Multiplying Fractions by Integers Worksheet for primary students, featuring visual and word problems.

Here are the solutions to the worksheet problems, broken down step by step.

Section 1: Pictures and Calculations

1a)
* Picture: There are 5 circles. Each circle has $\frac{2}{3}$ shaded.
* Calculation: You are multiplying the fraction by the number of items.
$$ \frac{2}{3} \times 5 = \frac{2 \times 5}{3} = \frac{10}{3} $$
* Simplest Form: Convert the improper fraction to a mixed number. 3 goes into 10 three times with 1 left over.
$$ \frac{10}{3} = 3 \frac{1}{3} $$

1b)
* Picture: There are 4 rectangles. Each rectangle is divided into 4 parts, and 3 are shaded red. So, each represents $\frac{3}{4}$.
* Calculation: The equation asks for $\text{\_\_\_} \times 4$. The missing number is the fraction shown in one block.
$$ \frac{3}{4} \times 4 = \frac{3 \times 4}{4} = \frac{12}{4} $$
* Simplest Form: 12 divided by 4 is exactly 3.
$$ \frac{12}{4} = 3 $$

1c)
* Picture: There are 3 blocks. Each block has 10 squares total (2 rows of 5). In each block, 8 squares are green. This represents the fraction $\frac{8}{10}$.
* Calculation: Multiply the fraction by the number of blocks (3).
$$ \frac{8}{10} \times 3 = \frac{8 \times 3}{10} = \frac{24}{10} $$
* Simplest Form: First, simplify the fraction $\frac{24}{10}$ by dividing top and bottom by 2, which gives $\frac{12}{5}$. Then convert to a mixed number. 5 goes into 12 two times with 2 left over.
$$ \frac{12}{5} = 2 \frac{2}{5} $$

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Section 2: Basic Multiplication

2a)
* Problem: $\frac{2}{11} \times 5$
* Step: Multiply the numerator (top number) by the integer. Keep the denominator (bottom number) the same.
$$ \frac{2 \times 5}{11} = \frac{10}{11} $$
* Check: Can $\frac{10}{11}$ be simplified? No, because 10 and 11 share no common factors.

2b)
* Problem: $3 \times \frac{4}{9}$
* Step: Think of 3 as $\frac{3}{1}$. Multiply across.
$$ \frac{3 \times 4}{9} = \frac{12}{9} $$
* Simplest Form: Both 12 and 9 can be divided by 3.
$$ \frac{12 \div 3}{9 \div 3} = \frac{4}{3} $$
Convert to a mixed number: 3 goes into 4 once with 1 left over.
$$ 1 \frac{1}{3} $$

2c)
* Problem: $7 \times 1 \frac{2}{35}$
* Step 1: Change the mixed number to an improper fraction.
$$ 1 \frac{2}{35} = \frac{(1 \times 35) + 2}{35} = \frac{37}{35} $$
* Step 2: Multiply by 7.
$$ 7 \times \frac{37}{35} = \frac{7 \times 37}{35} $$
* Step 3: Simplify before multiplying if possible. 7 and 35 are both divisible by 7.
$$ \frac{1 \times 37}{5} = \frac{37}{5} $$
* Step 4: Convert to a mixed number. 5 goes into 37 seven times ($5 \times 7 = 35$) with 2 left over.
$$ 7 \frac{2}{5} $$

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Section 3: Word Problems

Question 1
* Problem: Mrs Green needs $1 \frac{1}{4}$ packets for each of the 8 tables. How many total packets?
* Step 1: Convert $1 \frac{1}{4}$ to an improper fraction.
$$ 1 \frac{1}{4} = \frac{5}{4} $$
* Step 2: Multiply by 8 tables.
$$ \frac{5}{4} \times 8 = \frac{40}{4} $$
* Step 3: Divide.
$$ 40 \div 4 = 10 $$
* Answer: She should buy 10 packets.

Question 2
* Problem: Mo reads $\frac{3}{4}$ of a book each week. How many books after 12 weeks?
* Step 1: Set up the multiplication.
$$ \frac{3}{4} \times 12 $$
* Step 2: Calculate.
$$ \frac{3 \times 12}{4} = \frac{36}{4} $$
* Step 3: Divide.
$$ 36 \div 4 = 9 $$
* Answer: He has read 9 books.

Question 3
* Problem: Jen spent $1 \frac{1}{2}$ hours/day for 6 days. Jack spent $2 \frac{1}{4}$ hours/day for 4 days. Who spent more time and by how many minutes?
* Jen's Time:
$$ 1 \frac{1}{2} \times 6 = \frac{3}{2} \times 6 = \frac{18}{2} = 9 \text{ hours} $$
* Jack's Time:
$$ 2 \frac{1}{4} \times 4 = \frac{9}{4} \times 4 = \frac{36}{4} = 9 \text{ hours} $$
* Comparison:
Jen spent 9 hours. Jack spent 9 hours.
$$ 9 - 9 = 0 $$
* Answer: They spent the same amount of time. The difference is 0 minutes.

Question 4
* Problem: Fido eats $1 \frac{1}{3}$ cups per meal. Is a 20-cup bag enough for 15 meals? If yes, how much is left?
* Step 1: Calculate total food needed for 15 meals.
Convert $1 \frac{1}{3}$ to improper fraction: $\frac{4}{3}$.
$$ \frac{4}{3} \times 15 = \frac{4 \times 15}{3} $$
Simplify: $15 \div 3 = 5$.
$$ 4 \times 5 = 20 \text{ cups} $$
* Step 2: Compare with the bag size.
The bag has 20 cups. Fido needs exactly 20 cups.
* Answer: Yes, there is enough food. There is 0 cups left over.

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Final Answer:

1. Complete the calculations:
a) $\frac{2}{3} \times \mathbf{5} = \mathbf{3 \frac{1}{3}}$
b) $\mathbf{\frac{3}{4}} \times 4 = \mathbf{3}$
c) $\mathbf{\frac{8}{10}} \times \mathbf{3} = \mathbf{2 \frac{2}{5}}$ *(Note: $\frac{4}{5} \times 3 = 2 \frac{2}{5}$ is also correct if simplified first)*

2. Answer the questions:
a) $\mathbf{\frac{10}{11}}$
b) $\mathbf{1 \frac{1}{3}}$
c) $\mathbf{7 \frac{2}{5}}$

3. Word Problems:
1. She should buy 10 packets.
2. He has read 9 books.
3. They spent the same amount of time (difference is 0 minutes).
4. Yes, there is enough food. There is 0 cups left over.