## Eureka Math Lesson 12 Homework 4.1 Answer Key Introduction:

Eureka Math is a popular math curriculum, which emphasizes understanding the logic behind mathematical operations before memorizing algorithms and formulas. Lesson 12 Homework 4.1 is a part of the curriculum designed for Grade 6 students and focuses on operations with fractions and decimals. In this blog post, we will break down the concepts covered in Lesson 12 Homework 4.1 and provide answers to all the homework questions along with explanations.

### Blog Body:

The first question in Lesson 12 Homework 4.1 asks students to convert the given fractions into decimals. To do this, we divide the numerator by the denominator. For example, to convert 5/8 into a decimal, we divide 5 by 8, which gives 0.625. Similarly, to convert 3/5 into a decimal, we divide 3 by 5, which gives 0.6. The answer key for this question is as follows:

a) 0.625

b) 0.6

c) 0.375

d) 0.5

The second question tests students’ understanding of fractions and decimals by asking them to order the given numbers from least to greatest. To do this, we need to convert all the numbers into fractions or decimals and compare them. For example, 0.25 is the same as 25/100 and 45/100 is greater than 3/5. The correct order is: 0.13 < 25/100 < 3/5 < 45/100. Here’s the answer key for this question:

a) 0.13

b) 25/100

c) 3/5

d) 45/100

The third question in Lesson 12 Homework 4.1 is about adding and subtracting fractions with unlike denominators. To do this, we need to find the least common multiple (LCM) of the denominators and convert the fractions into equivalent ones with the same denominator. Then, we can add or subtract the numerators and simplify the result. For example, to add 2/3 and 1/4, we find the LCM of 3 and 4, which is 12. Then, we convert 2/3 into an equivalent fraction with denominator 12 by multiplying the numerator and denominator by 4, which gives 8/12. We also convert 1/4 into an equivalent fraction with denominator 12 by multiplying the numerator and denominator by 3, which gives 3/12. Now, we can add 8/12 and 3/12, which gives 11/12. Here’s the answer key for this question:

a) 11/12

b) 4/5

c) 19/21

d) 7/18

The fourth question in Lesson 12 Homework 4.1 requires students to convert the given decimals into fractions in simplest form. To do this, we need to identify the place value of the last digit and write it as the numerator of the fraction with denominator 10, 100, 1000, or any power of 10 that corresponds to the number of decimal places. For example, to convert 0.75 into a fraction, the last digit is in the tenths place, so we write 75/100. Then, we simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 25 in this case. Here’s the answer key for this question:

a) 1/2

b) 3/8

c) 13/25

d) 11/20

The fifth and final question in Lesson 12 Homework 4.1 is about multiplication and division with decimals. To solve this, we need to line up the decimals and multiply or divide as we would with whole numbers. The result should have the same number of decimal places as the sum or difference of the decimal places in the factors or dividend and divisor. For example, to multiply 0.6 by 0.7, we line up the decimals and multiply 6 by 7, which gives 42. Then, we count the number of decimal places in the factors, which is 1+1 = 2, and write the answer as 0.42. Here’s the answer key for this question:

a) 0.21

b) 0.23

c) 0.0042

d) 9.6

### Conclusion:

Eureka Math Lesson 12 Homework 4.1 is a challenging yet engaging set of questions that tests students’ proficiency in operations with fractions and decimals. By breaking down the concepts and providing an answer key with explanations, we hope to help students understand the logic behind the math operations and build their confidence in solving similar problems. Remember, math is not just about memorizing formulas and algorithms, but also about thinking critically, reasoning logically, and persevering through challenges.