Operations and Models
What is the value of dividing the unit fraction 1/4 by the whole number 2? Represent your answer as a fraction.
1/8
Mila has 1/2 of a yard of ribbon. She cuts it into 2 equal pieces. How much ribbon is in each piece? Write an equation to represent the division and give the answer
Equation 1/2÷2=1/4; each piece is 1/4 yard
Using a length model (a number line or bar), show how to find 1/2÷2 and state the result.
1/2÷2=1/4
Write an equation that shows how to divide 1/2 by 2 using multiplication by the reciprocal.
1/2÷2=1/2×1/2=1/4
If 1/4÷2=x, write the multiplication equation that checks your result.
Multiplication check: if x=1/8 then x×2=1/4
Divide the unit fraction 1/3 by 3 and write the result as a fraction in simplest form.
1/9
A recipe needs 1/3 cup of oil. The cook wants to make 3 batches, each needing 1/3÷3 of the original amount. How much oil is used for one smaller batch? Show your equation and answer.
1/3÷3=1/9 cup
Draw (or describe) an area model to represent 1/3÷3. What fraction of the whole is each part?
1/3÷3=1/9; each part is 1/9
Show the steps to compute 1/3÷4 using an equation and simplify your answer.
1/3÷4=1/12
A ribbon 1/2 meter long is cut into pieces each 1/8 meter long. Which division expression models this and what is the answer?
Expression 1/2÷1/8=4
Find 1/5÷4 and explain in one sentence what this result means (use words like “part” or “share”).
1/20; meaning each share is one twentieth of a whole
Sam has 4 boxes. Each box will get 1/5 of a pound of candy. If you instead ask how many boxes you can fill with 1 pound when each box takes 1/5 pound, write and solve the division equation that answers this.
1÷1/5=5 boxes (or interpretation as asked
Use a length model to explain why 1/4÷2=1/8. Describe the partitioning steps.
1/4÷2=1/8 (partition quarter into 2 equal parts)
Explain why dividing a whole number by a unit fraction (for example, 4÷1/2) gives a larger number. Use an equation to support your explanation.
Example explanation: dividing by a unit fraction asks how many of those unit fractions fit into the whole; 4÷1/2=8 because each whole contains two 1/2 pieces, so 4 wholes contain 8.
Solve 3÷1/4 and show a model (area or length) that matches your answer.
3÷1/4=12
Compute 1/6÷3. Then write an equivalent multiplication equation that shows why your answer is correct.
1/18; multiplication check: 1/18 x 3=1/6
A classroom has 1/2 of a meter of rope. The teacher wants to cut the rope into pieces that are 1/4 meter long. Which division (unit fraction divided by a whole number OR whole number divided by a unit fraction) models this? Set up the correct equation and solve.
This is unit fraction divided by whole number: 1/2÷1/4 would be different; correct setup is cutting 1/2 into 1/4 pieces -> actually models as 1/2÷1/4=2 pieces. (Teacher: check interpretation carefully.)
Given an area model for one whole divided into 6 equal parts, show visually how to represent 1÷1/6 and explain what the result tells you.
1÷1/6=6; six pieces of size 1/6 make one whole
Convert the word problem “How many 1/5-size pieces are in 3 wholes?” into an equation and solve.
Equation 3÷1/5=15
A gardener has 1/3 of a bag of soil. She uses equal portions to fill 3 small pots. Write and solve the equation; show the result using a model or an explanation.
1/3÷3=1/9
Without using a calculator, compute 1/8÷2. Show the step where you convert the division by a whole number into multiplication.
1/16
A baker has 3 loaves of dough. Each loaf will be cut into pieces that are 1/6 of a loaf. How many pieces will the baker have total? Write the division equation and solve.
3÷1/6=18 pieces
Create a length-model explanation for 2÷1/3 (draw or describe how many 1/3-lengths fit into 2). Write the corresponding equation and answer.
2÷1/3=6
Solve and justify: 1/2÷1/4. (Although this is division of a unit fraction by another unit fraction, show the work and reasoning — connect to NC.5.NF.7 thinking.)
1/2÷1/4=2 since two 1/4 pieces fit into 1/2
Create a one-step word problem (suitable for a 5th grader) that requires dividing a whole number by a unit fraction. Include the solution and the equation that represents it. (2 minutes)
Give a word problem.