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Sagot :
Let's break down each of the problems step-by-step to understand how to obtain the correct results.
### Subtraction of Mixed Numbers
#### d. [tex]\( 2 \frac{3}{8} - \frac{3}{8} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 2 + \frac{3}{8} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{3}{8} - \frac{3}{8} = 0 \)[/tex].
3. Combine with the whole number: [tex]\( 2 + 0 = 2 \)[/tex].
Result: [tex]\( 2 \)[/tex]
#### e. [tex]\( 1 \frac{2}{4} - \frac{1}{4} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 1 + \frac{2}{4} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{2}{4} - \frac{1}{4} = \frac{1}{4} \)[/tex].
3. Combine with the whole number: [tex]\( 1 + \frac{1}{4} = 1 \frac{1}{4} \)[/tex].
Result: [tex]\( 1 \frac{1}{4} \)[/tex]
#### f. [tex]\( 3 \frac{7}{8} - \frac{4}{8} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 3 + \frac{7}{8} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{7}{8} - \frac{4}{8} = \frac{3}{8} \)[/tex].
3. Combine with the whole number: [tex]\( 3 + \frac{3}{8} = 3 \frac{3}{8} \)[/tex].
Result: [tex]\( 3 \frac{3}{8} \)[/tex]
### Addition of Mixed Numbers and Fractions
#### a. [tex]\( 1 \frac{3}{4} + \frac{1}{4} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 1 + \frac{3}{4} \)[/tex].
2. Add the fractions: [tex]\( \frac{3}{4} + \frac{1}{4} = 1 \)[/tex] (since [tex]\( \frac{3}{4} + \frac{1}{4} = \frac{4}{4} \)[/tex]).
3. Combine with the whole number: [tex]\( 1 + 1 = 2 \)[/tex].
Result: [tex]\( 2 \)[/tex]
#### b. [tex]\( 3 \frac{2}{5} + \frac{1}{5} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 3 + \frac{2}{5} \)[/tex].
2. Add the fractions: [tex]\( \frac{2}{5} + \frac{1}{5} = \frac{3}{5} \)[/tex].
3. Combine with the whole number: [tex]\( 3 + \frac{3}{5} = 3 \frac{3}{5} \)[/tex].
Result: [tex]\( 3 \frac{3}{5} \)[/tex]
#### c. [tex]\( 5 \frac{4}{7} + \frac{1}{7} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 5 + \frac{4}{7} \)[/tex].
2. Add the fractions: [tex]\( \frac{4}{7} + \frac{1}{7} = \frac{5}{7} \)[/tex].
3. Combine with the whole number: [tex]\( 5 + \frac{5}{7} = 5 \frac{5}{7} \)[/tex].
Result: [tex]\( 5 \frac{5}{7} \)[/tex]
#### d. [tex]\( 2 \frac{3}{8} + 4 \frac{3}{8} \)[/tex]
1. Add the whole numbers: [tex]\( 2 + 4 = 6 \)[/tex].
2. Add the fractions: [tex]\( \frac{3}{8} + \frac{3}{8} = \frac{6}{8} = \frac{3}{4} \)[/tex].
3. Combine the results: [tex]\( 6 \frac{3}{4} \)[/tex].
Result: [tex]\( 6 \frac{3}{4} \)[/tex]
#### e. [tex]\( 2 \frac{2}{4} - 1 \frac{1}{4} \)[/tex]
1. Separate into whole numbers and fractions: [tex]\( (2 - 1) \)[/tex] and [tex]\( \frac{2}{4} - \frac{1}{4} \)[/tex].
2. Subtract the whole numbers: [tex]\( 2 - 1 = 1 \)[/tex].
3. Subtract the fractions: [tex]\( \frac{2}{4} - \frac{1}{4} = \frac{1}{4} \)[/tex].
4. Combine the results: [tex]\( 1 \frac{1}{4} \)[/tex].
Result: [tex]\( 1 \frac{1}{4} \)[/tex]
