When do children learn to simplify and compare fractions?

Equivalent fractions and comparing fractions with different denominators are grade 4 work in most curricula, and simplifying to lowest terms follows in grades 4 and 5. Both rest on the times tables: finding a common factor is a division fact read the other way.

Why do so many comparisons share a numerator or a denominator?

Those are the pairs children get wrong. With the same denominator only the numerators matter, but with the same numerator the larger denominator is the smaller fraction, which runs against the instinct that a bigger number means more. The sheet mixes both on purpose, along with pairs such as 2/4 and 3/6 that are equal.

Which denominator limit should I choose?

Up to 10 keeps to halves, thirds, quarters, fifths and tenths, which is where fractions start. Up to 12 adds sixths, eighths and twelfths for equivalent fractions, and up to 20 is for children who already simplify quickly and need larger common factors to find.

Fractions Worksheets

Simplify, find equivalent fractions and compare · Grades 4–5

Fraction practice written the way it is in a squared exercise book, numerator over denominator with the bar on the grid line: simplify a fraction to lowest terms, complete an equivalent fraction such as 2/3 = □/12, or compare two fractions with >, < or =. Comparisons set the traps children fall into: the same numerator over different denominators, one more on top and bottom, and pairs that look different but are equal. Denominators go up to 10, 12 or 20.

Skills: simplifying fractions, equivalent fractions, comparing fractions, common factors. Format: printable, randomized on every load.

Sheets are randomized, free to print, and carry no answer key on purpose – why Super Awesome Math works this way.

How to do it

Simplifying, comparing and finding equivalent fractions are all the same move: multiplying or dividing the top and the bottom by the same number, which changes how a fraction is written without changing what it is worth.

To simplify, find a number that divides both the numerator and the denominator, and divide both by it. For 12/18, 6 divides both, giving 2/3.
Keep going until nothing but 1 divides both. If you divided 12/18 by 2 first you get 6/9, which still simplifies to 2/3 – a slower route to the same place.
To find an equivalent fraction, multiply top and bottom by the same number instead: 2/3 = 4/6 = 8/12.
To compare two fractions, rewrite them with the same denominator and then compare the numerators. For 2/3 and 3/4, use twelfths: 8/12 against 9/12, so 3/4 is larger.

Where it goes wrong

Changing only one half. Dividing the numerator but not the denominator makes a different fraction, not a simpler one.
Comparing numerators across different denominators. 3/4 is larger than 2/3 even though 3 is smaller than 2 × 2.
Adding instead of multiplying. 2/3 is not equal to 3/4 just because both parts went up by one.

Frequently asked questions

When do children learn to simplify and compare fractions?: Equivalent fractions and comparing fractions with different denominators are grade 4 work in most curricula, and simplifying to lowest terms follows in grades 4 and 5. Both rest on the times tables: finding a common factor is a division fact read the other way.
Why do so many comparisons share a numerator or a denominator?: Those are the pairs children get wrong. With the same denominator only the numerators matter, but with the same numerator the larger denominator is the smaller fraction, which runs against the instinct that a bigger number means more. The sheet mixes both on purpose, along with pairs such as 2/4 and 3/6 that are equal.
Which denominator limit should I choose?: Up to 10 keeps to halves, thirds, quarters, fifths and tenths, which is where fractions start. Up to 12 adds sixths, eighths and twelfths for equivalent fractions, and up to 20 is for children who already simplify quickly and need larger common factors to find.

Settings

Practice: simplify, equivalent fractions, compare, or a mix of all three
Denominators: up to 10, 12 or 20
Columns: 2, 3 or 4 (16–32 problems)
Print an answer key

Example problems

6/8 = □/□
2/3 = □/12
3/4 □ 5/8
5/10 = □/□

More Fractions & decimals

Decimals – Column addition and subtraction, and × ÷ by 10, 100, 1000