Number and Operations-Fractions
What you must understand
Grade 4 focuses on equivalent fractions and comparing fractions with different numerators and denominators. You must generate equivalent fractions, recognize that multiplying numerator and denominator by the same number does not change the value, and compare fractions using benchmarks such as one-half or a common denominator. You also add and subtract fractions and mixed numbers with like denominators, multiply a fraction by a whole number, and understand decimal notation for fractions with denominators 10 and 100 (0.3 = 3/10, 0.25 = 25/100).
Traps to watch
- Adding denominators. 1/4 + 2/4 = 3/4, not 3/8. Only the numerators combine when denominators match.
- Comparing without reasoning. 3/5 is greater than 3/8 because fifths are larger pieces than eighths when the numerator is the same.
- Whole-number confusion. 5/5 equals 1, and 7/4 equals 1 3/4. Convert improper fractions before comparing with mixed numbers.
- Decimal place value. 0.4 is four tenths, and 0.40 equals 0.4; adding a zero after the last decimal digit does not change the value.
Rule of thumb
When fractions have unlike denominators, either rename them with a common denominator or compare each to one-half. When multiplying a fraction by a whole number, think of repeated addition: 3 x 2/5 means 2/5 + 2/5 + 2/5 = 6/5.
Worked example
Compare 3/4 and 5/8. Rename 3/4 as 6/8 by multiplying numerator and denominator by 2. Since 6/8 is greater than 5/8, 3/4 is the larger fraction.