#### f. [tex]\( 4 \frac{1}{8} + 4 \frac{4}{8} \)[/tex]
1. Add the whole numbers: [tex]\( 4 + 4 = 8 \)[/tex].
2. Add the fractions: [tex]\( \frac{1}{8} + \frac{4}{8} = \frac{5}{8} \)[/tex].
3. Combine the results: [tex]\( 8 \frac{5}{8} \)[/tex].
Result: [tex]\( 8 \frac{5}{8} \)[/tex]
### Subtraction and Addition of Mixed Numbers
#### 9. [tex]\( 7 \frac{3}{8} - 2 \frac{3}{8} \)[/tex]
1. Subtract the whole numbers: [tex]\( 7 - 2 = 5 \)[/tex].
2. Subtract the fractions: [tex]\( \frac{3}{8} - \frac{3}{8} = 0 \)[/tex].
3. Combine the results: [tex]\( 5 + 0 = 5 \)[/tex].
Result: [tex]\( 5 \)[/tex]
#### h. [tex]\( 9 \frac{2}{4} + 1 \frac{1}{4} \)[/tex]
1. Add the whole numbers: [tex]\( 9 + 1 = 10 \)[/tex].
2. Add the fractions: [tex]\( \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \)[/tex].
3. Combine the results: [tex]\( 10 \frac{3}{4} \)[/tex].
Result: [tex]\( 10 \frac{3}{4} \)[/tex]
#### i. [tex]\( 3 \frac{1}{8} - 3 \frac{4}{8} \)[/tex]
1. Subtract the whole numbers: [tex]\( 3 - 3 = 0 \)[/tex].
2. Since [tex]\( \frac{1}{8} < \frac{4}{8} \)[/tex], we convert [tex]\( 3 \frac{1}{8} \)[/tex] to [tex]\( 2 \frac{9}{8} \)[/tex].
1. [tex]\( \frac{9}{8} - \frac{4}{8} = \frac{5}{8} \)[/tex].
3. Combine the results: [tex]\( 0 + \frac{5}{8} = \frac{5}{8} \)[/tex].
Result: [tex]\( \frac{5}{8} \)[/tex]
### Subtraction of Mixed Numbers
#### d. [tex]\( 2 \frac{3}{8} - \frac{3}{8} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 2 + \frac{3}{8} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{3}{8} - \frac{3}{8} = 0 \)[/tex].
3. Combine with the whole number: [tex]\( 2 + 0 = 2 \)[/tex].
Result: [tex]\( 2 \)[/tex]
#### e. [tex]\( 1 \frac{2}{4} - \frac{1}{4} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 1 + \frac{2}{4} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{2}{4} - \frac{1}{4} = \frac{1}{4} \)[/tex].
3. Combine with the whole number: [tex]\( 1 + \frac{1}{4} = 1 \frac{1}{4} \)[/tex].
Result: [tex]\( 1 \frac{1}{4} \)[/tex]
#### f. [tex]\( 3 \frac{7}{8} - \frac{4}{8} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 3 + \frac{7}{8} \)[/tex].
2. Subtract the fractions: [tex]\( \frac{7}{8} - \frac{4}{8} = \frac{3}{8} \)[/tex].
3. Combine with the whole number: [tex]\( 3 + \frac{3}{8} = 3 \frac{3}{8} \)[/tex].
Result: [tex]\( 3 \frac{3}{8} \)[/tex]
### Addition of Mixed Numbers and Fractions
#### a. [tex]\( 1 \frac{3}{4} + \frac{1}{4} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 1 + \frac{3}{4} \)[/tex].
2. Add the fractions: [tex]\( \frac{3}{4} + \frac{1}{4} = 1 \)[/tex] (since [tex]\( \frac{3}{4} + \frac{1}{4} = \frac{4}{4} \)[/tex]).
3. Combine with the whole number: [tex]\( 1 + 1 = 2 \)[/tex].
Result: [tex]\( 2 \)[/tex]
#### b. [tex]\( 3 \frac{2}{5} + \frac{1}{5} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 3 + \frac{2}{5} \)[/tex].
