Divide Whole Numbers by Fractions
Name Period
Objectives / Objetivos
Content Objective: 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.
Language Objective: I can explain why multiplying by the reciprocal works, using the words fraction, reciprocal, quotient, and Keep, Change, Flip.
Key Idea / Idea clave
Dividing Whole Numbers by Fractions. Formula: a ÷ (b/c) = a × (c/b). 1. Name the question: 4 ÷ 1/2 asks how many 1/2s fit in 4. 2. Count with a model: each whole holds 2 halves, so 4 wholes hold 4 × 2 = 8 halves. 3. Shortcut: multiply by the reciprocal of the divisor, 6 ÷ 3/4 = 6 × 4/3 = 8, then check by multiplying: 8 × 3/4 = 6
I Notice / Observo
- How much total powder does Agent Park have?
- How much goes into each bag?
I Wonder / Me pregunto
- Why does dividing by 1/2 give a number larger than 4?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Divide Whole Numbers by Fractions Dividir números enteros entre fracciones | Find how many fractional groups fit in a whole number by multiplying by the reciprocal. Hallar cuántos grupos fraccionarios caben en un número entero multiplicando por el recíproco. |
| Whole Number Número 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. |
| Fraction Fracción | A number that shows part of a whole, like 3/4. Un número que muestra una parte de un todo, como 3/4. |
| Reciprocal Recíproco | A fraction turned upside down. Una fracción volteada de arriba abajo. |
| Keep, Change, Flip Mantener, cambiar, invertir | A shortcut for dividing fractions: keep the first number, change ÷ to ×, flip the second. It works because dividing by a fraction gives the same answer as multiplying by its reciprocal. Un atajo para dividir fracciones: deja el primer número, cambia ÷ por × y voltea el segundo. Funciona porque dividir entre una fracción da lo mismo que multiplicar por su recíproco. |
| Quotient Cociente | The answer when you divide. La respuesta cuando divides. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is 6 ÷ 1/3?
- A 2
- B 3
- C 6/3
- D 18
Answer:
2. Complete the table: Whole Number ÷ Fraction. Use the reciprocal shortcut.
Complete each empty cell. Show your reasoning below.
| Expression | Rewrite as Multiplication | Quotient |
|---|---|---|
| 5 ÷ 1/4 | ||
| 8 ÷ 1/2 | ||
| 3 ÷ 1/6 | ||
| 7 ÷ 1/3 |
3. Match each division expression to its quotient.
Write the letter of the matching item in the blank.
| 1. | 4 ÷ 1/3 | A. | 30 | |
| 2. | 7 ÷ 1/2 | B. | 14 | |
| 3. | 5 ÷ 1/6 | C. | 16 | |
| 4. | 2 ÷ 1/8 | D. | 30 | |
| 5. | 9 ÷ 1/4 | E. | 12 | |
| 6. | 6 ÷ 1/5 | F. | 36 |
4. Find the Division Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: