Which of the following expressions results in a value less than 1 ?

Options

A. `1 1/2 + 2/3`
B. `1 1/2 -2/3 `
C. `1 1/2 xx 2/3 `
D. `1 1/2 div 2/3`

Answer

To determine which of the given expressions results in a value less than 1, we will evaluate each option step by step.

### Step 1: Evaluate the First Option
**Expression:** \( 1 \frac{1}{2} + \frac{2}{3} \)

1. Convert the mixed number \( 1 \frac{1}{2} \) to an improper fraction:
\[ 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2} \]

2. Now, add \( \frac{3}{2} + \frac{2}{3} \). To do this, we need a common denominator. The least common multiple (LCM) of 2 and 3 is 6.
\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]
\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

3. Now, add the two fractions:
\[ \frac{9}{6} + \frac{4}{6} = \frac{13}{6} \]

4. Convert \( \frac{13}{6} \) to a decimal:
\[ \frac{13}{6} \approx 2.167 \]
This value is greater than 1.

### Step 2: Evaluate the Second Option
**Expression:** \( 1 \frac{1}{2} - \frac{2}{3} \)

1. Again, convert \( 1 \frac{1}{2} \) to an improper fraction:
\[ 1 \frac{1}{2} = \frac{3}{2} \]

2. Now, subtract \( \frac{3}{2} - \frac{2}{3} \). The common denominator is still 6.
\[ \frac{3}{2} = \frac{9}{6} \]
\[ \frac{2}{3} = \frac{4}{6} \]

3. Now, subtract the two fractions:
\[ \frac{9}{6} - \frac{4}{6} = \frac{5}{6} \]

4. Convert \( \frac{5}{6} \) to a decimal:
\[ \frac{5}{6} \approx 0.833 \]
This value is less than 1.

### Step 3: Evaluate the Third Option
**Expression:** \( 1 \frac{1}{2} \times \frac{2}{3} \)

1. Convert \( 1 \frac{1}{2} \) to an improper fraction:
\[ 1 \frac{1}{2} = \frac{3}{2} \]

2. Now, multiply \( \frac{3}{2} \times \frac{2}{3} \):
\[ \frac{3 \times 2}{2 \times 3} = \frac{6}{6} = 1 \]
This value is equal to 1.

### Step 4: Evaluate the Fourth Option
**Expression:** \( 1 \frac{1}{2} \div \frac{2}{3} \)

1. Convert \( 1 \frac{1}{2} \) to an improper fraction:
\[ 1 \frac{1}{2} = \frac{3}{2} \]

2. Now, divide \( \frac{3}{2} \div \frac{2}{3} \):
\[ \frac{3}{2} \times \frac{3}{2} = \frac{9}{4} \]

3. Convert \( \frac{9}{4} \) to a decimal:
\[ \frac{9}{4} = 2.25 \]
This value is greater than 1.

### Conclusion
After evaluating all options, the only expression that results in a value less than 1 is the second option: \( 1 \frac{1}{2} - \frac{2}{3} \).