Lesson 32 Homework 4.5 -

The primary objective of Lesson 32 (Module 5) in Grade 4 Eureka Math is to subtract a fraction from a mixed number. Key Methods for Subtraction

Students are expected to master three specific strategies to solve these problems:

Number Lines: Visualizing the subtraction by jumping backward from the mixed number.

The "Arrow Way": A mental math strategy where students subtract in steps to reach the nearest whole number first.

Decomposition: Breaking apart a whole number (e.g., changing ) to make it easier to subtract the fraction. Homework Problems & Solutions

Below are typical examples from the 4.5 (Grade 4, Module 5) homework set: 1. Simple Subtraction Problem: Process: Decompose . Combine the 15one-fifth 65six-fifths Solution: 2. Number Line Modeling Problem: Step 1: Plot on the number line. Step 2: Jump back 24two-fourths to reach the whole number Step 3: Jump back the remaining 14one-fourth Solution: 4344 and three-fourths 3. Decomposition Method Problem: Decomposition:

1118→10+118=10+9811 and one-eighth right arrow 10 plus 1 and one-eighth equals 10 plus nine-eighths Subtraction: Solution: 106810 and six-eighths Helpful Resources

You can find visual walkthroughs and answer keys on these platforms: lesson 32 homework 4.5

Watch step-by-step videos on YouTube (Math with Aubrey) for this specific lesson. Download the full answer key PDF from Thrillshare Assets. If you'd like, I can help you: Walk through a specific problem from your worksheet Explain the "Arrow Way" in more detail Check your final answers for accuracy Eureka Math Homework Time Grade 4 Module 5 Lesson 32

Subtracting Mixed Numbers Without Renaming

When subtracting, if the fraction in the first number is larger than the fraction in the second number, you can subtract directly. For instance, (4 \frac34 - 1 \frac14).

Step 1: Subtract the fractions. (\frac34 - \frac14 = \frac24 = \frac12). Step 2: Subtract the whole numbers. (4 - 1 = 3). Step 3: Combine. The answer is (3 \frac12).

Lesson 32 Homework 4.5

Section A: Fractions and Decimals Conversion

  1. Convert the following fractions into decimals:

    • 3/4
    • 1/2
    • 3/8

  2. Convert the following decimals into fractions:

    • 0.75
    • 0.5
    • 0.375

Section B: Percent, Fractions, and Decimals Relationship The primary objective of Lesson 32 (Module 5)

  1. Express the following fractions as percents:

    • 1/5
    • 3/10
    • 2/5

  2. Express the following percents as decimals and then as fractions (simplify if possible):

    • 25%
    • 10%
    • 50%

Section C: Solving Problems

  1. A bookshelf has 5 shelves, and 3/5 of them are currently filled with books. How many shelves are filled?

  2. A pizza was cut into 8 slices. If 2/4 of the pizza was eaten, how many slices were eaten?

Section D: Word Problems

  1. If a shirt is on sale for 25% off its original price of $40, how much will you pay for the shirt? Convert the following fractions into decimals:

  2. In a class of 40 students, 3/5 of them are girls. How many boys are in the class?

Challenge 3: Adding Denominators

Example: ( \frac13 + \frac13 = \frac26 ) (Wrong!)
Solution: Repeat the rule: "You add the numerators only. The denominator stays the same."

Example Problem (Direct from typical homework):

Solve: 2 3/4 + 1 2/4

Step 1: Add the fractions. 3/4 + 2/4 = 5/4

Step 2: Add the whole numbers. 2 + 1 = 3

Step 3: Combine and simplify. 3 + 5/4 = 3 + 1 1/4 = 4 1/4

Answer: 4 1/4

2. The Interpretation of Remainders

A staple of Lesson 32 Homework is word problems where the remainder dictates the answer.