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Sagot :
Let's solve the given mathematical problems step-by-step.
### Part 1: Evaluate the Sum and Difference of the Given Decimals
We need to evaluate the expression:
[tex]\[ 26.45 + 4.79 + 120.02 - 3.20 \][/tex]
#### Step-by-Step Solution:
1. Addition of Decimals:
- First, we add [tex]\(26.45\)[/tex] and [tex]\(4.79\)[/tex]:
[tex]\[ 26.45 + 4.79 = 31.24 \][/tex]
- Next, we add [tex]\(31.24\)[/tex] to [tex]\(120.02\)[/tex]:
[tex]\[ 31.24 + 120.02 = 151.26 \][/tex]
2. Subtraction of Decimals:
- Finally, we subtract [tex]\(3.20\)[/tex] from [tex]\(151.26\)[/tex]:
[tex]\[ 151.26 - 3.20 = 148.06 \][/tex]
Therefore,
[tex]\[ 26.45 + 4.79 + 120.02 - 3.20 = 148.06 \][/tex]
### Part 2: Add and Write the Fraction or Mixed Number for Given Fractions
We need to add the fractions:
[tex]\[ \frac{2}{5} + \frac{1}{4} + \frac{7}{10} \][/tex]
#### Step-by-Step Solution:
1. Finding a Common Denominator:
- The denominators of the given fractions are [tex]\(5\)[/tex], [tex]\(4\)[/tex], and [tex]\(10\)[/tex]. The least common multiple (LCM) of these numbers is [tex]\(20\)[/tex].
2. Converting Fractions to Equivalent Fractions with the Common Denominator:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \][/tex]
- Convert [tex]\(\frac{1}{4}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \][/tex]
- Convert [tex]\(\frac{7}{10}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20} \][/tex]
3. Adding the Equivalent Fractions:
- Now, add the fractions with a common denominator:
[tex]\[ \frac{8}{20} + \frac{5}{20} + \frac{14}{20} = \frac{8 + 5 + 14}{20} = \frac{27}{20} \][/tex]
4. Converting the Sum to a Mixed Number:
- [tex]\(\frac{27}{20}\)[/tex] is an improper fraction, which means it can be converted to a mixed number:
[tex]\[ \frac{27}{20} = 1 + \frac{7}{20} = 1\frac{7}{20} \][/tex]
Therefore,
[tex]\[ \frac{2}{5} + \frac{1}{4} + \frac{7}{10} = 1\frac{7}{20} \][/tex]
### Final Answers:
1. [tex]\( 26.45 + 4.79 + 120.02 - 3.20 = 148.06 \)[/tex]
2. [tex]\( \frac{2}{5} + \frac{1}{4} + \frac{7}{10} = 1\frac{7}{20} \)[/tex]
### Part 1: Evaluate the Sum and Difference of the Given Decimals
We need to evaluate the expression:
[tex]\[ 26.45 + 4.79 + 120.02 - 3.20 \][/tex]
#### Step-by-Step Solution:
1. Addition of Decimals:
- First, we add [tex]\(26.45\)[/tex] and [tex]\(4.79\)[/tex]:
[tex]\[ 26.45 + 4.79 = 31.24 \][/tex]
- Next, we add [tex]\(31.24\)[/tex] to [tex]\(120.02\)[/tex]:
[tex]\[ 31.24 + 120.02 = 151.26 \][/tex]
2. Subtraction of Decimals:
- Finally, we subtract [tex]\(3.20\)[/tex] from [tex]\(151.26\)[/tex]:
[tex]\[ 151.26 - 3.20 = 148.06 \][/tex]
Therefore,
[tex]\[ 26.45 + 4.79 + 120.02 - 3.20 = 148.06 \][/tex]
### Part 2: Add and Write the Fraction or Mixed Number for Given Fractions
We need to add the fractions:
[tex]\[ \frac{2}{5} + \frac{1}{4} + \frac{7}{10} \][/tex]
#### Step-by-Step Solution:
1. Finding a Common Denominator:
- The denominators of the given fractions are [tex]\(5\)[/tex], [tex]\(4\)[/tex], and [tex]\(10\)[/tex]. The least common multiple (LCM) of these numbers is [tex]\(20\)[/tex].
2. Converting Fractions to Equivalent Fractions with the Common Denominator:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \][/tex]
- Convert [tex]\(\frac{1}{4}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \][/tex]
- Convert [tex]\(\frac{7}{10}\)[/tex] to a fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[ \frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20} \][/tex]
3. Adding the Equivalent Fractions:
- Now, add the fractions with a common denominator:
[tex]\[ \frac{8}{20} + \frac{5}{20} + \frac{14}{20} = \frac{8 + 5 + 14}{20} = \frac{27}{20} \][/tex]
4. Converting the Sum to a Mixed Number:
- [tex]\(\frac{27}{20}\)[/tex] is an improper fraction, which means it can be converted to a mixed number:
[tex]\[ \frac{27}{20} = 1 + \frac{7}{20} = 1\frac{7}{20} \][/tex]
Therefore,
[tex]\[ \frac{2}{5} + \frac{1}{4} + \frac{7}{10} = 1\frac{7}{20} \][/tex]
### Final Answers:
1. [tex]\( 26.45 + 4.79 + 120.02 - 3.20 = 148.06 \)[/tex]
2. [tex]\( \frac{2}{5} + \frac{1}{4} + \frac{7}{10} = 1\frac{7}{20} \)[/tex]
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