Decimal-Fraction Equivalence

Grade 4 · fractions · 70 practice problems · read aloud

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Decimal-Fraction Equivalence 🧮

This is all about understanding that decimals and fractions are two different ways to show the same value! It's super useful because it helps you switch between them, making it easier to compare numbers, measure things, and solve real-world problems.

How to Convert Tenths and Hundredths

  1. Decimal to Fraction: Look at the place value of the last digit. If it's in the tenths place, write it over 10. If it's in the hundredths place, write it over 100.
  2. Simplify: See if you can make the fraction smaller by dividing the top and bottom by the same number.
  3. Fraction to Decimal: If the denominator is 10 or 100, the numerator tells you the digits. For 10, it's the tenths place. For 100, it's the hundredths place.

Visual Examples

Example 1: 0.7 as a fraction

The 7 is in the tenths place → 7/10. This fraction is already simple!

✅ 0.7 = 7/10

Example 2: 0.25 as a fraction

The 5 is in the hundredths place → 25/100. We can simplify: 25 ÷ 25 = 1 and 100 ÷ 25 = 4.

✅ 0.25 = 25/100 = 1/4

Example 3: 3/10 as a decimal

The denominator is 10, so the numerator 3 goes in the tenths place.

✅ 3/10 = 0.3

Common Mistakes to Avoid ⚠️

Miscounting Zeroes: For 0.05, it's 5/100 (hundredths), not 5/10. Always check the place value!

Forgetting to Simplify: Always check if your fraction can be made smaller, like turning 50/100 into 1/2.

Place Value Mix-Up: Remember: the first digit after the decimal is tenths, the second is hundredths.

Tips & Tricks

  • 💡 Think of money! $0.25 is a quarter, which is 25/100 of a dollar, or 1/4.
  • 📏 Use a ruler! The lines between inches are often in tenths or halves.
  • 🎯 For tenths, just one digit after the decimal. For hundredths, there are two digits.

How to Practice

  • Use flashcards to match decimals like 0.8 with fractions like 4/5.
  • Draw number lines and place both decimals and fractions on them.
  • Play online math games that focus on fraction-decimal conversion.
  • Practice with real items: If you eat 0.5 of a sandwich, you've eaten 1/2 of it!

Practice problems

6 of the 70, worked through step by step — try them before opening the answer.

1 0.8 = ?/5

Hint: Think about how many fifths make up eight tenths

Show the answer

Answer: 4

  1. We know 0.8 means eight tenths, which is 8/10
  2. We need to find how many fifths equal eight tenths
  3. To compare fractions with different denominators, we can find a common denominator
  4. The common denominator of 5 and 10 is 10
  5. Convert ?/5 to tenths: (?/5) = (2×?)/10
  6. Set up the equation: (2×?)/10 = 8/10
  7. Since the denominators are equal, the numerators must be equal: 2×? = 8
  8. Divide both sides by 2: ? = 8 ÷ 2
  9. ? = 4

The answer is 4.

2 0.4 = ?/5

Hint: Think about how many fifths would equal four tenths

Show the answer

Answer: 2

  1. We know 0.4 means 4/10
  2. Simplify 4/10 by dividing numerator and denominator by 2: 4 ÷ 2 = 2, 10 ÷ 2 = 5
  3. 4/10 = 2/5
  4. Therefore, 0.4 = 2/5

The answer is 2.

3 0.75 = ?/4

Hint: Think about how many quarters make up seventy-five cents.

Show the answer

Answer: 3

  1. Understand the equation. The problem says 0.75 equals some number divided by 4. So we can write: 0.75 = x / 4, where x is the unknown number.
  2. Eliminate the fraction. To solve for x, multiply both sides of the equation by 4: 0.75 * 4 = (x / 4) * 4
  3. Simplify. On the right side, (x / 4) * 4 = x. On the left side, 0.75 * 4 = 3. So we have: 3 = x
  4. Conclusion. Therefore, the unknown number is 3. Final check: 3/4 = 0.75, which matches the given 0.75. Answer: 3

We are given: 0.75 = ?/4

4 0.6 = ?/10

Hint: Think about how many tenths make up the decimal number

Show the answer

Answer: 6

  1. The decimal 0.6 means 6 tenths
  2. In fraction form, tenths are written with denominator 10
  3. So 0.6 = 6/10
  4. The numerator is 6

The answer is 6.

5 0.25 = ?/4

Hint: Think about how many quarters make a whole

Show the answer

Answer: 1

  1. We know 0.25 represents one quarter
  2. Since 1/4 means one quarter, and 0.25 also means one quarter
  3. Therefore, 0.25 = 1/4
  4. This means the numerator is 1
  5. The answer is 1

6 0.4 = ?/10

Hint: Think about how many tenths make up four tenths

Show the answer

Answer: 4

  1. The decimal 0.4 means 4 tenths
  2. To write this as a fraction with denominator 10, we need to find the numerator
  3. 0.4 = 4/10
  4. Therefore, the missing numerator is 4

The answer is 4.

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