Here are the step-by-step solutions for each problem on the worksheet.
1) Oliver's Homework Time
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Problem: Oliver spent $1/6$ hours on math and $1/6$ hours on reading. What is the total time?
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Step 1: Add the numerators (top numbers) because the denominators (bottom numbers) are the same.
$$1 + 1 = 2$$
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Step 2: Keep the denominator the same ($6$).
Result: $2/6$
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Step 3: Simplify to lowest terms. Both numbers can be divided by $2$.
$$2 \div 2 = 1$$
$$6 \div 2 = 3$$
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Answer: $1/3$ hours
2) Mike's Sandcastle
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Problem: The castle is $1/5$ feet high. The flag is $3/5$ feet high. What is the total height?
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Step 1: Add the numerators.
$$1 + 3 = 4$$
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Step 2: Keep the denominator the same ($5$).
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Step 3: Check if it simplifies. $4$ and $5$ share no common factors, so it stays as is.
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Answer: $4/5$ feet
3) Flour for the Recipe
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Problem: Use $5/9$ cups before baking and $3/9$ cups after baking. What is the total amount?
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Step 1: Add the numerators.
$$5 + 3 = 8$$
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Step 2: Keep the denominator the same ($9$).
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Step 3: Check if it simplifies. $8$ and $9$ share no common factors.
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Answer: $8/9$ cups
4) Bulldozer Weight
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Problem: Empty bulldozer is $2/9$ tons. Dirt is $3/9$ tons. What is the combined weight?
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Step 1: Add the numerators.
$$2 + 3 = 5$$
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Step 2: Keep the denominator the same ($9$).
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Step 3: Check if it simplifies. It cannot be simplified further.
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Answer: $5/9$ tons
5) Road Length
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Problem: First road is $6/7$ miles. Second road is $1/7$ miles. What is the combined length?
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Step 1: Add the numerators.
$$6 + 1 = 7$$
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Step 2: Keep the denominator the same ($7$).
Result: $7/7$
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Step 3: Simplify. Any number divided by itself equals $1$.
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Answer: $1$ mile
6) Tiffany and her Friend
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Problem: Tiffany picked up $5\ 5/8$ bags. Her friend picked up $4\ 1/8$ bags. How much *more* did Tiffany pick up?
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Step 1: This is a subtraction problem. Set it up vertically or side-by-side:
$$5\ 5/8 - 4\ 1/8$$
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Step 2: Subtract the whole numbers first.
$$5 - 4 = 1$$
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Step 3: Subtract the fractions.
$$5/8 - 1/8 = 4/8$$
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Step 4: Combine them: $1\ 4/8$.
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Step 5: Simplify the fraction part. Divide top and bottom by $4$.
$$4 \div 4 = 1$$
$$8 \div 4 = 2$$
So, $4/8$ becomes $1/2$.
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Answer: $1\ 1/2$ bags
7) Halloween Candy
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Problem: Lana had $7\ 4/8$ pounds. Her family ate $3\ 6/8$ pounds. How much is left?
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Step 1: Set up the subtraction:
$$7\ 4/8 - 3\ 6/8$$
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Step 2: Look at the fractions. You cannot subtract $6/8$ from $4/8$ because $6$ is bigger than $4$. You need to borrow from the whole number.
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Step 3: Borrow $1$ from the $7$. The $7$ becomes a $6$. That borrowed $1$ turns into $8/8$ (since the denominator is $8$).
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Step 4: Add that $8/8$ to the existing $4/8$.
$$8/8 + 4/8 = 12/8$$
Now the problem is: $6\ 12/8 - 3\ 6/8$
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Step 5: Subtract the fractions.
$$12/8 - 6/8 = 6/8$$
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Step 6: Subtract the whole numbers.
$$6 - 3 = 3$$
Result: $3\ 6/8$
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Step 7: Simplify the fraction. Divide top and bottom by $2$.
$$6 \div 2 = 3$$
$$8 \div 2 = 4$$
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Answer: $3\ 3/8$ pounds
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Final Answer:
1) 1/3 hours
2) 4/5 feet
3) 8/9 cups
4) 5/9 tons
5) 1 mile
6) 1 1/2 bags
7) 3 3/8 pounds
Parent Tip: Review the logic above to help your child master the concept of fraction word problem worksheet.
