Virginia SOL Math / Grade 3 / Number & Number Sense

3.NS.3

Fractions & Mixed Numbers

What you'll learn

  • Name and write fractions and mixed numbers from a model
  • Build a fraction from unit fractions, such as 1/4 + 1/4 + 1/4
  • Compare fractions to the benchmarks 0, 1/2, and 1
  • Compare two fractions with the same numerator or the same denominator
  • Find equivalent fractions

Words to know

Numerator —
the top number — how many parts you have
Denominator —
the bottom number — how many equal parts in all
Unit fraction —
a fraction with 1 as the numerator, like 1/4
Mixed number —
a whole number and a fraction together, like 1 1/2
Equivalent —
different fractions naming the same amount
Benchmark —
a familiar value (0, 1/2, 1) used to compare

Why it matters Fractions show up whenever we share fairly or measure carefully — cutting a pizza into equal slices, following a recipe that needs 3/4 cup, or reading the marks on a ruler.

Worked examples

Model ItI do

A bar is divided into 4 equal parts and 3 parts are shaded. Name the fraction.

The whole is divided into 4 equal parts, so the denominator is 4. Three parts are shaded, so the numerator is 3. The shaded amount is 3/4, read "three-fourths." It is built from three unit fractions: 1/4 + 1/4 + 1/4 = 3/4.

Try It TogetherWe do

Is 3/4 greater than or less than 1/2? Use the benchmark 1/2.

Half of the 4 parts is 2 parts, so 1/2 = 2/4. The model shows 3 parts shaded, and 3/4 is more than 2/4. So 3/4 is greater than 1/2 (3/4 > 1/2).

Model ItI do

Show that 3/4 and 6/8 are equivalent.

Both bars are the same length and the same amount is shaded. Splitting each fourth into two equal parts doubles the number of parts and the number shaded: 3/4 = 6/8. The fractions are equivalent.

Now YouYou do

Compare 2/3 and 2/6. Both fractions have the numerator 2.

When the numerators are the same, the fraction with the larger denominator has smaller pieces. Thirds are larger pieces than sixths, so 2/3 > 2/6.

Practice

Mastered 0 of 14

Warm-up

Ease in with the basics.

  1. 1.Write the fraction when 2 of 3 equal parts are shaded.

  2. 2.Build a fraction from 1/5 + 1/5 + 1/5.

  3. 3.Is 1/4 greater than or less than 1/2?

On Level

The core Quick Check from the book.

  1. 1.Write the fraction when 5 of 6 equal parts are shaded.

  2. 2.Write 7/4 as a mixed number.

  3. 3.Compare using >, <, or =: 3/5 ___ 3/8

  4. 4.Is 5/6 greater than or less than 1/2?

  5. 5.Name a fraction equivalent to 1/2 that has a denominator of 8.

  6. 6.Which is greater: 5/8 or 3/8?

  7. 7.Build 3/6 from unit fractions.

  8. 8.Compare using >, <, or =: 2/3 ___ 2/6

Challenge

Stretch your thinking.

  1. 1.Write >, <, or = : 4/6 ___ 4/10

  2. 2.Write 11/8 as a mixed number.

  3. 3.Which fraction is equivalent to 1/2?