Study guide: Equivalent Parts for Fraction Reasoning
Use equivalent fractions to compare amounts and count joined or repeated parts.
Ideas to explain in your own words
- Create a fraction with smaller equal parts that represents the same amount.
- Compare unlike denominators using a common part size.
- Add and subtract fractions that already share a denominator.
- Multiply a fraction by a whole number using repeated parts.
Watch your reasoning
- Multiply both counts by four: 2 × 4 = 8 and 3 × 4 = 12. Eight twelfths covers the same amount as two thirds.
- 2/3 = 8/12 and 3/4 = 9/12. Eight twelfths is less than nine twelfths, so 2/3 < 3/4.
- Seven tenths minus three tenths leaves four tenths: 7/10 − 3/10 = 4/10. The part size stays one tenth.
- 4 × 3/8 = 12/8 = 3/2 = 1 1/2 meters. Twelve eighth-meter parts total one and a half meters.
A worked review example
Build Equivalent Fractions: 3/5 = 6/10 because 3 × 2 = 6 and 5 × 2 = 10. The new pieces are half as big, so twice as many represent the same shaded amount. Rename Fractions to Compare Them: 3/4 = 6/8, and 6/8 > 5/8, so 3/4 > 5/8. The difference is one eighth of the matching whole. Join and Remove Like Fraction Parts: 3/8 + 2/8 = 5/8. Removing 2/8 gives 5/8 − 2/8 = 3/8. Both actions count eighth-sized parts. Count Several Equal Fraction Lengths: 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5 meters. Six fifths exceed the five fifths needed for one meter.
Make a practice plan
- Try the supplied lesson problems without looking at the answers.
- Compare your method with the worked examples and explain any correction.
- Use the new review cases, then complete the transfer task on paper or in your own document.