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Sagot :
Sure, let's solve these word problems step-by-step:
### Problem a:
"A milk bottle contains [tex]\(1 \frac{1}{2}\)[/tex] liters of milk. How much milk do 15 such bottles contain?"
1. First, convert the mixed number to an improper fraction:
[tex]\(1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\)[/tex].
2. Now, multiply the amount of milk per bottle by the number of bottles:
[tex]\[ \frac{3}{2} \times 15 \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{3 \times 15}{2} = \frac{45}{2} = 22.5 \][/tex]
So, 15 bottles will contain 22.5 liters of milk.
### Problem b:
"One shirt requires [tex]\(2 \frac{1}{4}\)[/tex] meters of cloth. How much cloth is required for 28 such shirts?"
1. Convert the mixed number to an improper fraction:
[tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\)[/tex].
2. Now, multiply the amount of cloth per shirt by the number of shirts:
[tex]\[ \frac{9}{4} \times 28 \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{9 \times 28}{4} = \frac{252}{4} = 63 \][/tex]
So, 28 shirts will require 63 meters of cloth.
### Problem c:
"Shobhit's car covers [tex]\(18 \frac{1}{2}\)[/tex] km in one litre of petrol. How many kilometers will it cover in [tex]\(8 \frac{1}{4}\)[/tex] litres?"
1. Convert the mixed numbers to improper fractions:
[tex]\[ 18 \frac{1}{2} = 18 + \frac{1}{2} = \frac{36}{2} + \frac{1}{2} = \frac{37}{2} \][/tex]
and
[tex]\[ 8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \][/tex]
2. Now, multiply the distance per litre by the number of litres:
[tex]\[ \frac{37}{2} \times \frac{33}{4} \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{37 \times 33}{2 \times 4} = \frac{1221}{8} = 152.625 \][/tex]
So, Shobhit's car will cover 152.625 kilometers.
### Problem d:
"Ritesh needs [tex]\(14 \frac{3}{2}\)[/tex] dozens of bananas. If the cost of 1 dozen bananas is [tex]\(₹ 5 \frac{1}{2}\)[/tex], how much money does Ritesh need to buy the bananas?"
1. Convert the mixed numbers to improper fractions:
[tex]\[ 14 \frac{3}{2} = 14 + \frac{3}{2} = \frac{28}{2} + \frac{3}{2} = \frac{31}{2} \][/tex]
and
[tex]\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \][/tex]
2. Now, multiply the number of dozens needed by the cost per dozen:
[tex]\[ \frac{31}{2} \times \frac{11}{2} \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{31 \times 11}{2 \times 2} = \frac{341}{4} = 85.25 \][/tex]
So, Ritesh will need ₹ 85.25 to buy the required dozens of bananas.
### Problem a:
"A milk bottle contains [tex]\(1 \frac{1}{2}\)[/tex] liters of milk. How much milk do 15 such bottles contain?"
1. First, convert the mixed number to an improper fraction:
[tex]\(1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\)[/tex].
2. Now, multiply the amount of milk per bottle by the number of bottles:
[tex]\[ \frac{3}{2} \times 15 \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{3 \times 15}{2} = \frac{45}{2} = 22.5 \][/tex]
So, 15 bottles will contain 22.5 liters of milk.
### Problem b:
"One shirt requires [tex]\(2 \frac{1}{4}\)[/tex] meters of cloth. How much cloth is required for 28 such shirts?"
1. Convert the mixed number to an improper fraction:
[tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\)[/tex].
2. Now, multiply the amount of cloth per shirt by the number of shirts:
[tex]\[ \frac{9}{4} \times 28 \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{9 \times 28}{4} = \frac{252}{4} = 63 \][/tex]
So, 28 shirts will require 63 meters of cloth.
### Problem c:
"Shobhit's car covers [tex]\(18 \frac{1}{2}\)[/tex] km in one litre of petrol. How many kilometers will it cover in [tex]\(8 \frac{1}{4}\)[/tex] litres?"
1. Convert the mixed numbers to improper fractions:
[tex]\[ 18 \frac{1}{2} = 18 + \frac{1}{2} = \frac{36}{2} + \frac{1}{2} = \frac{37}{2} \][/tex]
and
[tex]\[ 8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \][/tex]
2. Now, multiply the distance per litre by the number of litres:
[tex]\[ \frac{37}{2} \times \frac{33}{4} \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{37 \times 33}{2 \times 4} = \frac{1221}{8} = 152.625 \][/tex]
So, Shobhit's car will cover 152.625 kilometers.
### Problem d:
"Ritesh needs [tex]\(14 \frac{3}{2}\)[/tex] dozens of bananas. If the cost of 1 dozen bananas is [tex]\(₹ 5 \frac{1}{2}\)[/tex], how much money does Ritesh need to buy the bananas?"
1. Convert the mixed numbers to improper fractions:
[tex]\[ 14 \frac{3}{2} = 14 + \frac{3}{2} = \frac{28}{2} + \frac{3}{2} = \frac{31}{2} \][/tex]
and
[tex]\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \][/tex]
2. Now, multiply the number of dozens needed by the cost per dozen:
[tex]\[ \frac{31}{2} \times \frac{11}{2} \][/tex]
3. Performing the multiplication:
[tex]\[ \frac{31 \times 11}{2 \times 2} = \frac{341}{4} = 85.25 \][/tex]
So, Ritesh will need ₹ 85.25 to buy the required dozens of bananas.
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