Unit Fractions
What is the unit fraction for 3/7?
3 x 1/7
Use a model or write an equation to show 3×1/4. What is the product?
3 x 1/4 = 3/4
Compute 2×2/3 and show the multiplication as repeated addition.
Repeated addition:2/3+2/3=4/3= 1 1/3
If school starts at 8:15 AM and class lasts 1/2 hour, what time does class end? Show your work.
1/2 hour = 30 minutes. 8:15+0:30=8:45 AM8:15+0:30=8:45 AM.
1/2 hour = 30 minutes. 8:15+0:30=8:45 AM 8:15+0:30=8:45 AM.
You buy 1/2 pound of strawberries. You eat 1/4 of that amount. What fraction of a pound did you eat? Show steps.
Amount eaten = 1/4×1/2=1/8 pound.
Write 4/5 as a multiple of the unit fraction 1/5 using repeated addition (show an equation).
4/5= 1/5+1/5+1/5+1/5= 4 x 1/5
A recipe needs 1/3 cup of oil. You triple the recipe. Write an equation to show how much oil you need. Compute the total.
3 x 1/3. You will need one cup of oil
Use an area model (or describe one) to represent 5×1/2 and find the product.
Five rectangles each shaded to show 1/2; total area 5×1/2 = 5/2 = 2 1/2
A video is 3/4 hour long. If you watch it twice, how many minutes did you watch? Show equation(s).
2×3/4 = 6/4 = 3/2 hours = 1 1/2 hours = 90 minutes.
A craft uses 2/5 yard of ribbon per bow. You make 3 bows. How much ribbon is needed? Show a model or equation.
3×2/5=6/5=1 1/5 yards.
Write 6/8 as a unit fraction, solve it, then simplify the fraction
6 x 1/8 = 3/4
Draw or describe a fraction-bar model for 4× 2/5 and compute the product. Show the equation you used.
Four copies of 2/5 (each bar showing 2/5 shaded) equals 4×2/5=8/5= 1 3/5
Write an equation to solve: Sam ate 33 slices, each slice is 1/6 of a pizza. How much pizza did Sam eat? Show the product as a fraction.
3×1/6=3/6=1/2 of the pizza.
Maria spent 2/3 hour reading and 1/4 hour writing. How long did she spend altogether? Use the four operations if needed and show steps.
Convert to common denominator 12: 2/3=8/12 Sum: 8/12+3/12= 11/12 hour = 55 minutes.
A gardener plants 3/4 of a row with flowers and the row is 12 meters long. How many meters of the row have flowers? Show multiplication and explain your steps.
12×3/4 = 12×0.75 =9 meters. Or 12×3/4=36/4=9
Draw or describe a model (fraction bars or number line) that shows why 5/6 = 5 x 1/6. Explain in one sentence.
Varied Responses (A fraction bar divided into 6 equal parts with 5 parts shaded)
Use repeated addition and multiplication to explain why 6×3/8=18/8. Then rewrite the answer as a mixed number in simplest form.
3/8+3/8+3/8+3/8+3/8+3/8=18/8. Simplify: 18/8=9/4 = 2 1/4.
A mural uses 3/10 of a can of paint per panel. How much paint is needed for 8 panels? Show an equation and model. Simplify the result.
8×3/10=24/10=12/5=2 2/5 cans.
A bus trip takes 2 hours and 1/2 hour. If the bus stops for 3/4 hour along the way, how much actual driving time was there? Show an equation and solve.
1 hour 45 minutes.
A baker makes 2/3 of a batch of cookies each hour. How many batches are made in 5 hours? Use equations and show reasoning.
5×2/3=10/3=3 1/3 batches.
A student says 9/4 cannot be written as a sum of unit fractions. Is the student correct? Write an equation showing 9/4 as a sum of unit fractions and interpret it as a multiple of a unit fraction.
The student is incorrect. 1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4=9 x 1/4
9/4 = 2 1/4
A class walks 2/3 mile each day. How far do they walk in 7 days? Write an equation and show a visual or number-line reasoning that supports your answer.
Equation: 7×2/3=14/3=4 2/3 miles.
Explain and compute 9×4/9. Use the unit-fraction idea and explain why the product simplifies to a whole number.
9×4/9 = 36/9 = 4. Interpretation: nine copies of 4/9 combine to 4 whole ones because 4/9=4×1/9 and summing nine of those gives 4 x1 = 4.
Convert 5/6 of an hour into minutes. Then, if a student works for 5/6 of an hour each day for 9 days, how many total minutes did they work? Show all steps and operations used.
One hour = 60 minutes. 5/6×60 = 5×10 = 50 minutes per day. For 9 days: 9×50 = 4/5×50 = 450 minutes = 7 hours 30 minutes.