[tex]\frac{7}{9} \div \frac{35}{45}[/tex]
Answer (2)
Rewrite the division as multiplication by the reciprocal: 9 7 ÷ 45 35 = 9 7 × 35 45 .
Simplify the fractions: 35 7 = 5 1 and 9 45 = 5 .
Multiply the simplified fractions: 5 1 × 5 = 1 .
The final result is 1 .
Explanation
Understanding the Problem We are asked to evaluate the expression 9 7 ÷ 45 35 . This involves dividing one fraction by another.
Rewriting the Division To divide fractions, we multiply by the reciprocal of the second fraction. So, we rewrite the expression as 9 7 × 35 45 .
Simplifying Fractions Now, we can simplify the fractions before multiplying. We notice that 7 is a factor of 35 and 9 is a factor of 45. We can rewrite the expression as 9 7 × 35 45 = 35 7 × 9 45 .
Simplifying Further We simplify each fraction: 35 7 = 5 1 and 9 45 = 5 .
Multiplying Simplified Fractions Now we multiply the simplified fractions: 5 1 × 5 = 1 .
Final Result Therefore, the final result is 1.
Examples
Understanding fraction division is crucial in many real-life scenarios. For instance, if you're baking and a recipe calls for 9 7 of a cup of flour, but you only have a scoop that measures 45 35 of a cup, you need to know how many scoops to use. In this case, dividing 9 7 by 45 35 tells you that you need exactly one scoop. This concept extends to various fields, including cooking, construction, and finance, where proportional calculations are essential.
To divide 9 7 by 45 35 , we multiply by the reciprocal of the second fraction, resulting in 9 7 × 35 45 . After simplifying, we find the answer is 1.Thus, 9 7 ÷ 45 35 = 1 .
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