5th Grade Math Worksheets - Free Printable

Here are the step-by-step solutions for each part of your worksheet.

Part 1: Find the Rule

Problem: Look at the Input and Output numbers to find the pattern.
* Input: 15 $\rightarrow$ Output: 105
* Input: 12 $\rightarrow$ Output: 84
* Input: 20 $\rightarrow$ Output: 140

Step-by-step:
Let's check if we are multiplying.
$15 \times ? = 105$. If we divide 105 by 15, we get 7.
Let's test this rule (multiply by 7) on the next row:
$12 \times 7 = 84$. This matches!
Let's test it on the third row:
$20 \times 7 = 140$. This matches too!

So, the rule is: Multiply by 7.

Now fill in the missing outputs:
* Input 14: $14 \times 7 = 98$
* Input 18: $18 \times 7 = 126$

*(Note: The image already has these answers filled in correctly as 98 and 126).*

---

Part 2: Multiply Fractions

Problem 1: $\frac{1}{2} \times \frac{7}{10}$

Step-by-step:
To multiply fractions, you multiply the top numbers (numerators) together and the bottom numbers (denominators) together.
* Top: $1 \times 7 = 7$
* Bottom: $2 \times 10 = 20$

Answer: $\frac{7}{20}$

Problem 2: $\frac{5}{8} \times \frac{3}{5}$

Step-by-step:
* Top: $5 \times 3 = 15$
* Bottom: $8 \times 5 = 40$
Result: $\frac{15}{40}$

The problem says "Simplify if possible." Both 15 and 40 can be divided by 5.
* $15 \div 5 = 3$
* $40 \div 5 = 8$

Answer: $\frac{3}{8}$

*(Alternatively, you can cross-cancel the 5s before multiplying: $\frac{1}{8} \times \frac{3}{1} = \frac{3}{8}$)*

---

Part 3: Subtract Decimals

Problem 1: $7.4 - 2.9$

Step-by-step:
Line up the decimal points. Since you can't subtract 9 from 4, you need to borrow from the 7.
* The 7 becomes a 6.
* The 4 becomes a 14.
* $14 - 9 = 5$
* $6 - 2 = 4$

Answer: 4.5

Problem 2: $65.1 - 9.8$

Step-by-step:
Line up the decimals.
* Ones place: You can't take 8 from 1. Borrow from the 5 (in the ones place). The 5 becomes 4, and the 1 becomes 11.
* $11 - 8 = 3$
* Ones place (after borrowing): Now we have $4 - 9$. We can't do that, so borrow from the 6 (in the tens place). The 6 becomes 5, and the 4 becomes 14.
* $14 - 9 = 5$
* Tens place: $5 - 0 = 5$

Answer: 55.3

---

Part 4: Find the Difference

Problem: Find the difference between 46.3 and 13.5.

Step-by-step:
"Difference" means subtraction. So, calculate $46.3 - 13.5$.
* Tenths place: Can't take 5 from 3. Borrow from the 6. The 6 becomes 5, and the 3 becomes 13.
* $13 - 5 = 8$
* Ones place: $5 - 3 = 2$
* Tens place: $4 - 1 = 3$

Answer: 32.8

---

Part 5: Ordered Pairs on Graph

Problem: Write the point located at each ordered pair $(x, y)$. Remember: Go along the bottom ($x$) first, then go up ($y$).

1. (4, 4)
* Go right to 4 on the x-axis.
* Go up to 4 on the y-axis.
* This lands on point A.

2. (9, 0)
* Go right to 9 on the x-axis.
* Go up 0 (stay on the line).
* This lands on point B.

3. (7, 10)
* Go right to 7 on the x-axis.
* Go up to 10 on the y-axis.
* This lands on point C.

4. (2, 11)
* Go right to 2 on the x-axis.
* Go up to 11 on the y-axis.
* This lands on point D.

Final Answer:
Rule: Multiply by 7
Multiplication:
$\frac{1}{2} \times \frac{7}{10} = \frac{7}{20}$
$\frac{5}{8} \times \frac{3}{5} = \frac{3}{8}$

Subtraction:
$7.4 - 2.9 = 4.5$
$65.1 - 9.8 = 55.3$

Difference:
$46.3 - 13.5 = 32.8$

Ordered Pairs:
(4, 4) $\rightarrow$ A
(9, 0) $\rightarrow$ B
(7, 10) $\rightarrow$ C
(2, 11) $\rightarrow$ D