Lesson 1 Decimals and Fractions Page 95 Answer Key: A Detailed Guide for Students
When you open a mathematics workbook to Lesson 1 on decimals and fractions, page 95 often contains the answer key that lets you check your work after completing the practice exercises. Understanding why each answer is correct is just as important as getting the right number, because it builds the foundation for more advanced topics such as ratios, percentages, and algebra. This article walks through the typical concepts covered in Lesson 1, explains the reasoning behind the answers you’ll find on page 95, and offers strategies to strengthen your grasp of decimals and fractions.
Some disagree here. Fair enough.
Introduction: Why Decimals and Fractions Matter
Decimals and fractions are two ways of expressing parts of a whole. In real terms, in everyday life you encounter them when measuring ingredients, calculating discounts, or interpreting test scores. Mastery of converting between these forms, comparing their sizes, and performing basic operations prepares you for higher‑level math and real‑world problem solving. The answer key on page 95 is designed to reinforce these skills by showing the correct results and, when used thoughtfully, the logical steps that lead to them.
Core Concepts Covered in Lesson 1
Before diving into the answer key, it helps to review the main ideas that Lesson 1 usually introduces:
| Concept | Description | Typical Example |
|---|---|---|
| Place value in decimals | Each digit to the right of the decimal point represents tenths, hundredths, thousandths, etc. | In 3.Consider this: 47, the 4 is in the tenths place and the 7 is in the hundredths place. In real terms, |
| Equivalent fractions | Fractions that name the same part of a whole, even if numerators and denominators differ. | ½ = 2⁄4 = 3⁄6. |
| Converting fractions to decimals | Divide the numerator by the denominator (often using long division). | 3⁄8 = 0.375. |
| Converting decimals to fractions | Write the decimal as a fraction with a power of ten as denominator, then simplify. Because of that, | 0. 65 = 65⁄100 = 13⁄20 after simplification. |
| Comparing decimals and fractions | Convert to a common form (either both decimals or both fractions) before comparing. On top of that, | Compare 0. 4 and 3⁄5 → 0.4 = 2⁄5, 3⁄5 > 2⁄5. |
| Adding and subtracting with like denominators | Keep the denominator, add or subtract numerators. | 2⁄7 + 3⁄7 = 5⁄7. In practice, |
| Adding and subtracting decimals | Align decimal points, then add/subtract as whole numbers. Think about it: | 12. 3 + 4.56 = 16.86. |
These topics are the building blocks for the exercises whose answers appear on page 95. Knowing them lets you verify each solution and understand any mistakes you might have made.
Step‑by‑Step Walkthrough of Typical Page 95 Problems
Below is a representative set of problems that often appear in Lesson 1, paired with the answer key explanations you would find on page 95. (Numbers may vary slightly depending on the textbook, but the methodology remains the same.)
Problem Set A: Converting Fractions to Decimals
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Convert 7⁄20 to a decimal.
Answer key: 0.35
Explanation: Divide 7 by 20. Since 20 goes into 70 three times (3 × 20 = 60), remainder 10. Bring down a zero → 100 ÷ 20 = 5. So the quotient is 0.35 Still holds up.. -
Convert 5⁄8 to a decimal.
Answer key: 0.625
Explanation: 5 ÷ 8 = 0 remainder 5 → bring down 0 → 50 ÷ 8 = 6 (6 × 8 = 48) remainder 2 → bring down 0 → 20 ÷ 8 = 2 (2 × 8 = 16) remainder 4 → bring down 0 → 40 ÷ 8 = 5. The decimal terminates at 0.625. -
Convert 9⁄25 to a decimal.
Answer key: 0.36
Explanation: Because 25 × 4 = 100, multiply numerator and denominator by 4: (9 × 4)⁄(25 × 4) = 36⁄100 = 0.36 No workaround needed..
Problem Set B: Converting Decimals to Fractions
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Write 0.45 as a fraction in simplest form.
Answer key: 9⁄20
Explanation: 0.45 = 45⁄100. Divide numerator and denominator by their greatest common divisor (GCD), which is 5: (45÷5)⁄(100÷5) = 9⁄20 Simple, but easy to overlook.. -
Write 0.125 as a fraction in simplest form.
Answer key: 1⁄8
Explanation: 0.125 = 125⁄1000. GCD of 125 and 1000 is 125 → (125÷125)⁄(1000÷125) = 1⁄8. -
Write 2.6 as a mixed number.
Answer key: 2 3⁄5
Explanation: Separate the whole number (2) and the decimal part (0.6). 0.6 = 6⁄10 = 3⁄5 after dividing by 2. Combine → 2 3⁄5 Easy to understand, harder to ignore. That's the whole idea..
Problem Set C: Comparing Values
- Which is larger: 0.42 or 5⁄12?
Answer key: 5⁄12 is larger.
Explanation: Convert 5⁄12 to a decimal: 5 ÷ 12 ≈ 0.4166… (repeating). Since 0.42 > 0.4166…, 0.42 is actually larger. Wait—check the answer key. If the key says 5⁄12 is larger, then the textbook likely expects you to convert 0.42 to a fraction: 0.42 = 42⁄100 = 21⁄50. Find a common denominator with 5⁄12: LCM of 50 and 12 is 300. 21⁄50 = 126⁄300; 5⁄12
