Division Expressions with Fractions and Whole Numbers
Name Period
Objectives / Objetivos
Content Objective: I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.
Language Objective: I can explain why dividing by a unit fraction gives the same answer as multiplying by its reciprocal, using the words reciprocal, divisor, and quotient.
Key Idea / Idea clave
Dividing Whole Numbers & Fractions. 1. Name the question: 3 ÷ 1/4 asks how many 1/4s fit in 3, and 1/2 ÷ 4 asks how much is in each of 4 equal shares. 2. Use the model: each whole holds 4 fourths, so 3 wholes hold 3 × 4 = 12 fourths, and 3 ÷ 1/4 = 12. 3. Check by multiplying: 12 × 1/4 = 3. Shortcut: dividing by 1/4 gives the same answer as multiplying by its reciprocal, 4
I Notice / Observo
- What total length is being divided?
- What is the size of each section?
I Wonder / Me pregunto
- What does it mean to divide by a fraction?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Division of Fractions División de fracciones | Finding how many groups of one fraction fit inside another amount. Hallar cuántos grupos de una fracción caben dentro de otra cantidad. |
| Reciprocal Recíproco | A fraction turned upside down. Una fracción volteada de arriba abajo. |
| Quotient Cociente | The answer when you divide. La respuesta cuando divides. |
| Dividend Dividendo | The total number being divided into equal groups (the number inside the division bracket). El número total que se divide en partes iguales (el número dentro de la casilla de división). |
| Divisor Divisor | The number of equal groups you are dividing into (the number outside the division bracket). El número de partes iguales en las que divides (el número fuera de la casilla de división). |
| Unit fraction Fracción unitaria | A fraction with 1 on top, like 1/4. Una fracción con 1 arriba, como 1/4. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What does 3 ÷ 1/4 mean?
- A How many 1/4-size pieces fit into 3
- B 1/4 of 3
- C 3 groups of 1/4
- D 3 minus 1/4
Answer:
2. Match each division expression to its quotient.
Write the letter of the matching item in the blank.
| 1. | 5 ÷ 1/2 | A. | 12 | |
| 2. | 6 ÷ 1/3 | B. | 14 | |
| 3. | 2 ÷ 1/6 | C. | 15 | |
| 4. | 4 ÷ 1/4 | D. | 18 | |
| 5. | 3 ÷ 1/5 | E. | 10 | |
| 6. | 7 ÷ 1/2 | F. | 16 |
3. Use the bar model to count how many 1/6-size pieces fit into 3 wholes. All 3 wholes are shown, each split into sixths.
How many 1/6-size pieces fit into 3 wholes?
4. Find the Interpretation Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: