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Answer :
To find out how much concrete Harriet can make, we need to use the information given:
1. Amount of Sand Harriet Has: Harriet has [tex]\(4 \frac{1}{5}\)[/tex] tonnes of sand.
2. Sand Required for Concrete: It takes [tex]\(\frac{3}{8}\)[/tex] tonnes of sand to make a tonne of concrete.
Let's break down the solution step-by-step:
### Step 1: Convert Mixed Number to an Improper Fraction
First, convert the mixed number for how much sand Harriet has into an improper fraction:
- [tex]\(4 \frac{1}{5}\)[/tex] can be written as:
[tex]\[ 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \text{ tonnes of sand} \][/tex]
### Step 2: Calculate the Amount of Concrete
We know that [tex]\(\frac{3}{8}\)[/tex] tonnes of sand are required to make 1 tonne of concrete. To find out how much concrete can be made with [tex]\(\frac{21}{5}\)[/tex] tonnes of sand, we divide the total sand by the sand needed per tonne of concrete:
[tex]\[
\frac{21}{5} \div \frac{3}{8} = \frac{21}{5} \times \frac{8}{3}
\][/tex]
To multiply two fractions, multiply the numerators and multiply the denominators:
[tex]\[
= \frac{21 \times 8}{5 \times 3} = \frac{168}{15}
\][/tex]
### Step 3: Simplify the Fraction
Simplify [tex]\(\frac{168}{15}\)[/tex] to its simplest form by finding the greatest common divisor of 168 and 15, which is 3:
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{168 \div 3}{15 \div 3} = \frac{56}{5}
\][/tex]
Therefore, Harriet can make [tex]\(\frac{56}{5}\)[/tex] tonnes of concrete. This is the final answer.
1. Amount of Sand Harriet Has: Harriet has [tex]\(4 \frac{1}{5}\)[/tex] tonnes of sand.
2. Sand Required for Concrete: It takes [tex]\(\frac{3}{8}\)[/tex] tonnes of sand to make a tonne of concrete.
Let's break down the solution step-by-step:
### Step 1: Convert Mixed Number to an Improper Fraction
First, convert the mixed number for how much sand Harriet has into an improper fraction:
- [tex]\(4 \frac{1}{5}\)[/tex] can be written as:
[tex]\[ 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \text{ tonnes of sand} \][/tex]
### Step 2: Calculate the Amount of Concrete
We know that [tex]\(\frac{3}{8}\)[/tex] tonnes of sand are required to make 1 tonne of concrete. To find out how much concrete can be made with [tex]\(\frac{21}{5}\)[/tex] tonnes of sand, we divide the total sand by the sand needed per tonne of concrete:
[tex]\[
\frac{21}{5} \div \frac{3}{8} = \frac{21}{5} \times \frac{8}{3}
\][/tex]
To multiply two fractions, multiply the numerators and multiply the denominators:
[tex]\[
= \frac{21 \times 8}{5 \times 3} = \frac{168}{15}
\][/tex]
### Step 3: Simplify the Fraction
Simplify [tex]\(\frac{168}{15}\)[/tex] to its simplest form by finding the greatest common divisor of 168 and 15, which is 3:
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{168 \div 3}{15 \div 3} = \frac{56}{5}
\][/tex]
Therefore, Harriet can make [tex]\(\frac{56}{5}\)[/tex] tonnes of concrete. This is the final answer.
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