Add the signed numerators only after choosing a common denominator.
4. Using numerator 7, which comparison of the supplied negative fractions is true?
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.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Write 9/8 as an exact decimal. Candidate answers: (A) 0.1125 (B) 0.8889 (C) 1.125 (D) 2.25. 2. Convert 0.888… (the digit 8 repeats forever) to a fraction. Candidate answers: (A) 1 (B) 4/5 (C) 8/9 (D) 8/99. 3. Compute −9/3 + 10/4 exactly. Candidate answers: (A) -1/2 (B) -9/7 (C) 1/7 (D) 11/2. 4. 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.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 1.125. Divide 9 by 8, or rename the denominator as 1000: 9/8=1125/1000=1.125. 2. 8/9. Let x=0.888…. Then 10x=8.888…. Subtract x to get 9x=8, so x=8/9. This is an exact repeating decimal. 3. -1/2. Rename both fractions in twelfths: −36/12+30/12=(-6)/12=-1/2. The sign belongs to the numerator. 4. −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.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.