Adding Fractions

Ages 9–13

Difficulty adapts to you

Adding Fractions

Fractions must name equal-sized parts before you add them. If the denominators match, add the numerators and keep the denominator. If they differ, first write equivalent fractions with a common denominator.

Your goals

✓You can add fractions with like and unlike denominators.
✓You can use common denominator, equivalent fraction correctly.
✓You can make denominators equal before adding numerators.

Words to know

common denominator:: A denominator shared by both fractions.
equivalent fraction:: A fraction with the same value but different numbers.

Examples

11/5 + 2/5 = 3/5 because both fractions count fifths.
21/3 + 1/4 = 4/12 + 3/12 = 7/12.

More than one way to solve it

Try each method, then choose the one you can explain and check most clearly.

Method 1

Equivalent-fraction method

Best for: Unlike denominators

1.Find a common denominator.
2.Create equivalent fractions.
3.Add numerators and simplify.

Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

Method 2

Visual area model

Best for: Seeing why a common denominator works

1.Draw equal-sized wholes.
2.Partition both into the same number of parts.
3.Shade and combine.

Example: A 3-by-4 grid shows thirds and quarters together as twelfths.

Check these

• Do not add the denominators.
• Keep every number, symbol, label, and unit in its correct place.
• Choose the method that makes each step easiest to explain and check.

Helpful habits

• Read the whole question before choosing what to do.
• Show one clear step at a time and check each step.
• If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own adding fractions example, solve it, and explain how you checked it.

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