Study guide: Extend Fractions to Mixed Numbers and Decimals
Operate on mixed numbers and connect tenths and hundredths with decimal notation.
Ideas to explain in your own words
- A mixed number joins wholes and a fraction.
- Decimal places represent fractions of a whole.
- A tenth contains ten hundredths.
- Decimals should be compared by place value, not by counting digits.
Useful vocabulary
- mixed number
- A whole-number part together with a fractional part.
- hundredth
- One of one hundred equal parts of a whole.
Watch your reasoning
- Reduce the whole-number count when exchanging one whole for parts.
- Seven hundredths and seven tenths are different values.
- Keep the common denominator; do not add the denominators.
- More written decimal digits do not automatically mean a larger number.
A worked review example
For 3 1/5−1 4/5, rename the first amount as 2 6/5. Subtracting gives one whole and two fifths: 1 2/5. Check 1 2/5+1 4/5=2 6/5=3 1/5. The exchanged whole contributes five fifths. One whole equals denominator-many parts. Reduce the whole-number count when exchanging one whole for parts. Draw whole bars subdivided into the stated denominator and mark the exchanged whole.
Make a practice plan
- Regroup a Whole into Fraction Parts: Find 4 2/6−2 5/6. Expected: 1 3/6=1 1/2.
- Connect Tenths and Hundredths to Decimal Digits: Write 4/100 and 4/10. Expected: 0.04 and 0.4.
- Join Tenths and Hundredths with a Common Unit: Find 6/10+14/100. Expected: 74/100=0.74.
- Compare Decimals Using Equal Place Values: Compare 0.4 and 0.40. Expected: equal; the trailing zero changes notation, not value.