Study guide: Measure with Fraction Operations
Join, remove, select, and count fraction lengths using consistent units.
Ideas to explain in your own words
- Use equal-sized parts before adding fractions of the same whole.
- Subtract unlike fractions by finding a shared part size.
- Use a partitioned model to multiply two fractions.
- Divide a whole-number length by a unit fraction.
Watch your reasoning
- One half equals 3/6. Adding 1/6 gives 4/6, which equals 2/3. The denominator stays six while counting sixths; reducing both counts by two gives 2/3.
- 3/4 = 9/12 and 1/6 = 2/12. Subtracting leaves 7/12. It is less than 3/4, as a positive amount was removed.
- 3/5 × 2/3 = 6/15 = 2/5 meter. Selecting three fifths leaves less than the starting two thirds of a meter.
- Each meter holds two half-meter pieces. Three meters hold six: 3 ÷ 1/2 = 6. Checking 6 × 1/2 = 3 confirms the total.
A worked review example
Add Fractions with Different Denominators: For matching strips, 1/2 + 1/4 = 2/4 + 1/4 = 3/4. Three selected quarter-parts make three quarters of one whole. Rename Before Subtracting: 5/6 − 1/4 = 10/12 − 3/12 = 7/12 meter. Adding the removed 3/12 back gives 10/12 = 5/6. Find a Fraction of a Fraction: 2/3 of 3/4 meter is 2/3 × 3/4 = 6/12 = 1/2 meter. The model selects 2/4 meter by choosing two of the three quarter-meter sections. Count Unit-Fraction Pieces in a Whole Length: 2 ÷ 1/4 = 8 pieces. The check is 8 × 1/4 = 8/4 = 2 meters, so all the original length is accounted for.
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.