Week 4 Slides: Fractions & Decimals

Week 4

Operations with Fractions & Decimals

Student Notes & Practice

Part 1

Operations with Fractions

Topic: Adding & Subtracting Fractions

Goal: A simple way to find a common denominator is to multiply the two denominators together.

Adding Fractions: "I Do"

I Do (Teacher Example)

Problem: You eat \(\frac{1}{2}\) of a pizza and a friend eats \(\frac{1}{3}\). How much did you eat together?

We need to solve: \( \frac{1}{2} + \frac{1}{3} \)

  • Step 1: Multiply the denominators. This is your new common denominator.
    \( 2 \times 3 = \) 6
  • Step 2: Rewrite the fractions with the new denominator. Multiply the numerator of each fraction by the denominator of the *other* fraction.
    For \(\frac{1}{2}\): \(1 \times 3 = \) 3. So, \(\frac{1}{2} = \) \( \frac{3}{6} \)
    For \(\frac{1}{3}\): \(1 \times 2 = \) 2. So, \(\frac{1}{3} = \) \( \frac{2}{6} \)
  • Step 3: Add the numerators. Keep the common denominator.
    \( \frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \) \( \frac{5}{6} \)
  • Step 4: Simplify if needed. \( \frac{5}{6} \) is already in simplest form.

Answer: Together you ate \( \frac{5}{6} \) of the pizza.

Practice: Adding/Subtracting Fractions

We Do (Let's Try Together)

Problem: \( \frac{3}{4} - \frac{1}{8} \)

  • Multiply the denominators: \( 4 \times 8 \) =
  • Rewrite the fractions: \( \frac{3}{4} = \frac{\_\_\_}{32} \) and \( \frac{1}{8} = \frac{\_\_\_}{32} \)
  • Now, subtract: - =
  • Can you simplify the answer? (Hint: Divide top and bottom by 4)

You Do (Your Turn!)

Problem: \( \frac{2}{5} + \frac{1}{10} \)

Show your steps below:

Topic: Multiplying Fractions

Goal: This is easier! Just multiply straight across.

I Do (Teacher Example)

Problem: Find \( \frac{1}{2} \) of \( \frac{3}{4} \). ("Of" means multiply.)

  • Step 1: Multiply the numerators (tops). \( 1 \times 3 = \) 3
  • Step 2: Multiply the denominators (bottoms). \( 2 \times 4 = \) 8
  • Step 3: Write the new fraction. Answer = \( \frac{3}{8} \)

Practice: Multiplying Fractions

We Do (Let's Try Together)

Problem: \( \frac{2}{3} \times \frac{4}{5} \)

  • Multiply the numerators: \( \times \) =
  • Multiply the denominators: \( \times \) =
  • Final Answer:

You Do (Your Turn!)

Problem: \( \frac{1}{4} \times \frac{2}{5} \)

Show your steps below:

Fractions: Independent Practice

Choose the level you feel comfortable starting with. Try to challenge yourself!

Green Level

Add/Subtract

\( \frac{1}{8} + \frac{5}{8} \)

Multiply

\( \frac{3}{5} \times \frac{1}{2} \)

Yellow Level

Add/Subtract

\( \frac{5}{6} - \frac{1}{3} \)

Multiply

\( \frac{3}{4} \times \frac{2}{5} \)

Red Level

Add/Subtract

You walk \( \frac{2}{3} \) of a mile. Your friend walks \( \frac{1}{4} \) of a mile. How much farther do you walk?

Multiply

A recipe needs \( \frac{3}{4} \) cup of sugar. You make 3 batches. How much sugar do you need?

Fractions: Exit Ticket

Show what you learned about fractions!

1. Solve: \( \frac{2}{3} + \frac{1}{6} \)

2. You have \(\frac{3}{4}\) of a pizza and you eat \(\frac{1}{2}\) of it. What fraction of the whole pizza did you eat?

Part 2

Operations with Decimals

Topic: Operations with Decimals (Review)

Remember the key rules!

Adding & Subtracting Decimals

The most important rule: Line up the decimal points!

Multiplying Decimals

1. Multiply the numbers ignoring the decimals.
2. Count the total number of decimal places in both numbers you multiplied.
3. Place the decimal in your answer so it has that many places.

Example: \(1.2 \times 0.3\)

  • Multiply: \(12 \times 3 = \) 36
  • Count places: 1.2 (1 place) + 0.3 (1 place) = 2 total places.
  • Place decimal: The answer needs 2 decimal places. So, 0.36.

Decimals: "I Do"

I Do (Teacher Example)

Problem 1 (Add): 5.2 + 12.75

5.20

+12.75

17.95

Problem 2 (Multiply): A bag of chips costs $3.45. How much would 3 bags cost? (\(3.45 \times 3\))

  • Multiply \(345 \times 3 = \) 1035.
  • 3.45 has 2 decimal places. 3 has 0. Total = 2.
  • Answer: $10.35

Practice: Decimals

We Do (Let's Try Together)

Problem: 20.5 - 8.1

Line up the decimals and subtract.

You Do (Your Turn!)

A pen costs $1.25. You buy 4 pens. What is the total cost?

Show your steps below:

Decimals: Independent Practice

Choose the level you feel comfortable starting with.

Green Level

1. 10.5 + 4.2

2. \(5 \times 1.5\)

Yellow Level

1. A shirt is $15.75 and socks are $4.50. What is the total cost?

2. A movie ticket costs $9.50. How much would 4 tickets cost?

Red Level

1. You buy lunch for $8.67 and pay with a $20 bill. What is your change?

2. Gas costs $3.50 per gallon. Your car holds 10.5 gallons. How much to fill the tank?

Decimals: Exit Ticket

Show what you learned about decimals!

1. You have $15.50 and spend $8.25 on a movie ticket. How much money do you have left?

2. A garden is 5.5 ft long and 2 ft wide. What is its area? (Area = length \( \times \) width)