6. [tex]2 \frac{1}{3}+1 \frac{3}{6}=[/tex]
7. [tex]1 \frac{3}{4} \div 2 \frac{1}{2} \div 2 \frac{1}{3}=[/tex]
8. [tex]2 \frac{1}{7} \div 1 \frac{3}{4}=[/tex]
Answer (2)
Convert mixed numbers to improper fractions.
Perform addition, subtraction, multiplication, or division as indicated.
Simplify the resulting fractions.
The results are: 7 6 5 , 1 2 1 , and 49 60 .
Final Answers: 7 6 5 , 1 2 1 , 49 60
Explanation
Introduction We are given three arithmetic expressions to evaluate. Let's solve them one by one.
Evaluating the first expression First expression: 6.2 3 1 + 1 6 3 .
We can rewrite this as 6 + 3 1 + 1 + 6 3 .
Combining the whole numbers, we get 7 + 3 1 + 2 1 .
To add the fractions, we need a common denominator, which is 6. So, we have 7 + 6 2 + 6 3 .
Adding the fractions, we get 7 + 6 5 .
Therefore, the first expression evaluates to 7 6 5 .
Evaluating the second expression Second expression: 8.1 4 3 ÷ 2 2 1 ÷ 2 3 1 .
First, convert the mixed numbers to improper fractions: 8 4 3 = 4 35 , 2 2 1 = 2 5 , and 2 3 1 = 3 7 .
So the expression becomes 4 35 ÷ 2 5 ÷ 3 7 .
To divide fractions, we multiply by the reciprocal. So, we have 4 35 × 5 2 × 7 3 .
Multiplying the numerators and denominators, we get 4 × 5 × 7 35 × 2 × 3 = 140 210 .
Simplifying the fraction, we get 2 3 , which is equal to 1 2 1 .
Evaluating the third expression Third expression: 9.2 7 1 ÷ 1 4 3 .
First, convert the mixed numbers to improper fractions: 2 7 1 = 7 15 and 1 4 3 = 4 7 .
So the expression becomes 7 15 ÷ 4 7 .
To divide fractions, we multiply by the reciprocal. So, we have 7 15 × 7 4 .
Multiplying the numerators and denominators, we get 7 × 7 15 × 4 = 49 60 .
Final Answer Therefore, the results are: 6.2 3 1 + 1 6 3 = 7 6 5 8.1 4 3 ÷ 2 2 1 ÷ 2 3 1 = 1 2 1 9.2 7 1 ÷ 1 4 3 = 49 60
Examples
Understanding mixed number arithmetic is crucial in everyday situations, such as cooking and construction. For instance, when doubling a recipe that calls for 2 4 1 cups of flour, you need to accurately calculate 2 × 2 4 1 = 4 2 1 cups. Similarly, in construction, if you need to cut a wooden plank into 3 equal pieces and the plank is 5 2 1 feet long, you must divide 5 2 1 by 3 to determine the length of each piece, which is 1 6 5 feet. These calculations ensure precision and efficiency in practical tasks.
The three expressions evaluate to: 1) 2 \frac{5}{6} for 2 \frac{1}{3} + 1 \frac{3}{6}, 2) 1 \frac{1}{2} for 1 \frac{3}{4} \div 2 \frac{1}{2} \div 2 \frac{1}{3}, and 3) \frac{60}{49} for 2 \frac{1}{7} \div 1 \frac{3}{4}.
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