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Which is greater: a) 2/7 of 3/4 or 3/5 of 5/8? b) 1/2 of 6/7 or 2/3 of 3/7?
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Step-by-step solution
18 stepsHere are the solutions to the problems.
4. Which is greater:
- a) of or of
Calculate the first product.
$$ \frac{2}{7} \text{ of } \frac{3}{4} = \frac{2}{7} \times \frac{3}{4} = \frac{2 \times 3}{7 \times 4} = \frac{6}{28} = \frac{3}{14} $$Calculate the second product.
$$ \frac{3}{5} \text{ of } \frac{5}{8} = \frac{3}{5} \times \frac{5}{8} = \frac{3 \times 5}{5 \times 8} = \frac{15}{40} = \frac{3}{8} $$Compare the two fractions and .
To compare, find a common denominator, which is 56. Since , then is greater.
Therefore, of is greater.- b) of or of
Calculate the first product.
$$ \frac{1}{2} \text{ of } \frac{6}{7} = \frac{1}{2} \times \frac{6}{7} = \frac{1 \times 6}{2 \times 7} = \frac{6}{14} = \frac{3}{7} $$Calculate the second product.
$$ \frac{2}{3} \text{ of } \frac{3}{7} = \frac{2}{3} \times \frac{3}{7} = \frac{2 \times 3}{3 \times 7} = \frac{6}{21} = \frac{2}{7} $$Compare the two fractions and .
Since the denominators are the same, compare the numerators. $3 > 2$. Therefore, $\frac{3}{7}$ is greater. $$ \boxed{\frac{1}{2} \text{ of } \frac{6}{7}} $$5. Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is m. Find the distance between the first and the last sapling.
Determine the number of gaps between the saplings.
For 4 saplings planted in a row, there are gaps.
Calculate the total distance.
The distance between the first and the last sapling is the number of gaps multiplied by the distance between adjacent saplings.
Perform the multiplication.
Convert the improper fraction to a mixed number.
The distance between the first and the last sapling is .
6. Lipika reads a book for hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Convert the daily reading time from a mixed number to an improper fraction.
Calculate the total hours required to read the book.
Total hours = (Hours read per day) (Number of days)
Perform the multiplication.
Simplify the fraction and convert to a mixed number.
Lipika required to read the book.
7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using litres of petrol.
Convert the amount of petrol from a mixed number to an improper fraction.
Calculate the total distance covered.
Distance covered = (Distance per litre) (Total litres of petrol)
Perform the multiplication.
Simplify the expression.
The car will cover .
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