Texas TEKS5th GradeMath

5.3H— Adding and Subtracting Fractions with Unlike Denominators

Number and operations · b.3: Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to:

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What this standard means: In this lesson, your child will learn how to add and subtract fractions that have different denominators but still refer to the same whole. They will use area models to see why the pieces must be the same size before fractions can be combined. The lesson shows how to make equivalent fractions with a common denominator, and how to regroup when subtracting mixed numbers. Your child will study worked examples, find the mistakes in incorrect answers, and then correct them. They will practice turning halves and thirds into sixths, and use that understanding to solve fraction problems accurately.

What the standard says, word for word · §111.7.b.3.H

represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations
Read it at the source: Texas Education Agency (TEA)
← Builds on · Grade 4§111.6.b.3.E Adding and Subtracting Fractions on a Number Line
You are here · Grade 55.3H Adding and Subtracting Fractions with Unlike Denominators

What’s inside

What you get, and who it’s for

Everything below is measured from the actual lesson and the actual file. Nothing here is an estimate.

Time to run
About 22 minutes. 7 min lesson, then 15 min of practice.
In the download
7 printable pages: the full lesson, the worked examples, the visual models, and 7 practice problems with space to work. An educator answer key is included at the end, so the student pages come first and it is still ready to hand out. The lesson’s worked examples do show their solutions, because that is how they teach.
Question set
The download carries all 7 questions. The page shows 7 of them as a sample.
Question format
Every question is numeric answer. Students show their work on the page.
Assumed before this

Students who are shaky on these will struggle with 5.3H. Worth a quick check first.

  • b.1.A(5th Grade) Students should already be able to identify fractions and mixed numbers that name the same whole and use equivalent fractions with common denominators. They also need practice adding and subtracting fractions with like denominators, including regrouping in mixed numbers, before working with unequal denominators.
Dates
Published September 11, 2026. Not revised since.

The sample intervention

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5.3H

Mission: Fix the Fraction Errors

Represent and solve addition and subtraction of fractions with unequal denominators that refer to the same whole, including mixed numbers, by using area models, equivalent fractions, and regrouping.

Read the passages and examples below to learn about adding and subtracting fractions with unequal denominators that refer to the same whole. Study each incorrect calculation, its error, and the corrected fraction solution.

Fractions can be added or subtracted only when their denominators describe equal-sized parts of the same whole. An area model makes this visible: two same-size solar panels represent equal wholes, and each panel must be divided into the same number of equal sections. To create a common denominator, multiply or divide both the numerator and denominator by the same whole number. For example, sixths can represent both halves and thirds because 1/2 = 3/6 and 1/3 = 2/6.
Adding the bottom numbers changes the size of the pieces, so the answer no longer matches the picture. In 1/2 + 1/3, the expression 2/5 is incorrect because halves and thirds cannot become fifths by addition. Using sixths gives 3/6 + 2/6 = 5/6. Mixed-number subtraction may also require regrouping one whole into fractional parts before subtracting the numerators.
Fraction bars

1/2 and 1/3 rewritten as sixths: 3/6 and 2/6.

Worked exampleIncorrect work: A space-station plan combines 1 1/2 panels and 1 1/3 panels. The calculation 1 1/2 + 1 1/3 = 2 2/5 is incorrect. In two same-size area models, divide each whole panel into sixths: 1 1/2 = 1 3/6 and 1 1/3 = 1 2/6. Correct solution: 1 3/6 + 1 2/6 = 2 5/6 panels. The incorrect work added unequal-sized parts and treated them as fifths.
Worked exampleIncorrect work: A lunar-rover route calculation shows 3 1/4 − 1 2/3 = 2 5/12. First use twelfths: 3 1/4 = 3 3/12 and 1 2/3 = 1 8/12. The work is incorrect because 3/12 is less than 8/12, so the fractional parts cannot be subtracted without regrouping. Regroup one whole: 3 3/12 = 2 15/12. Correct solution: 2 15/12 − 1 8/12 = 1 7/12.

Practice questions

  1. 1

    A communications dish has 1/4 of its surface painted silver and 2/5 painted white. A student adds 1/4 + 2/5 = 3/9. What fraction of the dish’s same-size surface is painted?

  2. 2

    A rover used 3/4 of a full battery charge, then recovered 2/5 of that same full charge. A student writes, “3/4 − 2/5 = 1/1 = 1.” What fraction of a full charge has been used, net of the recovery?

  3. 3

    Two oxygen supplies hold 1 2/5 tanks and 2 1/2 tanks of the same size. A student writes 1 2/5 = 1 4/10, 2 1/2 = 2 1/10, and totals 3 5/10 tanks. How many tanks of oxygen are there in all?

  4. 4

    A telescope's storage holds 2 3/8 units of images and 1 1/4 units of recordings. A student correctly changes 1 1/4 to 1 2/8 but then writes 2 3/8 + 1 2/8 = 3 5/16 units. How many units of storage are used?

  5. 5

    An astronaut planned 4 1/5 hours of training and completed 2 3/4 hours. A student avoids regrouping and writes 2 11/20 hours remaining. How many hours remain?

  6. 6

    A meteorite bin is 5/6 full, and scientists remove 1/3 of the same bin’s capacity. A student adds the denominators, rewrites the fractions as 5/9 and 1/9, and gets 4/9. What fraction of the bin remains full?

  7. 7

    A habitat begins with 1 3/10 tanks of water, receives 4/5 of a tank, and uses 1/4 of a tank. A student calculates 4/5 − 1/4 = 3/1 and reports 4 3/10 tanks. How much water remains?

Part of the question set is shown. Generate the whole intervention, freshly themed and with an answer key, for your own class in the product.

Watch for this

Common mistakes

Adding or subtracting the denominators instead of finding a common denominator

Students often treat fractions like whole numbers and add the bottom numbers, or subtract without first rewriting both fractions in equal-sized parts. This leads to answers like 3/9, 2 5/16, or 1/1, even though the pieces are not the same size. Mixed numbers add another step, because students may also forget to regroup one whole into fractional parts before subtracting.

Vocabulary

Key terms

denominator
The bottom number in a fraction, which tells how many equal parts make the whole.
numerator
The top number in a fraction, which tells how many parts are being counted.
common denominator
A common denominator is the same bottom number used to show fractions as equal-sized parts of the same whole.
regrouping
Regrouping means changing one whole into fractional parts to help subtract fractions.

In the classroom

How to use this intervention

Use this 15-minute worksheet after a short whole-class reminder about finding common denominators and regrouping mixed numbers, then let students work independently so they can explain each error and corrected sum or difference. If needed, pull a small group to the side to reteach with an area model while the rest of the class finishes the items on their own.

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Questions educators ask

Educator FAQ

What grade is this worksheet for?

This worksheet is for Grade 5.

Which TEKS standard does it align to?

It aligns to TEKS §111.7.b.3.H on representing and solving addition and subtraction of fractions with unequal denominators that refer to the same whole, including mixed numbers.

Does the worksheet include an answer key?

Yes, the examples and corrected solutions are included in the lesson context.