Answer :
To solve the problem, we need to determine how much concrete Jacob can make with the sand he has. Here's a step-by-step explanation:
1. Understand the Relationship: We know it takes [tex]\(\frac{4}{7}\)[/tex] tonnes of sand to produce 1 tonne of concrete. This means that for every tonne of concrete, we need [tex]\(\frac{4}{7}\)[/tex] tonnes of sand.
2. Total Sand Jacob Has: Jacob has [tex]\(4 \frac{4}{5}\)[/tex] tonnes of sand. First, we need to convert this mixed number into an improper fraction.
- Convert the whole number part (4) to a fraction: [tex]\(\frac{4}{1} = \frac{20}{5}\)[/tex].
- Add the fraction part [tex]\(\frac{4}{5}\)[/tex]: [tex]\(\frac{20}{5} + \frac{4}{5} = \frac{24}{5}\)[/tex].
- So, Jacob has [tex]\(\frac{24}{5}\)[/tex] tonnes of sand.
3. Calculate the Amount of Concrete: To find out how much concrete he can make, we divide the total amount of sand by the amount of sand needed per tonne of concrete.
[tex]\[
\text{Concrete produced} = \frac{\text{Total sand Jacob has}}{\text{Sand needed per tonne of concrete}} = \frac{24}{5} \div \frac{4}{7}
\][/tex]
4. Perform the Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\[
\frac{24}{5} \div \frac{4}{7} = \frac{24}{5} \times \frac{7}{4}
\][/tex]
5. Multiply the Fractions:
[tex]\[
\frac{24 \times 7}{5 \times 4} = \frac{168}{20}
\][/tex]
6. Simplify the Fraction: To simplify [tex]\(\frac{168}{20}\)[/tex], find the greatest common divisor (GCD) of 168 and 20, which is 4.
- Divide the numerator and the denominator by 4:
[tex]\[
\frac{168 \div 4}{20 \div 4} = \frac{42}{5}
\][/tex]
7. Final Answer: The amount of concrete Jacob can make is [tex]\(\frac{42}{5}\)[/tex] tonnes.
Therefore, Jacob can produce [tex]\(\frac{42}{5}\)[/tex] tonnes of concrete with the sand he has.
1. Understand the Relationship: We know it takes [tex]\(\frac{4}{7}\)[/tex] tonnes of sand to produce 1 tonne of concrete. This means that for every tonne of concrete, we need [tex]\(\frac{4}{7}\)[/tex] tonnes of sand.
2. Total Sand Jacob Has: Jacob has [tex]\(4 \frac{4}{5}\)[/tex] tonnes of sand. First, we need to convert this mixed number into an improper fraction.
- Convert the whole number part (4) to a fraction: [tex]\(\frac{4}{1} = \frac{20}{5}\)[/tex].
- Add the fraction part [tex]\(\frac{4}{5}\)[/tex]: [tex]\(\frac{20}{5} + \frac{4}{5} = \frac{24}{5}\)[/tex].
- So, Jacob has [tex]\(\frac{24}{5}\)[/tex] tonnes of sand.
3. Calculate the Amount of Concrete: To find out how much concrete he can make, we divide the total amount of sand by the amount of sand needed per tonne of concrete.
[tex]\[
\text{Concrete produced} = \frac{\text{Total sand Jacob has}}{\text{Sand needed per tonne of concrete}} = \frac{24}{5} \div \frac{4}{7}
\][/tex]
4. Perform the Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\[
\frac{24}{5} \div \frac{4}{7} = \frac{24}{5} \times \frac{7}{4}
\][/tex]
5. Multiply the Fractions:
[tex]\[
\frac{24 \times 7}{5 \times 4} = \frac{168}{20}
\][/tex]
6. Simplify the Fraction: To simplify [tex]\(\frac{168}{20}\)[/tex], find the greatest common divisor (GCD) of 168 and 20, which is 4.
- Divide the numerator and the denominator by 4:
[tex]\[
\frac{168 \div 4}{20 \div 4} = \frac{42}{5}
\][/tex]
7. Final Answer: The amount of concrete Jacob can make is [tex]\(\frac{42}{5}\)[/tex] tonnes.
Therefore, Jacob can produce [tex]\(\frac{42}{5}\)[/tex] tonnes of concrete with the sand he has.
