Here are the step-by-step solutions for each problem on the worksheet.
1) James and four of his friends each have $\frac{5}{7}$ of a bag of candy. How many bags of candy do they have in total?
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Step 1: Count the total number of people. It is James plus his four friends.
$1 + 4 = 5$ people.
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Step 2: Multiply the number of people by the amount of candy each person has.
$5 \times \frac{5}{7}$
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Step 3: To multiply a whole number by a fraction, multiply the whole number by the top number (numerator). Keep the bottom number (denominator) the same.
$5 \times 5 = 25$
The denominator stays 7.
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Step 4: Write the final fraction.
$\frac{25}{7}$
2) Moses eats $\frac{2}{5}$ of a sushi roll for lunch for three days in a row. How much sushi did he eat during those three days?
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Step 1: Identify the amount eaten per day ($\frac{2}{5}$) and the number of days (3).
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Step 2: Multiply the daily amount by the number of days.
$3 \times \frac{2}{5}$
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Step 3: Multiply the whole number by the numerator.
$3 \times 2 = 6$
The denominator stays 5.
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Step 4: Write the final fraction.
$\frac{6}{5}$
3) Rick has 8 glass bottles that are $\frac{3}{4}$ filled with ketchup. If he pours all of the ketchup together, how many of the glass bottles can he fill completely?
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Step 1: Multiply the number of bottles (8) by the fraction filled ($\frac{3}{4}$).
$8 \times \frac{3}{4}$
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Step 2: Multiply the whole number by the numerator.
$8 \times 3 = 24$
So, we have $\frac{24}{4}$.
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Step 3: Simplify the fraction by dividing the top by the bottom.
$24 \div 4 = 6$
4) There are 15 people at a pizza party. If each person eats $\frac{3}{10}$ of a pizza, how many pizzas will be needed to feed everyone at the party?
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Step 1: Multiply the number of people (15) by the amount each person eats ($\frac{3}{10}$).
$15 \times \frac{3}{10}$
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Step 2: Multiply the whole number by the numerator.
$15 \times 3 = 45$
So, we have $\frac{45}{10}$.
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Step 3: Convert this improper fraction into a mixed number or decimal to see how many whole pizzas are needed.
$\frac{45}{10} = 4.5$ (or $4 \frac{1}{2}$)
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Step 4: Since you cannot buy half a pizza usually, and you need enough to feed *everyone*, you must round up to the next whole number. 4 pizzas would not be enough (that's only 40 slices worth), so you need 5.
5) Jeanie is a baker. She is using a chocolate cupcake recipe that calls for using $\frac{3}{4}$ of a bag of cocoa powder to make one dozen cupcakes. How many bags of cocoa powder will she need if she wants to make 10 dozen chocolate cupcakes?
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Step 1: Multiply the number of dozens (10) by the amount of powder needed for one dozen ($\frac{3}{4}$).
$10 \times \frac{3}{4}$
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Step 2: Multiply the whole number by the numerator.
$10 \times 3 = 30$
So, we have $\frac{30}{4}$.
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Step 3: Convert this into a mixed number.
4 goes into 30 seven times ($4 \times 7 = 28$), with a remainder of 2.
So, the answer is $7 \frac{2}{4}$, which simplifies to $7 \frac{1}{2}$ bags.
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Step 4: Just like the pizza problem, if she needs $7 \frac{1}{2}$ bags, she needs to open an 8th bag to get that last half. Therefore, she needs 8 bags total.
Final Answer:
1) $\frac{25}{7}$ (or $3 \frac{4}{7}$) bags
2) $\frac{6}{5}$ (or $1 \frac{1}{5}$) sushi rolls
3) 6 bottles
4) 5 pizzas
5) 8 bags
Parent Tip: Review the logic above to help your child master the concept of word problems worksheet 4th.
