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5TH GRADE MATH · FREE LESSON

How to add fractions with different denominators

Before you add thirds and fourths, give the pieces the same size. This lesson explains common denominators, shows why the denominator stays fixed when you add, and gives you a chance to try the method yourself.

Start the lesson
BEFORE YOU BEGIN

A quick starting check.

  • Know what a numerator and denominator describe.
  • Make equivalent fractions by multiplying both numbers by the same factor.
  • Find small multiples of a whole number.
UNDERSTAND THE IDEA

Build the method, one step at a time.

Why do the denominators need to match?

The denominator names the size of the parts. A third and a fourth of the same whole are different-sized pieces. Adding the numerators immediately would count unlike pieces as if they were interchangeable.

A common denominator gives both fractions equal-sized parts. Imagine two one-meter strips: mark one in thirds and the other in fourths. Splitting both into twelfths lets you measure either length with the same small unit.

Find a common denominator and rename both fractions

List multiples until you find a number shared by both denominators. The multiples of 3 include 3, 6, 9 and 12; the multiples of 4 include 4, 8 and 12. Twelve is their least common multiple.

The least common denominator keeps the numbers manageable, but any common multiple works. For each fraction, multiply the numerator and denominator by the same factor. The written fraction changes while its value stays the same.

Add the counts, then check the result

Once the units match, add the numerators and keep the common denominator. Four twelfths plus three twelfths is seven twelfths: the pieces are still twelfths after combining them.

Simplify if the numerator and denominator have a common factor. A sum can be larger than one whole; that is not an error. For two positive fractions, your sum should be greater than either fraction alone. Estimate before calculating to catch an unlikely answer.

1/3 = 4/12
1/4 = 3/12
Sum: 7/12
Every full strip is the same whole, divided into twelfths. Four shaded parts plus three shaded parts makes seven twelfths.
SEE IT WORK

Two worked examples.

EXAMPLE 1

Add 1/31/3 + 1/41/4

  1. Choose twelfths as the common unit because 12 is a multiple of both 3 and 4.
  2. Rename the first fraction: 1/3=4/121/3 = 4/12. Rename the second: 1/4=3/121/4 = 3/12.
  3. Add the equal-sized pieces: 4/12+3/12=7/124/12 + 3/12 = 7/12. Seven and twelve have no common factor greater than 1.

Check your reasoning: Each original fraction is less than one half, so the total is less than one. It is also greater than one half because 1/31/3 is greater than 1/41/4; two fourths would make one half.

EXAMPLE 2

Join 3/43/4 meter and 5/65/6 meter of ribbon

  1. There is no overlap, so add the two lengths. Use twelfths: 3/4=9/123/4 = 9/12 and 5/6=10/125/6 = 10/12.
  2. Add: 9/12+10/12=19/129/12 + 10/12 = 19/12 meters.
  3. Separate one whole: 19/12=12/12+7/12=171219/12 = 12/12 + 7/12 = 1\frac{7}{12} meters.

Check your reasoning: Both pieces are longer than one half meter and shorter than one meter. Their total should be between one and two meters, which matches the answer.

YOUR TURN

Try it before you reveal it.

Write down your thinking. Open a hint if you get stuck, then compare your method with the explanation.

Practice 1

Find 1/6+1/31/6 + 1/3 in simplest form.

Show a hint

You can keep sixths as the common unit.

Show the answer and explanation

1/21/2

1/3=2/61/3 = 2/6, so 1/6+2/6=3/6=1/21/6 + 2/6 = 3/6 = 1/2. Divide the last numerator and denominator by 3.

Practice 2

Find 2/5+1/42/5 + 1/4.

Show a hint

What is the smallest positive multiple shared by 5 and 4?

Show the answer and explanation

13/2013/20

Use twentieths: 2/5=8/202/5 = 8/20 and 1/4=5/201/4 = 5/20. The sum is 13/2013/20, which is already in simplest form.

Practice 3

A container holds 2/32/3 liter. You add 3/43/4 liter. How much liquid is there now? Assume nothing spills.

Show a hint

The sum is larger than one liter. Use twelfths first.

Show the answer and explanation

15121\frac{5}{12} liters

2/3+3/4=8/12+9/12=17/12=15122/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1\frac{5}{12}. Seventeen twelfths contains one whole group of twelve twelfths and five more.

KEEP THIS IDEA

What to take with you.

Same whole, same-sized parts, then add. Be able to explain each equivalent fraction instead of only memorizing the steps.

Try explaining one example without looking at the steps. If a step is hard to explain, revisit that part before moving on.

A PROMPT TO TRY IN STUDY

Give me an addition problem with unlike denominators. Ask me to choose a common denominator and explain my equivalent fractions before checking my sum.

Eligible students ages 13 and older with Study access can sign in and use this prompt for more practice. Check AI explanations against your class materials.

Continue in Study

Written by FutureSteps for study and review. This lesson expands a topic in our Texas starter collection. Course reference: Texas TEKS · Grade 5 Mathematics (§111.7(b)(3)(H); §111.7(b)(3)(K)). These references do not imply endorsement, complete standard coverage or assessed mastery. Follow your school’s materials and course sequence.

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