MathPractice
Fractions · Grade 5

Estimate fraction sums and differences

Use 0, one half, and one whole to reason about a result before calculating. A useful estimate checks the size of an answer.

Grade 58 questions per setNo account needed
Practice 8 questions Download worksheet

US Letter PDF · A4 version · Answer key

What we’re working onChoose a justified range for a fraction sum or difference and explain the benchmark used.

First page of the Estimate fraction answers worksheet, with visible questions and room to work.Open worksheet PDF · 8 questions · US Letter
See how it works

Worked examples

Example 1

Compare a sum with one

Is 5/8 + 7/10 less than 1, equal to 1, or greater than 1?

  1. Five eighths is greater than four eighths, which is one half.
  2. Seven tenths is greater than five tenths, which is one half.
  3. Adding two amounts each greater than one half gives a sum greater than one.

Greater than 1

Example 2

Bound a difference

Is 11/12 − 1/4 between 0 and 1/2, equal to 1/2, or between 1/2 and 1?

  1. Eleven twelfths is greater than three fourths, because three fourths is nine twelfths.
  2. Subtracting one fourth therefore leaves more than two fourths, or one half.
  3. The starting amount is less than 1. Taking away a positive amount leaves less than 1.

Between 1/2 and 1

A question from this worksheet

Is 3/12 + 1/8 less than, equal to, or greater than 1?

See the explanation

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3/12 + 1/8 = 6/24 + 3/24 = 3/8. This is less than 1.

Choose how to practice

Pick the support you need.

Each set has eight questions. The online practice and prepared worksheet use the same questions.

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For the grown-up beside them

Help the thinking along.

A useful question

Which familiar value is each fraction near? Can you rule out an answer without finding the exact result?

What to look for

The learner gives a reason for a range and knows that an estimate does not have to equal the exact answer.

A common sticking point

Rounding every fraction down and treating that result as exact.

Help without giving the answer

Place the fractions beside 0, 1/2, and 1 on a line. Ask which side of a benchmark each value lies on.

Keep the words clear

Words in this skill.

estimate
Find an approximate amount or a useful range instead of an exact value.
benchmark
A familiar value used for comparison.
reasonable
Consistent with the size and meaning of the amounts in the problem.
range
A set of possible values between stated limits.

What these sets cover.

  • Begin with clear comparisons to 1/2 and 1.
  • Practice choices use disjoint ranges and avoid nearest-benchmark ties.
  • Generated unlike-denominator examples use denominators 2 to 12 and a least common denominator no greater than 60.

Common questions

Can different estimates both be useful?

Yes. Different benchmarks can give different useful approximations. In practice questions here, the choices name separate ranges so there is a clear answer.

Does estimating replace exact calculation?

No. It helps you predict and check the result. If a problem asks exactly how much remains, calculate the exact difference too.

Try next

Add and subtract unlike fractions

Next, find exact sums and differences by renaming unlike fractions with equal-size parts.

Explore this skill

Related standards: 5.NF.2. These materials focus on this skill, not every part of a grade-level curriculum. How we check materials.