- 6.25 pounds he used.
- 3.75 pounds he has left.
Further explanation
Given:
- A gardener has 10 pounds of soil.
- He used [tex]\frac{5}{8}[/tex] of the soil for his garden.
Question:
- How many pounds of soil did he use in the garden?
- How many pounds did he have left?
The Process:
[tex]Let \ us \ prepare \boxed{10 \div 8 = \frac{10}{8}}[/tex]
From the information above, let us create a suitable diagram as follows:
[tex]\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}} = 10 \ pounds[/tex]
[tex]\boxed{\frac{10 \div 2}{8 \div 2} \rightarrow \frac{5}{4}}[/tex]. The diagram has rewritten as follows:
[tex]\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}}\boxed{\frac{5}{4}} = 10 \ pounds[/tex]
[tex]\boxed{ \ Hence, \ 1 \ unit = \frac{5}{4} \ pounds \ }[/tex]
He used [tex]\frac{5}{8}[/tex] of the soil for his garden, or 5 of 8 units of 10 pounds. It means he has left 3 of 8 units.
Let us calculate how many pounds of soil did he use in the garden.
[tex]\boxed{ \ = 5 \times \frac{5}{4} \ pounds \ }[/tex]
[tex]\boxed{\boxed{ \ \frac{25}{4} \ pounds \ }}[/tex]
In mixed fraction:
[tex]\boxed{\boxed{ \ \frac{25}{4} = \frac{24}{4} + \frac{1}{4} = 6\frac{1}{4} \ pounds \ }}[/tex]
In decimal:
[tex]\boxed{\boxed{ \ \frac{25}{4} \times \frac{25}{25} = \frac{625}{100} = 6.25 \ pounds \ }}[/tex]
It could also be like this:
[tex]\boxed{\boxed{ \ 6\frac{1}{4} = 6\frac{25}{100} = 6.25 \ pounds \ }}[/tex]
Let us calculate how many pounds of soil did he have left.
[tex]\boxed{ \ = 10 - \frac{25}{4} \ pounds \ }[/tex]
[tex]\boxed{ \ = \frac{40}{4} - \frac{25}{4} \ pounds \ }}[/tex]
[tex]\boxed{\boxed{ \ \frac{15}{4} \ pounds \ }}[/tex]
In mixed fraction:
[tex]\boxed{\boxed{ \ \frac{15}{4} = \frac{12}{4} + \frac{3}{4} = 3\frac{3}{4} \ pounds \ }}[/tex]
In decimal:
[tex]\boxed{\boxed{ \ \frac{15}{4} \times \frac{25}{25} = \frac{375}{100} = 3.75 \ pounds \ }}[/tex]
It could also be like this:
[tex]\boxed{\boxed{ \ 3\frac{3}{4} = 3\frac{75}{100} = 3.75 \ pounds \ }}[/tex]
- - - - - - - - - -
Quick Steps:
He used [tex]\frac{5}{8}[/tex] of the soil for his garden.
[tex]\boxed{ \ = \frac{5}{8} \times 10 \ pounds \ }[/tex]
[tex]\boxed{ \ = \frac{50}{8} \ pounds \ }[/tex]
[tex]\boxed{ \ = \frac{50 \div 2}{8 \div 2} = \frac{25}{4} \ pounds \ }[/tex]
[tex]\boxed{\boxed{ \ \frac{25}{4} = 6\frac{1}{4} \ pounds \ }}[/tex]
[tex]\boxed{\boxed{ \ \frac{25}{4} \times \frac{25}{25} = \frac{625}{100} = 6.25 \ pounds \ }}[/tex]
He has left [tex]\frac{3}{8}[/tex] of the soil.
[tex]\boxed{ \ = \frac{3}{8} \times 10 \ pounds \ }[/tex]
[tex]\boxed{ \ = \frac{30}{8} \ pounds \ }[/tex]
[tex]\boxed{ \ = \frac{30 \div 2}{8 \div 2} = \frac{15}{4} \ pounds \ }[/tex]
[tex]\boxed{\boxed{ \ \frac{15}{4} = 3\frac{3}{4} \ pounds \ }}[/tex]
[tex]\boxed{\boxed{ \ \frac{15}{4} \times \frac{25}{25} = \frac{375}{100} = 3.75 \ pounds \ }}[/tex]
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Keywords: a gardener, has, 10 pounds of soil, he used, 5/8, the soil for his garden, how many, in the garden, have left, 3/8, 6.25, 3.75
