Division Expressions with Fractions and Mixed Numbers
Name Period
Objectives / Objetivos
Content Objective: 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.
Language Objective: I can explain why multiplying by the reciprocal works, using the words reciprocal, improper fraction, mixed number, and simplify.
Key Idea / Idea clave
Dividing Fractions by Fractions. Formula: a/b ÷ c/d = a/b × d/c. 1. Name the question: 3/4 ÷ 1/8 asks how many 1/8s fit in 3/4. 2. Use common denominators: 3/4 = 6/8, and 6 eighths ÷ 1 eighth = 6. 3. Shortcut: multiply by the reciprocal of the divisor, 3/4 × 8/1 = 24/4 = 6, then check by multiplying: 6 × 1/8 = 6/8 = 3/4
I Notice / Observo
- What is the total weight being divided?
- What is the size of each portion?
I Wonder / Me pregunto
- How is dividing fractions different from multiplying them?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Divide Fractions Dividir fracciones | Multiply the first fraction by the reciprocal of the second fraction. Multiplicar la primera fracción por el recíproco de la segunda fracción. |
| 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). |
| Reciprocal Recíproco | A fraction turned upside down. Una fracción volteada de arriba abajo. |
| Quotient Cociente | The answer when you divide. La respuesta cuando divides. |
| Simplify Simplificar | To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. Escribir una fracción con números más pequeños que nombra la misma cantidad, como 2/4 = 1/2. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the reciprocal of 3/5?
- A 1/3
- B 3/5
- C 5/3
- D 5/5
Answer:
2. Divide each pair of fractions using the reciprocal shortcut.
Complete each empty cell. Show your reasoning below.
| Problem | Multiply by the reciprocal | Quotient |
|---|---|---|
| 1/2 ÷ 1/6 | ||
| 3/4 ÷ 1/4 | ||
| 2/3 ÷ 1/3 | ||
| 5/8 ÷ 1/4 |
3. Match each fraction division to its quotient.
Write the letter of the matching item in the blank.
| 1. | 4/5 ÷ 2/5 | A. | 3 1/2 | |
| 2. | 3/4 ÷ 3/8 | B. | 2 1/2 | |
| 3. | 5/6 ÷ 1/3 | C. | 2 | |
| 4. | 2/3 ÷ 1/6 | D. | 4 | |
| 5. | 7/8 ÷ 1/4 | E. | 2/3 | |
| 6. | 1/2 ÷ 3/4 | F. | 2 |
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: