Divide Whole Numbers by Fractions Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.NOS.1) · Lesson 6-9
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I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.Puedo explicar qué significa dividir un número entero entre una fracción (cuántas partes caben o cuánto hay en un entero), hallar el cociente con un modelo o multiplicando por el recíproco, y comprobarlo multiplicando.

MissionMisión · Rooftop GardenJardín en la azotea · night shiftturno de noche

Grow your skills.Haz crecer tus habilidades.

A storm is on the way, so the garden crew plans the evening watering with leftovers, comparisons, and checks. Every can and every bag has to be counted exactly before the rain arrives.

Se acerca una tormenta, así que el equipo del jardín planea el riego de la tarde con sobrantes, comparaciones y comprobaciones. Cada regadera y cada bolsa deben contarse con exactitud antes de que llegue la lluvia.

Word bankBanco de palabras 5 words5 palabrasreciprocal, quotient, Keep, Change, Flip, …recíproco, cociente, Mantener, cambiar, invertir, …
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.
Keep, Change, FlipMantener, cambiar, invertir
A shortcut for dividing fractions: keep the first number, change ÷ to ×, flip the second.Un atajo para dividir fracciones: deja el primer número, cambia ÷ por × e invierte el segundo.
fractionfracción
A number that shows part of a whole, like 3/4.Un número que muestra una parte de un todo, como 3/4.
whole numbernúmero entero
A counting number with no fraction or decimal, like 0, 1, 2, 3.Un número de contar sin fracción ni decimal, como 0, 1, 2, 3.

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. A pizza shop has 8 whole pizzas. Each serving is 2/3 of a pizza. How many servings can they make? Write and solve an equation, then explain why the answer is greater than 8.
  3. The rain barrel holds 10 gallons. The garden club keeps 2 gallons in reserve and pours the rest into watering cans that each hold 2/5 gallon. How many full cans can they fill?
  4. A gardener used 9 liters of compost to fill the shaded part of the trench bar, which is 3/5 of the trench. How many liters would fill the whole trench?
    • 5 2/5 liters
    • 45 liters
    • 3 liters
    • 15 liters
  5. The club has 5 meters of hose. Each tomato row needs 5/6 meter of hose. Each herb row needs 1/6 meter of hose. How many more herb rows than tomato rows can the 5 meters supply?
  6. Sofia has 5 cups of chopped cilantro. Each jar of salsa uses 2/3 cup. She fills as many whole jars as she can. How many cups of cilantro are left over?

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. Sort each garden question: do you divide to see how many pieces fit, or multiply to find a part of an amount?
  2. Write your own ribbon order with a whole-number length and a fraction piece size. Show the Keep, Change, Flip step, report the quotient with a unit, and check it 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. Tavi divided 12 by 3/8 to find how many 3/8-liter scoops fill 12 liters of soil. Tap the step where his work goes wrong.
  2. Mina worked out how many 5/6-pound seed packs she can make from 4 pounds of seed. Tap the step where her work goes wrong.
  3. How many 2/3-cup scoops are in 6 cups of seed? Ola solved it. Tap the step where her thinking goes wrong.
  4. Kira says 6 ÷ 1/2 must be 3, because dividing always makes a number smaller. Mateo says it is 12, because there are 2 halves in each whole. Who is right?
    • Kira: dividing always makes a number smaller.
    • Mateo: 2 halves fit in each whole; 6 × 2 = 12.
    • Both are right: the answer can be 3 or 12.
    • Neither: the answer is 6, because 6 ÷ 1 is 6.
  5. What is the best next move?
    • Stop here, because 12 is a whole number.
    • Check by multiplying 12 × 6/5.
    • Check: 12 × 5/6 = 10.
    • Check by dividing 12 by 5/6.
  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. What is 14 ÷ 7/9?
  2. Without finishing the calculations, which quotient is the greatest?
    • 15 ÷ 5/6
    • 15 ÷ 3/5
    • 15 ÷ 1/4
    • 15 ÷ 3/4
  3. Matías found that 18 ÷ 3/4 = 24. Which multiplication checks his answer?
    • 24 × 3/4 = 18
    • 18 × 3/4 = 13 1/2
    • 24 × 4/3 = 32
    • 18 × 24 = 432
  4. Which expression finds how many 1/6-pound bags of seed can be filled from 4 pounds of seed?
    • 1/6 ÷ 4
    • 4 × 1/6
    • 4 + 1/6
    • 4 ÷ 1/6
  5. Dara has 5 gallons of water. How many FULL 3/8-gallon jugs can she fill?
  6. Create your own Rooftop Garden problem that divides a whole number by a fraction. Solve it with the reciprocal, check it by multiplying, and explain why your answer is greater than the whole number.