Calculate the following sums and differences without converting to improper fractions. Give your answer as a mixed number. $$ \begin{array}{lll} ext { a } 5 \frac{7}{8}-4 \frac{3}{8} & ext { b } 5 \frac{3}{8}-4 \frac{7}{8} & ext { e } 4 \frac{7}{8}-5 \frac{3}{8} \ ext { d } 4 \frac{3}{8}-5 \frac{7}{8} & ext { e } 5 \frac{7}{8}+4 \frac{3}{8} & ext { f }-5 \frac{7}{8}+\left(-4 \frac{3}{8} ight)\end{array} $$

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Calculate the following sums and differences without converting to improper fractions. Give your answer as a mixed number. $$ \begin{array}{lll}	ext { a } 5 \frac{7}{8}-4 \frac{3}{8} & 	ext { b } 5 \frac{3}{8}-4 \frac{7}{8} & 	ext { e } 4 \frac{7}{8}-5 \frac{3}{8} \ 	ext { d } 4 \frac{3}{8}-5 \frac{7}{8} & 	ext { e } 5 \frac{7}{8}+4 \frac{3}{8} & 	ext { f }-5 \frac{7}{8}+\left(-4 \frac{3}{8}ight)\end{array} $$

UpStudy AI · Accepted Answer

Let's solve each of the sums and differences step by step without converting to improper fractions, and we will express the final answers as mixed numbers.

### a) $$ 5 \frac{7}{8} - 4 \frac{3}{8} $$

1. Subtract the whole numbers: $$ 5 - 4 = 1 $$
2. Subtract the fractions: $$ \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2} $$
3. Combine the results: $$ 1 + \frac{1}{2} = 1 \frac{1}{2} $$

**Answer: $$ 1 \frac{1}{2} $$**

### b) $$ 5 \frac{3}{8} - 4 \frac{7}{8} $$

1. Subtract the whole numbers: $$ 5 - 4 = 1 $$
2. Subtract the fractions: $$ \frac{3}{8} - \frac{7}{8} = -\frac{4}{8} = -\frac{1}{2} $$
3. Combine the results: $$ 1 - \frac{1}{2} = \frac{1}{2} $$

**Answer: $$ \frac{1}{2} $$**

### c) $$ 4 \frac{7}{8} - 5 \frac{3}{8} $$

1. Subtract the whole numbers: $$ 4 - 5 = -1 $$
2. Subtract the fractions: $$ \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2} $$
3. Combine the results: $$ -1 + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2} $$

**Answer: $$ -\frac{1}{2} $$**

### d) $$ 4 \frac{3}{8} - 5 \frac{7}{8} $$

1. Subtract the whole numbers: $$ 4 - 5 = -1 $$
2. Subtract the fractions: $$ \frac{3}{8} - \frac{7}{8} = -\frac{4}{8} = -\frac{1}{2} $$
3. Combine the results: $$ -1 - \frac{1}{2} = -\frac{2}{2} - \frac{1}{2} = -\frac{3}{2} = -1 \frac{1}{2} $$

**Answer: $$ -1 \frac{1}{2} $$**

### e) $$ 5 \frac{7}{8} + 4 \frac{3}{8} $$

1. Add the whole numbers: $$ 5 + 4 = 9 $$
2. Add the fractions: $$ \frac{7}{8} + \frac{3}{8} = \frac{10}{8} = 1 \frac{2}{8} = 1 \frac{1}{4} $$
3. Combine the results: $$ 9 + 1 \frac{1}{4} = 10 \frac{1}{4} $$

**Answer: $$ 10 \frac{1}{4} $$**

### f) $$ -5 \frac{7}{8} + (-4 \frac{3}{8}) $$

1. Convert to positive: $$ -5 \frac{7}{8} - 4 \frac{3}{8} $$
2. Add the whole numbers: $$ -5 - 4 = -9 $$
3. Add the fractions: $$ -\frac{7}{8} - \frac{3}{8} = -\frac{10}{8} = -1 \frac{2}{8} = -1 \frac{1}{4} $$
4. Combine the results: $$ -9 - 1 \frac{1}{4} = -10 \frac{1}{4} $$

**Answer: $$ -10 \frac{1}{4} $$**

### Summary of Answers:
- a) $$ 1 \frac{1}{2} $$
- b) $$ \frac{1}{2} $$
- c) $$ -\frac{1}{2} $$
- d) $$ -1 \frac{1}{2} $$
- e) $$ 10 \frac{1}{4} $$
- f) $$ -10 \frac{1}{4} $$
a) $$ 1 \frac{1}{2} $$ b) $$ \frac{1}{2} $$ c) $$ -\frac{1}{2} $$ d) $$ -1 \frac{1}{2} $$ e) $$ 10 \frac{1}{4} $$ f) $$ -10 \frac{1}{4} $$

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