Here are the step-by-step solutions for the word problems on the worksheet.
1. Brownies Problem
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Step 1: Find out how much of the pan was left before John arrived. The whole pan is 1. If $1/4$ was eaten, we subtract that from the whole:
$$1 - 1/4 = 3/4$$
So, $3/4$ of the pan was left.
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Step 2: Calculate how much John ate. He ate $2/3$ of what was *left* ($3/4$). To find this, multiply the fractions:
$$2/3 \times 3/4 = 6/12$$
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Step 3: Simplify the fraction. Both numbers can be divided by 6:
$$6 \div 6 = 1$$
$$12 \div 6 = 2$$
So, John ate $1/2$ of the whole pan.
2. Donuts Problem
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Step 1: Identify the total number of donuts (6) and the fraction for the friend ($2/3$).
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Step 2: Multiply the total by the fraction to find the friend's share:
$$6 \times 2/3$$
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Step 3: First, divide 6 by the bottom number (3):
$$6 \div 3 = 2$$
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Step 4: Then, multiply that result by the top number (2):
$$2 \times 2 = 4$$
The friend gets 4 donuts.
3. Baker's Oil Problem
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Step 1: We have 15 cups of oil total. Each cake needs $1/4$ cup. To find how many cakes can be made, we divide the total oil by the amount needed per cake:
$$15 \div 1/4$$
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Step 2: When dividing by a fraction, you flip the fraction and multiply (multiply by the reciprocal). The reciprocal of $1/4$ is $4/1$ (or just 4).
$$15 \times 4 = 60$$
She can make 60 cakes.
4. Granola Servings Problem
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Step 1: The box has 32 cups. One serving is $1/2$ cup. We need to divide the total cups by the serving size:
$$32 \div 1/2$$
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Step 2: Flip the fraction $1/2$ to get 2, and multiply:
$$32 \times 2 = 64$$
There are 64 servings in the box.
5. Vests Fabric Problem
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Step 1: We have 18 yards of fabric. Each vest uses $2/3$ of a yard. Divide the total fabric by the amount per vest:
$$18 \div 2/3$$
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Step 2: Flip the fraction $2/3$ to get $3/2$, and multiply:
$$18 \times 3/2$$
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Step 3: It is easier to divide first. Divide 18 by the bottom number (2):
$$18 \div 2 = 9$$
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Step 4: Multiply that result by the top number (3):
$$9 \times 3 = 27$$
They can make 27 vests.
6. Candies Problem
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Step 1: Find the total fraction of candies eaten. Add Billy's, Bob's, and Buck's shares together:
$$2/12 + 3/12 + 5/12$$
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Step 2: Since the bottom numbers are all the same, just add the top numbers:
$$2 + 3 + 5 = 10$$
So, they ate $10/12$ of the candies.
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Step 3: Find the fraction left over. The whole bowl is $12/12$. Subtract the eaten part:
$$12/12 - 10/12 = 2/12$$
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Step 4: Calculate the actual number of candies left. Find $2/12$ of 120:
First, divide 120 by 12:
$$120 \div 12 = 10$$
Then, multiply by 2:
$$10 \times 2 = 20$$
There were 20 candies left.
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Final Answer:
1. 1/2 of the pan
2. 4 donuts
3. 60 cakes
4. 64 servings
5. 27 vests
6. 20 candies
Parent Tip: Review the logic above to help your child master the concept of word problem fractions worksheet.
