Divide Mixed Numbers
Name Period
Objectives / Objetivos
Content Objective: I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.
Language Objective: I can explain my steps and why they work, using the words mixed number, improper fraction, convert, reciprocal, and simplify.
Key Idea / Idea clave
Dividing Mixed Numbers. 1. Convert each mixed number to an improper fraction: 3 1/2 = 7/2. 2. Name the question and divide: 7/2 ÷ 1/4 asks how many 1/4s fit in 7/2. With common denominators, 7/2 = 14/4, and 14 fourths ÷ 1 fourth = 14, or multiply by the reciprocal: 7/2 × 4/1 = 28/2 = 14. 3. Simplify, then check by multiplying: 14 × 1/4 = 14/4 = 3 1/2
I Notice / Observo
- What is the total distance of the route?
- How long is each segment?
I Wonder / Me pregunto
- Why do we need to convert mixed numbers before dividing?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Divide Mixed Numbers Dividir números mixtos | Change mixed numbers to improper fractions, then multiply by the reciprocal. Cambiar los números mixtos a fracciones impropias y luego multiplicar por el recíproco. |
| Mixed Number Número mixto | A whole number plus a fraction, like 2 1/3. Un número entero más una fracción, como 2 1/3. |
| Improper Fraction Fracción impropia | A fraction where the top is bigger than or equal to the bottom, like 7/4. Una fracción donde el número de arriba es mayor o igual al de abajo, como 7/4. |
| Convert Convertir | To change a number to a new form but keep the same value. Cambiar un número a otra forma sin cambiar su valor. |
| 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. |
| Reciprocal Recíproco | A fraction turned upside down. Dividing by a fraction gives the same answer as multiplying by its reciprocal. Una fracción volteada al revés. Dividir entre una fracción da lo mismo que multiplicar por su recíproco. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is 1 1/2 ÷ 3/4?
- A 1 1/8
- B 2
- C 3/4
- D 9/8
Answer:
2. Convert each mixed number to an improper fraction, then divide.
Complete each empty cell. Show your reasoning below.
| Problem | Convert to Improper | The reciprocal shortcut | Quotient |
|---|---|---|---|
| 3 1/2 ÷ 1/4 | |||
| 1 3/4 ÷ 1/2 | |||
| 2 1/3 ÷ 7/6 | |||
| 4 1/5 ÷ 3/5 |
3. Match each mixed number division to its quotient.
Write the letter of the matching item in the blank.
| 1. | 2 1/4 ÷ 3/4 | A. | 2 | |
| 2. | 4 1/2 ÷ 9/8 | B. | 4 | |
| 3. | 1 2/3 ÷ 5/6 | C. | 5 | |
| 4. | 3 1/3 ÷ 2/3 | D. | 6 | |
| 5. | 5 1/4 ÷ 3/4 | E. | 7 | |
| 6. | 1 1/2 ÷ 1/4 | F. | 3 |
4. Find the Mixed Number Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: