Division Expressions with Fractions and Mixed Numbers Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.NOS.1) · Lesson 6-2
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I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.Puedo explicar qué significa dividir una fracción entre una fracción, hallar el cociente con denominadores comunes o multiplicando por el recíproco, y comprobarlo multiplicando.

MissionMisión · Home FieldCancha local · night shiftturno de noche

Train like a champion.Entrena como un campeón.

It is the day of the big tournament, and the supply cart is full of odd amounts. Check each plan carefully: a wrong flip means too few cups and not enough paint.

Es el día del gran torneo y el carrito de suministros está lleno de cantidades raras. Revisa cada plan con cuidado: un volteo equivocado significa muy pocos vasos y poca pintura.

Word bankBanco de palabras 5 words5 palabrasreciprocal, quotient, mixed number, …recíproco, cociente, número mixto, …
reciprocalrecíproco
A fraction turned upside down. The reciprocal of 3/4 is 4/3.Una fracción volteada de arriba abajo. El recíproco de 3/4 es 4/3.
quotientcociente
The answer when you divide.La respuesta cuando divides.
mixed numbernúmero mixto
A whole number and a fraction together, like 2 1/2.Un número entero y una fracción juntos, como 2 1/2.
improper fractionfracción impropia
A fraction whose top number is greater than or equal to its bottom number, like 5/2.Una fracción cuyo numerador es mayor o igual que su denominador, como 5/2.
simplifysimplificar
To write a fraction with smaller numbers that names the same amount.Escribir una fracción con números más pequeños que nombra la misma cantidad.

Stage 1 of 5Etapa 1 de 5

Start StrongEmpieza fuerte

Each rung is harder than the last, and the numbers change every time.

Cada peldaño es más difícil que el anterior y los números cambian cada vez.

  1. 6 fresh problems with new numbers each time (interactive only).

Stage 2 of 5Etapa 2 de 5

Stretch Your ThinkingAmplía tu pensamiento

Plan, solve, then check that your answer makes sense.

Planea, resuelve y revisa que tu respuesta tenga sentido.

  1. Find the Division Error
  2. Is 3/4 ÷ 1/2 the same as 1/2 ÷ 3/4? Solve both and explain why or why not. What does this tell you about the order in division?
  3. The Home Field grounds crew has 3 1/2 gallons of white paint. Marking one practice field takes 3/4 gallon. How many fields can the crew mark completely?
    • 4 2/3 fields
    • 4 fields
    • 5 fields
    • 2 5/8 fields
  4. A relay course is 2 1/4 miles long. It is split into legs that are each 3/8 mile. How many legs are there?
  5. Home Field fills cups from three sports-drink coolers. Write each amount as an improper fraction, then find how many cups each cooler fills.
  6. A sprinter runs 2/3 of a mile in 1/6 of an hour. At that steady speed, how many miles does the sprinter run in 1 whole hour?
    • 1/9 mile
    • 1/4 mile
    • 5/6 mile
    • 4 miles

Stage 3 of 5Etapa 3 de 5

InvestigateInvestiga

Use the model to test an idea. Then check it.

Usa el modelo para probar una idea. Luego compruébala.

  1. Match each division to its quotient.
  2. Design your own food-truck problem. Use a mixed-number supply and a fraction serving size. Write the division, solve it with the reciprocal, and check your quotient by multiplying.
  3. 4 fresh problems with new numbers each time (interactive only).

Stage 4 of 5Etapa 4 de 5

Find and FixEncuentra y corrige

Somebody made a mistake. Find the step and fix it.

Alguien cometió un error. Encuentra el paso y corrígelo.

  1. Tomás divides 7/8 ÷ 3/4. Tap the step where his work first goes wrong.
  2. Aisha finds 1 1/2 ÷ 1/4. Tap the step where her work first goes wrong.
  3. Wen divides 3/5 ÷ 3/10. Tap the step where his work first goes wrong.
  4. Mia says 3/4 ÷ 1/8 is greater than 1, because 1/8 fits into 3/4 many times. Leo says it is less than 1, because dividing makes numbers smaller. Who is right?
    • Leo, because dividing always gives a smaller number
    • Both, because the answer is exactly 1
    • Mia, because 1/8 is much smaller than 3/4
    • Neither, because the divisor is the bigger fraction
  5. What is the best next move?
    • Stop here, because 40/20 is the quotient.
    • Divide 40/20 by 4/5 to check.
    • Flip 40/20 to 20/40.
    • Write 40/20 in simplest form.
  6. 1 fresh problem with new numbers each time (interactive only).

Stage 5 of 5Etapa 5 de 5

Prove Your UnderstandingDemuestra tu comprensión

Say how sure you are, solve, then create a problem of your own.

Di qué tan seguro estás, resuelve y luego crea un problema tuyo.

  1. A coach has a 3 1/2-yard rope. She cuts it into jump-rope pieces that are each 7/8 yard long. How many pieces does she get?
  2. Which division has a quotient greater than 1?
    • 3/4 ÷ 1/2
    • 2/5 ÷ 4/5
    • 1/3 ÷ 2/3
    • 1/4 ÷ 5/8
  3. A water tank on the sidelines holds 5/6 of a gallon. Each bottle takes 5/9 of a gallon. How many bottles can the tank fill? Give your answer as a fraction or mixed number.
  4. 9/10 ÷ 3/5 = 3/2. Which multiplication checks this answer?
    • 3/2 × 3/5 = 9/10
    • 9/10 × 3/5 = 27/50
    • 3/2 × 5/3 = 5/2
    • 3/2 × 9/10 = 27/20
  5. A practice session lasts 2 1/4 hours. It is split into drills that each take 1 1/2 hours. How many drills fit? Give your answer as a fraction or mixed number.
  6. Create your own Home Field problem that is solved by dividing one fraction or mixed number by another. Write the division, solve it, and explain the steps, including what you did with any mixed number.