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Answer :
To solve this problem, we need to determine how much concrete Jacob can make with the sand he has. Let's go through the process step-by-step:
1. Understand the Ratio: It takes [tex]\(\frac{4}{7}\)[/tex] tonnes of sand to create 1 tonne of concrete. This means that for every 1 tonne of concrete, you require [tex]\(\frac{4}{7}\)[/tex] tonnes of sand.
2. Amount of Sand Jacob Has: Jacob has [tex]\(4 \frac{4}{5}\)[/tex] tonnes of sand. First, convert this mixed number into an improper fraction.
- [tex]\(4 \frac{4}{5} = \frac{24}{5} + \frac{4}{5} = \frac{24 + 4}{5} = \frac{28}{5}\)[/tex].
3. Calculate the Concrete: To find out how much concrete Jacob can make, we divide the amount of sand he has by the amount of sand needed to make 1 tonne of concrete. This is calculated as:
[tex]\[
\text{Concrete made} = \frac{\frac{28}{5}}{\frac{4}{7}}
\][/tex]
4. Perform the Division: Dividing by a fraction is the same as multiplying by its reciprocal. So:
[tex]\[
\frac{\frac{28}{5}}{\frac{4}{7}} = \frac{28}{5} \times \frac{7}{4}
\][/tex]
5. Multiply the Fractions:
- [tex]\(\frac{28 \times 7}{5 \times 4} = \frac{196}{20}\)[/tex].
6. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 196 and 20, which is 4.
- So, [tex]\(\frac{196}{20} \div \frac{4}{4} = \frac{49}{5}\)[/tex].
Thus, Jacob can make [tex]\(\frac{49}{5}\)[/tex] tonnes of concrete with the sand he has, which is already in its simplest form.
1. Understand the Ratio: It takes [tex]\(\frac{4}{7}\)[/tex] tonnes of sand to create 1 tonne of concrete. This means that for every 1 tonne of concrete, you require [tex]\(\frac{4}{7}\)[/tex] tonnes of sand.
2. Amount of Sand Jacob Has: Jacob has [tex]\(4 \frac{4}{5}\)[/tex] tonnes of sand. First, convert this mixed number into an improper fraction.
- [tex]\(4 \frac{4}{5} = \frac{24}{5} + \frac{4}{5} = \frac{24 + 4}{5} = \frac{28}{5}\)[/tex].
3. Calculate the Concrete: To find out how much concrete Jacob can make, we divide the amount of sand he has by the amount of sand needed to make 1 tonne of concrete. This is calculated as:
[tex]\[
\text{Concrete made} = \frac{\frac{28}{5}}{\frac{4}{7}}
\][/tex]
4. Perform the Division: Dividing by a fraction is the same as multiplying by its reciprocal. So:
[tex]\[
\frac{\frac{28}{5}}{\frac{4}{7}} = \frac{28}{5} \times \frac{7}{4}
\][/tex]
5. Multiply the Fractions:
- [tex]\(\frac{28 \times 7}{5 \times 4} = \frac{196}{20}\)[/tex].
6. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 196 and 20, which is 4.
- So, [tex]\(\frac{196}{20} \div \frac{4}{4} = \frac{49}{5}\)[/tex].
Thus, Jacob can make [tex]\(\frac{49}{5}\)[/tex] tonnes of concrete with the sand he has, which is already in its simplest form.
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