Write + or - in each $$ \bigcirc $$ to make each equation true. (a) $$ \frac{13}{18} \bigcirc \frac{1}{9} \bigcirc \frac{1}{2} \bigcirc \frac{2}{3}=1 $$ (b) $$ \frac{3}{4} \bigcirc \frac{13}{24} \bigcirc \frac{5}{8} \bigcirc \frac{1}{6}=1 $$

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UpStudy AI · Accepted Answer

To solve each equation, we'll determine where to place the addition (+) and subtraction (−) signs to achieve the desired result of 1.

### Problem (a)

**Equation:**  
$$
\frac{13}{18} \bigcirc \frac{1}{9} \bigcirc \frac{1}{2} \bigcirc \frac{2}{3} = 1
$$

**Solution:**  
We need to find the correct combination of $$ + $$ and $$ - $$ for each $$ \bigcirc $$:

$$
\frac{13}{18} + \frac{1}{9} - \frac{1}{2} + \frac{2}{3} = 1
$$

**Verification:**

1. Convert all fractions to a common denominator (18):
   $$
   \frac{13}{18} + \frac{2}{18} - \frac{9}{18} + \frac{12}{18}
   $$
2. Sum them up:
   $$
   \frac{13 + 2 - 9 + 12}{18} = \frac{18}{18} = 1
   $$

**Thus, the correct sequence is:**  
$$
+ \, - \, +
$$

### Problem (b)

**Equation:**  
$$
\frac{3}{4} \bigcirc \frac{13}{24} \bigcirc \frac{5}{8} \bigcirc \frac{1}{6} = 1
$$

**Solution:**  
We aim to find the correct combination of $$ + $$ and $$ - $$:

$$
\frac{3}{4} - \frac{13}{24} + \frac{5}{8} + \frac{1}{6} = 1
$$

**Verification:**

1. Convert all fractions to a common denominator (24):
   $$
   \frac{18}{24} - \frac{13}{24} + \frac{15}{24} + \frac{4}{24}
   $$
2. Sum them up:
   $$
   \frac{18 - 13 + 15 + 4}{24} = \frac{24}{24} = 1
   $$

**Thus, the correct sequence is:**  
$$
- \, + \, +
$$

### Final Answer

(a) $$ + \, - \, + $$

(b) $$ - \, + \, + $$
(a) $$ + \, - \, + $$ (b) $$ - \, + \, + $$

Write + or - in each to make each equation true.
(a)
(b)

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