Study guide: Use Fractions for Sharing and Scaling
Interpret whole-number division, resize quantities, multiply mixed numbers, and divide unit fractions into equal shares.
Ideas to explain in your own words
- A fraction a/b can describe a whole-number division: a wholes shared equally among b recipients.
- Multiplication can shrink a positive quantity when its factor is between zero and one.
- A mixed number can be renamed as an improper fraction by counting all of its denominator-sized parts.
- Dividing a unit fraction by a whole number makes smaller equal parts of that fraction.
Useful vocabulary
- reciprocal
- A number whose product with the original nonzero number is one.
- scaling
- Multiplying a quantity by a factor to resize its value.
Watch your reasoning
- A share can exceed one whole when there are more wholes than recipients.
- Multiplication by a positive fraction below one makes a positive quantity smaller.
- Do not multiply whole parts and fraction parts separately while ignoring their cross-products.
- The share is smaller than the starting unit fraction, not three times larger.
A worked review example
Share five identical whole strips among four people. Each whole is divided into fourths, and each person receives five fourths: 5/4=1 1/4 strips. Four people with five fourths each total five strips, so every original whole is accounted for. The numerator counts supplied wholes and denominator counts equal recipients. A share can exceed one whole when there are more wholes than recipients. Divide each whole bar into the same number of recipient shares.
Make a practice plan
- Interpret a Fraction as Sharing Whole Units: Share seven wholes among four people. Expected: 7/4=1 3/4 per person.
- Predict Whether a Positive Quantity Grows or Shrinks: Predict 18×11/12 and 18×13/12. Expected: smaller and larger than 18.
- Multiply Mixed-Number Measures Exactly: Find area for 2 1/4 by 1 2/3. Expected: 15/4=3 3/4 square units.
- Divide a Unit Fraction into Equal Shares: Share 1/5 of a whole among four people: 1/20 each. Then make a line plot for supplied measurements 1/8,1/8,1/4,1/2 L. Expected marks: two at 1/8, one at 1/4, one at 1/2. Total volume is 1 L; redistributed equally across all four observations, each share is 1/4 L.