Fractions and Decimals — Pre-Algebra Unit 2 practice.
This unit covers fraction operations, decimal conversions, mixed numbers and comparing fractions — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers fraction operations, decimal conversions, mixed numbers and comparing fractions — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Fraction Operations
Students must be able to add, subtract, multiply, and divide fractions, including those with unlike denominators. For addition and subtraction, finding a common denominator is required. For multiplication, multiply numerators and denominators straight across; for division, multiply by the reciprocal of the second fraction.
Key Points
- Add/subtract fractions: find the LCD, convert fractions, then combine numerators
- Multiply fractions: numerator × numerator, denominator × denominator, then simplify
- Divide fractions: keep the first fraction, flip the second, then multiply (Keep-Change-Flip)
- Always simplify your final answer to lowest terms
Solve: 3/4 ÷ 2/5
Keep 3/4, change ÷ to ×, and flip 2/5 to get 5/2, giving 3/4 × 5/2. Multiply across: (3×5)/(4×2) = 15/8. Since 15/8 is already in lowest terms, the final answer is 15/8 or 1 and 7/8.
2 Decimal Conversions
Students must convert between fractions and decimals in both directions. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a fraction, use the place value of the last digit as the denominator, then simplify.
Key Points
- Fraction to decimal: divide numerator ÷ denominator (e.g., 3/4 = 3 ÷ 4 = 0.75)
- Decimal to fraction: the number of decimal places determines the denominator (tenths, hundredths, thousandths)
- Repeating decimals (e.g., 0.333...) equal common fractions (1/3); memorize the most common ones
- Simplify the resulting fraction by dividing numerator and denominator by their GCF
Convert 0.36 to a fraction in simplest form.
The decimal 0.36 ends in the hundredths place, so write it as 36/100. Find the GCF of 36 and 100, which is 4. Divide both by 4: 36 ÷ 4 = 9 and 100 ÷ 4 = 25, giving a final answer of 9/25.
3 Mixed Numbers
Students must convert between mixed numbers and improper fractions, and perform operations with mixed numbers. The most reliable exam strategy is to convert mixed numbers to improper fractions before operating, then convert back at the end if needed.
Key Points
- Mixed to improper: multiply the whole number by the denominator, add the numerator, keep the same denominator
- Improper to mixed: divide numerator by denominator; quotient is the whole number, remainder is the new numerator
- When adding or subtracting mixed numbers, borrowing may be required if the fraction part of the top number is smaller
- Always convert back to a mixed number if the answer is an improper fraction, unless told otherwise
Calculate: 2 and 1/3 + 1 and 3/4
Convert both to improper fractions: 2 1/3 = 7/3 and 1 3/4 = 7/4. Find the LCD of 3 and 4, which is 12, then rewrite as 28/12 + 21/12 = 49/12. Divide 49 ÷ 12 = 4 remainder 1, so the final answer is 4 and 1/12.
4 Comparing Fractions
Students must determine which fraction is greater, less than, or equal to another, and order a set of fractions from least to greatest or greatest to least. The two main methods tested are finding a common denominator and cross-multiplication.
Key Points
- Common denominator method: convert all fractions to the same denominator, then compare numerators directly
- Cross-multiplication method: multiply the numerator of each fraction by the other's denominator and compare the products
- To order multiple fractions, convert them all to equivalent fractions with the LCD, then sort by numerator
- Benchmark fractions (0, 1/2, 1) are useful for quick estimation on multiple-choice questions
Which is greater: 5/8 or 7/12?
Using cross-multiplication, multiply 5 × 12 = 60 and 7 × 8 = 56. Compare the products: 60 > 56, and 60 corresponds to 5/8, so 5/8 is greater than 7/12.
Questions, answered.
What is Fractions and Decimals?
Fractions and Decimals is Unit 2 of Pre-Algebra, covering fraction operations, decimal conversions, mixed numbers and comparing fractions.
How to study for Pre-Algebra Unit 2?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.