Mathematics · Grades 3–6
Fractions as equal shares and numbers
Use the same whole and equal-size parts when interpreting fractions.
Learn the idea
Equal parts
A denominator describes how many equal parts make one whole.
Equivalent values
Multiplying numerator and denominator by the same nonzero number preserves a fraction.
Comparison
With a common positive denominator, compare numerators. Different wholes require extra information.
Reasonableness
Use benchmarks such as 0, one half and 1 before accepting a calculation.
Worked examples
A whole is split into four unequal pieces. Is each piece automatically one quarter?
Counting pieces alone is insufficient; quarters have equal value or area for the specified whole.
No; the pieces must be equal shares.
Write 3/8 + 2/8 as one fraction.
The parts have the same size, so add the numerators and retain the denominator.
5/8
Check your understanding
Find the missing numerator: 2/3 = ?/12.
Which fraction is closest to one whole?
- 7/8
- 3/8
- 1/8
A 24-page booklet has 3/4 of its pages read. How many pages is that?
Answers and marking notes
Answers and marking notes
- 8
The denominator is multiplied by four, so the numerator is also multiplied by four.
- 7/8
Seven eighths is only one eighth below one.
- 18 pages
24 divided by 4 is 6, and 3 groups of 6 make 18.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.