2. Add the fractions: [tex]\( \frac{2}{5} + \frac{1}{5} = \frac{3}{5} \)[/tex].
3. Combine with the whole number: [tex]\( 3 + \frac{3}{5} = 3 \frac{3}{5} \)[/tex].
Result: [tex]\( 3 \frac{3}{5} \)[/tex]
#### c. [tex]\( 5 \frac{4}{7} + \frac{1}{7} \)[/tex]
1. Separate the whole number and the fraction: [tex]\( 5 + \frac{4}{7} \)[/tex].
2. Add the fractions: [tex]\( \frac{4}{7} + \frac{1}{7} = \frac{5}{7} \)[/tex].
3. Combine with the whole number: [tex]\( 5 + \frac{5}{7} = 5 \frac{5}{7} \)[/tex].
Result: [tex]\( 5 \frac{5}{7} \)[/tex]
#### d. [tex]\( 2 \frac{3}{8} + 4 \frac{3}{8} \)[/tex]
1. Add the whole numbers: [tex]\( 2 + 4 = 6 \)[/tex].
2. Add the fractions: [tex]\( \frac{3}{8} + \frac{3}{8} = \frac{6}{8} = \frac{3}{4} \)[/tex].
3. Combine the results: [tex]\( 6 \frac{3}{4} \)[/tex].
Result: [tex]\( 6 \frac{3}{4} \)[/tex]
#### e. [tex]\( 2 \frac{2}{4} - 1 \frac{1}{4} \)[/tex]
1. Separate into whole numbers and fractions: [tex]\( (2 - 1) \)[/tex] and [tex]\( \frac{2}{4} - \frac{1}{4} \)[/tex].
2. Subtract the whole numbers: [tex]\( 2 - 1 = 1 \)[/tex].
3. Subtract the fractions: [tex]\( \frac{2}{4} - \frac{1}{4} = \frac{1}{4} \)[/tex].
4. Combine the results: [tex]\( 1 \frac{1}{4} \)[/tex].
Result: [tex]\( 1 \frac{1}{4} \)[/tex]
#### f. [tex]\( 4 \frac{1}{8} + 4 \frac{4}{8} \)[/tex]
1. Add the whole numbers: [tex]\( 4 + 4 = 8 \)[/tex].
2. Add the fractions: [tex]\( \frac{1}{8} + \frac{4}{8} = \frac{5}{8} \)[/tex].
3. Combine the results: [tex]\( 8 \frac{5}{8} \)[/tex].
Result: [tex]\( 8 \frac{5}{8} \)[/tex]
### Subtraction and Addition of Mixed Numbers
#### 9. [tex]\( 7 \frac{3}{8} - 2 \frac{3}{8} \)[/tex]
1. Subtract the whole numbers: [tex]\( 7 - 2 = 5 \)[/tex].
2. Subtract the fractions: [tex]\( \frac{3}{8} - \frac{3}{8} = 0 \)[/tex].
3. Combine the results: [tex]\( 5 + 0 = 5 \)[/tex].
Result: [tex]\( 5 \)[/tex]
#### h. [tex]\( 9 \frac{2}{4} + 1 \frac{1}{4} \)[/tex]
1. Add the whole numbers: [tex]\( 9 + 1 = 10 \)[/tex].
2. Add the fractions: [tex]\( \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \)[/tex].
3. Combine the results: [tex]\( 10 \frac{3}{4} \)[/tex].
Result: [tex]\( 10 \frac{3}{4} \)[/tex]
#### i. [tex]\( 3 \frac{1}{8} - 3 \frac{4}{8} \)[/tex]
1. Subtract the whole numbers: [tex]\( 3 - 3 = 0 \)[/tex].
2. Since [tex]\( \frac{1}{8} < \frac{4}{8} \)[/tex], we convert [tex]\( 3 \frac{1}{8} \)[/tex] to [tex]\( 2 \frac{9}{8} \)[/tex].
1. [tex]\( \frac{9}{8} - \frac{4}{8} = \frac{5}{8} \)[/tex].
3. Combine the results: [tex]\( 0 + \frac{5}{8} = \frac{5}{8} \)[/tex].
Result: [tex]\( \frac{5}{8} \)[/tex]
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