$$ \frac{1}{4}+3=+2, \frac{3}{8}+2=3 $$ $$ 12+\frac{1}{3}= $$ (4) $$ \frac{1}{2}+7= $$ (b) $$ \frac{2}{9}+5= $$ $$ 4+\frac{1}{6}= $$ (3) $$ 8+\frac{2}{3}= $$ (10) $$ \frac{3}{4}+7= $$ (12) $$ 4 \div \frac{5}{9}= $$ (14) $$ 2+\frac{7}{8}= $$ $$ \frac{3}{4} \div 8= $$ (16) $$ 7+\frac{3}{4}= $$

Question

UpStudy AI · Accepted Answer

We will work through each expression step by step.

---

**1. Evaluate**  
$$
12+\frac{1}{3}
$$

Write the whole number $$12$$ as a mixed number with denominator 3:
$$
12=\frac{36}{3}.
$$
Then add:
$$
12+\frac{1}{3}=\frac{36}{3}+\frac{1}{3}=\frac{37}{3}.
$$
In mixed number form this is 
$$
12\tfrac{1}{3}.
$$

---

**2. Evaluate**  
$$
\frac{1}{2}+7
$$

Write $$7$$ as a fraction with denominator 2:
$$
7=\frac{14}{2}.
$$
Then add:
$$
\frac{1}{2}+7=\frac{1}{2}+\frac{14}{2}=\frac{15}{2},
$$
which is the mixed number
$$
7\tfrac{1}{2}.
$$

---

**3. Evaluate**  
$$
\frac{2}{9}+5
$$

Write $$5$$ with denominator 9:
$$
5=\frac{45}{9}.
$$
Then add:
$$
\frac{2}{9}+5=\frac{2}{9}+\frac{45}{9}=\frac{47}{9}.
$$
In mixed number form this is 
$$
5\tfrac{2}{9}.
$$

---

**4. Evaluate**  
$$
4+\frac{1}{6}
$$

Write $$4$$ with denominator 6:
$$
4=\frac{24}{6}.
$$
Then add:
$$
4+\frac{1}{6}=\frac{24}{6}+\frac{1}{6}=\frac{25}{6}.
$$
This equals the mixed number 
$$
4\tfrac{1}{6}.
$$

---

**5. Evaluate**  
$$
8+\frac{2}{3}
$$

Write $$8$$ as a fraction with denominator 3:
$$
8=\frac{24}{3}.
$$
Then add:
$$
8+\frac{2}{3}=\frac{24}{3}+\frac{2}{3}=\frac{26}{3},
$$
which is the mixed number
$$
8\tfrac{2}{3}.
$$

---

**6. Evaluate**  
$$
\frac{3}{4}+7
$$

Write $$7$$ as a fraction with denominator 4:
$$
7=\frac{28}{4}.
$$
Then add:
$$
\frac{3}{4}+7=\frac{3}{4}+\frac{28}{4}=\frac{31}{4},
$$
or in mixed number form
$$
7\tfrac{3}{4}.
$$

---

**7. Evaluate**  
$$
4\div \frac{5}{9}
$$

Dividing by a fraction is the same as multiplying by its reciprocal:
$$
4\div \frac{5}{9}=4\times \frac{9}{5}=\frac{36}{5}.
$$
This improper fraction can be written as the mixed number 
$$
7\tfrac{1}{5}.
$$

---

**8. Evaluate**  
$$
2+\frac{7}{8}
$$

Write $$2$$ as a fraction with denominator 8:
$$
2=\frac{16}{8}.
$$
Then add:
$$
2+\frac{7}{8}=\frac{16}{8}+\frac{7}{8}=\frac{23}{8},
$$
which is 
$$
2\tfrac{7}{8}.
$$

---

**9. Evaluate**  
$$
\frac{3}{4}\div 8
$$

Dividing by a whole number is the same as multiplying by its reciprocal:
$$
\frac{3}{4}\div 8=\frac{3}{4}\times \frac{1}{8}=\frac{3}{32}.
$$

---

**10. Evaluate**  
$$
7+\frac{3}{4}
$$

Write $$7$$ as a fraction with denominator 4:
$$
7=\frac{28}{4}.
$$
Then add:
$$
7+\frac{3}{4}=\frac{28}{4}+\frac{3}{4}=\frac{31}{4},
$$
or as a mixed number 
$$
7\tfrac{3}{4}.
$$

---

These are the step‐by‐step results for all the expressions.
$$ 12+\frac{1}{3} = 12\tfrac{1}{3} $$ $$ \frac{1}{2}+7 = 7\tfrac{1}{2} $$ $$ \frac{2}{9}+5 = 5\tfrac{2}{9} $$ $$ 4+\frac{1}{6} = 4\tfrac{1}{6} $$ $$ 8+\frac{2}{3} = 8\tfrac{2}{3} $$ $$ \frac{3}{4}+7 = 7\tfrac{3}{4} $$ $$ 4 \div \frac{5}{9} = 7\tfrac{1}{5} $$ $$ 2+\frac{7}{8} = 2\tfrac{7}{8} $$ $$ \frac{3}{4} \div 8 = \frac{3}{32} $$ $$ 7+\frac{3}{4} = 7\tfrac{3}{4} $$

\[ \frac{1}{4}+3=+2, \frac{3}{8}+2=3 \] \[ 12+\frac{1}{3}= \] (4) \[ \frac{1}{2}+7= \] (b) \[ \frac{2}{9}+5= \] \[ 4+\frac{1}{6}= \] (3) \[ 8+\frac{2}{3}= \] (10) \[ \frac{3}{4}+7= \] (12) \[ 4 \div \frac{5}{9}= \] (14) \[ 2+\frac{7}{8}= \] \[ \frac{3}{4} \div 8= \] (16) \[ 7+\frac{3}{4}= \]

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