Here are the solutions to the problems on the worksheet, broken down step by step.
1. Math Buzz (Input/Output Table)
Goal: Find the rule that turns the "Input" number into the "Output" number.
*
Step 1: Look at the first pair: Input $15 \rightarrow$ Output $105$.
* Let's try multiplying: $15 \times 7 = 105$. This works.
*
Step 2: Check if this rule works for the next pair: Input $12 \rightarrow$ Output $84$.
* $12 \times 7 = 84$. This also works.
*
Step 3: Check the rest to be sure.
* $20 \times 7 = 140$ (Correct)
* $14 \times 7 = 98$ (Correct)
* $18 \times 7 = 126$ (Correct)
Rule: Multiply by 7 ($\times 7$)
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2. Subtract
Problem A: $7.4 - 2.9$
* Line up the decimal points.
* You cannot subtract $9$ from $4$, so borrow $1$ from the $7$. The $7$ becomes a $6$, and the $4$ becomes $14$.
* $14 - 9 = 5$
* $6 - 2 = 4$
* Bring down the decimal point.
*
Answer: $4.5$
Problem B: $65.1 - 9.8$
* Line up the decimal points. Add a zero placeholder to make it easier to see: $65.1 - 09.8$.
* You cannot subtract $8$ from $1$, so borrow $1$ from the $5$. The $5$ becomes a $4$, and the $1$ becomes $11$.
* $11 - 8 = 3$
* Now look at the ones place: $4 - 9$. You can't do this, so borrow $1$ from the $6$. The $6$ becomes a $5$, and the $4$ becomes $14$.
* $14 - 9 = 5$
* Finally, $5 - 0 = 5$.
*
Answer: $55.3$
Problem C: Find the difference between $46.3$ and $13.5$.
* Set it up as a subtraction problem: $46.3 - 13.5$.
* Borrow from the $6$ (it becomes $5$) to make the $3$ a $13$.
* $13 - 5 = 8$
* $5 - 3 = 2$
* $4 - 1 = 3$
*
Answer: $32.8$
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3. Multiply
Problem A: $\frac{1}{2} \times \frac{7}{10}$
* Multiply the top numbers (numerators): $1 \times 7 = 7$
* Multiply the bottom numbers (denominators): $2 \times 10 = 20$
*
Answer: $\frac{7}{20}$
Problem B: $\frac{5}{6} \times \frac{5}{3}$
* Multiply the top numbers: $5 \times 5 = 25$
* Multiply the bottom numbers: $6 \times 3 = 18$
*
Answer: $\frac{25}{18}$ (This can also be written as $1 \frac{7}{18}$)
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4. Ordered Pairs
To find the ordered pair $(x, y)$, start at $0$, go right along the bottom line to find the x-number, then go up to find the y-number.
*
Point A: Go right to
4, go up to
4.
* Answer:
(4, 4)
*
Point B: Go right to
9, stay on the line (
0).
* Answer:
(9, 0)
*
Point C: Go right to
7, go up to
10.
* Answer:
(7, 10)
*
Point D: Go right to
2, go up to
11.
* Answer:
(2, 11)
──────────────────────────────────────
Final Answer:
Math Buzz Rule: $\times 7$
Subtract:
$7.4 - 2.9 = \mathbf{4.5}$
$65.1 - 9.8 = \mathbf{55.3}$
Difference between $46.3$ and $13.5 = \mathbf{32.8}$
Multiply:
$\frac{1}{2} \times \frac{7}{10} = \mathbf{\frac{7}{20}}$
$\frac{5}{6} \times \frac{5}{3} = \mathbf{\frac{25}{18}}$
Ordered Pairs:
A: $\mathbf{(4, 4)}$
B: $\mathbf{(9, 0)}$
C: $\mathbf{(7, 10)}$
D: $\mathbf{(2, 11)}$
Parent Tip: Review the logic above to help your child master the concept of everyday math 4th grade worksheet.
