It looks like you've uploaded a worksheet titled
"Proportion or Not a Proportion", where students are asked to determine whether given pairs of ratios form a proportion.
Let's go through each problem one by one, analyze the ratios, and decide whether they are
proportions (i.e., equal) or
not proportions.
---
Understanding Proportions
Two ratios are in proportion if their cross products are equal. That is:
$$
\frac{a}{b} = \frac{c}{d} \quad \text{if and only if} \quad a \cdot d = b \cdot c
$$
We'll use this method for each item.
---
1. $\frac{12}{18}$ and $\frac{2}{3}$
- Cross multiply: $12 \times 3 = 36$, $18 \times 2 = 36$
- Since $36 = 36$,
yes, it’s a proportion.
✔ Proportion
---
2. $\frac{10}{25}$ and $\frac{4}{10}$
- Cross multiply: $10 \times 10 = 100$, $25 \times 4 = 100$
- $100 = 100$ →
Yes, proportion.
✔ Proportion
---
3. $\frac{20}{30}$ and $\frac{12}{15}$
- Simplify both:
- $\frac{20}{30} = \frac{2}{3}$
- $\frac{12}{15} = \frac{4}{5}$
- $ \frac{2}{3} \neq \frac{4}{5} $
- Cross multiply: $20 \times 15 = 300$, $30 \times 12 = 360$
- $300 \neq 360$ →
Not a proportion
✘ Not a Proportion
---
4. $\frac{5}{7}$ and $\frac{3}{21}$
- Cross multiply: $5 \times 21 = 105$, $7 \times 3 = 21$
- $105 \neq 21$ →
Not a proportion
✘ Not a Proportion
---
5. $\frac{12}{16}$ and $\frac{3}{4}$
- Simplify: $\frac{12}{16} = \frac{3}{4}$, so they are equal.
- Cross multiply: $12 \times 4 = 48$, $16 \times 3 = 48$
- Equal →
Proportion
✔ Proportion
---
6. $\frac{3}{4}$ and $\frac{18}{24}$
- Simplify: $\frac{18}{24} = \frac{3}{4}$
- So, same as above →
Proportion
✔ Proportion
---
7. $\frac{3}{4}$ and $\frac{2}{3}$
- Cross multiply: $3 \times 3 = 9$, $4 \times 2 = 8$
- $9 \neq 8$ →
Not a proportion
✘ Not a Proportion
---
8. $\frac{2}{3}$ and $\frac{10}{15}$
- Simplify: $\frac{10}{15} = \frac{2}{3}$
- So they are equal →
Proportion
✔ Proportion
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Final Answers:
| Number | Ratios | Is it a Proportion? |
|--------|---------------------------|---------------------|
| 1 | $\frac{12}{18}, \frac{2}{3}$ |
✔ Yes |
| 2 | $\frac{10}{25}, \frac{4}{10}$ |
✔ Yes |
| 3 | $\frac{20}{30}, \frac{12}{15}$ |
✘ No |
| 4 | $\frac{5}{7}, \frac{3}{21}$ |
✘ No |
| 5 | $\frac{12}{16}, \frac{3}{4}$ |
✔ Yes |
| 6 | $\frac{3}{4}, \frac{18}{24}$ |
✔ Yes |
| 7 | $\frac{3}{4}, \frac{2}{3}$ |
✘ No |
| 8 | $\frac{2}{3}, \frac{10}{15}$ |
✔ Yes |
---
Summary of Answers:
1.
Proportion
2.
Proportion
3.
Not a Proportion
4.
Not a Proportion
5.
Proportion
6.
Proportion
7.
Not a Proportion
8.
Proportion
Let me know if you'd like this formatted into a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of proportions worksheet with answers.
