decompose a fraction review 2025

Multiple Choice

DO NOW:

Jake built a bookshelf that is 6 feet tall. How many inches tall is the bookshelf that Jake built?

• 62 in.

• 2 in.

• 18 in.

• 72 in.

Multiple Choice

What does decompose mean?

• to put together

• to combine

• to add

• to break apart

Multiple Choice

What does it mean to decompose a fraction into a sum of fractions with the same denominator?

• To break a fraction into smaller fractions that add up to the original, all with the same denominator.

• To multiply the numerator and denominator by the same number.

• To change the denominator to a different number.

• To convert the fraction to a decimal.

Open Ended

What does it mean to decompose a fraction?

Multiple Select

Which of the following are correct ways to decompose $$\frac{8}{10}$$ into a sum of fractions with the same denominator? Select all that apply.

• $$\frac{6}{10\ }\ +\ \frac{1}{10\ }\ +\ \frac{1}{10}$$

• $$\frac{4}{10\ }\ +\ \frac{3}{10\ }\ +\ \frac{1}{10}$$

• $$\frac{2}{10\ }\ +\ \frac{6}{10\ }\$$

• $$\frac{5}{10\ }\ +\ \frac{2}{10\ }\ +\ \frac{2}{10}$$

Multiple Choice

What was the answer again?

• 1/3 + 2/3

• 1/5 + 2/5

• 1/3 + 1/3 + 1/3

• 1/5 + 1/5 + 1/5

Multiple Choice

What is NOT a way to represent $$\frac{5}{10}$$

Multiple Choice

What is NOT a way to represent $$\frac{11}{12}$$

Fill in the Blanks

Name that fraction

Multiple Select

Which expression is equivalent to the shaded portion of the model shown above? Select TWO correct answers.

Multiple Choice

Which equation shows that the two models represent the same fraction?

Multiple Select

Which expression shows two different ways to represent the mixed number as a sum?

Multiple Select

Select TWO correct answers.

• 6/5 + 1/3

• 1/8 + 7/8

• 3/8 + 3/8 + 1/8

• 2/8 + 5/8

Open Ended

Which answer choice did you eliminate and why?

Multiple Choice

What does $$\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$$  equal?

• $$\frac{5}{5}$$  

• $$\frac{4}{20}$$  

• $$\frac{5}{20}$$  

• $$\frac{4}{5}$$  

Multiple Choice

Using the model, create an equation that uses unit fractions for the fraction strip.

• $$\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{4}{4}$$

• $$\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{4}{6}$$

• $$\frac{2}{6}+\frac{2}{6}=\frac{4}{6}$$

• $$\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{6}{6}$$

Multiple Select

Select all of the correct ways you could decompose $$\frac{7}{8}$$  

• $$\frac{1}{8}+\ \frac{1}{8}+\ \frac{1}{8}\ +\frac{1}{8}\ +\frac{1}{8}\$$  

• $$\frac{2}{8}\ +\ \frac{4}{8}\ +\frac{1}{8}$$  

• $$\frac{6}{8}\ +\ \frac{1}{8}$$  

• $$\frac{2}{8}+\frac{2}{8}\ +\frac{2}{8}+\frac{1}{8}$$  

Multiple Choice

Mrs. Burdick took the fraction $$\frac{3}{3}$$  and decomposed it into a sum of unit fractions. 

She decomposed it like this  $$\frac{3}{3}=\frac{1}{1}+\frac{1}{1}+\frac{1}{1}$$  

Do you think Mrs. Burdick is correct or incorrect in her work? Why?

• Mrs. Burdick is correct because  $$\frac{1}{1}+\frac{1}{1}+\frac{1}{1}=\frac{3}{3}$$   .  $$1+1+1=3$$  for the numerator and denominator.

• Mrs. Burdick is correct because she did it right. 

• Mrs. Burdick is incorrect because she added it wrong.

• Mrs. Burdick is incorrect because the denominator did not stay the same. Also,  $$\frac{1}{1}$$  is not a unit fraction. It is a whole.  $$\frac{1}{1}+\frac{1}{1}+\frac{1}{1}=\frac{3}{1}$$  

Open Ended

What is something useful or interesting you discovered about decomposing fractions?