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MA19.5.9
Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

### COS Examples

*Example: Recognize an incorrect result* $\frac{2}{5} + \frac{1}{2} = \frac{3}{7}$ *by observing that* $\frac{3}{7} < \frac{1}{2}$.

Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

### COS Examples

*Example: Recognize an incorrect result* $\frac{2}{5} + \frac{1}{2} = \frac{3}{7}$ *by observing that* $\frac{3}{7} < \frac{1}{2}$.

### Unpacked Content

### Knowledge

- The meaning and magnitude of fractions expressed in units of halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, and hundredths.
- Strategies to find sums of two or more fractions with like denominators.
- Strategies to find the difference of two fractions with like denominators.
- How to decompose a fraction greater than 1 and express as a mixed number.

Example: 7/3 = 3/3 + 3/3 + 1/3 = 2 1/3.

### Skills

- Solve real-word problems involving addition and subtraction of fractions with unlike denominators.
- Represent problems using fraction models or equations.
- Assess reasonableness of answers using estimation and benchmark fractions.

### Understanding

- solving word problems involving addition and subtraction of fractions with unlike units
- Require strategies to find equivalent fractions in a common unit, and the sum or difference will be expressed in the common unit.
- Can be assessed for reasonableness of answers using estimation strategies.

### Vocabulary

- Fraction
- Benchmark fraction
- Denominator
- Fraction model
- Estimate
- Reasonableness
- Equation
- Unlike denominator
- Unlike units