Proportions worksheet with 12 math problems to find the missing number.

To solve these proportion problems, we need to find the value of $x$ that makes the two fractions equal. A common way to do this is by using cross-multiplication.

Here is how it works:
If you have $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.
Then, divide by the number next to $x$ to get the answer.

Let's solve each one step-by-step:

1) $\frac{x}{35} = \frac{10}{20}$
* Cross-multiply: $20 \cdot x = 35 \cdot 10$
* $20x = 350$
* Divide by 20: $x = \frac{350}{20} = 17.5$

2) $\frac{x}{50} = \frac{24}{28}$
* Cross-multiply: $28 \cdot x = 50 \cdot 24$
* $28x = 1200$
* Divide by 28: $x = \frac{1200}{28} \approx 42.86$ (or as a fraction $\frac{300}{7}$)

3) $\frac{x}{36} = \frac{19}{60}$
* Cross-multiply: $60 \cdot x = 36 \cdot 19$
* $60x = 684$
* Divide by 60: $x = \frac{684}{60} = 11.4$

4) $\frac{x}{30} = \frac{34}{38}$
* Cross-multiply: $38 \cdot x = 30 \cdot 34$
* $38x = 1020$
* Divide by 38: $x = \frac{1020}{38} \approx 26.84$ (or as a fraction $\frac{510}{19}$)

5) $\frac{x}{36} = \frac{28}{29}$
* Cross-multiply: $29 \cdot x = 36 \cdot 28$
* $29x = 1008$
* Divide by 29: $x = \frac{1008}{29} \approx 34.76$

6) $\frac{x}{16} = \frac{30}{33}$
* Cross-multiply: $33 \cdot x = 16 \cdot 30$
* $33x = 480$
* Divide by 33: $x = \frac{480}{33} \approx 14.55$ (or as a fraction $\frac{160}{11}$)

7) $\frac{x}{24} = \frac{44}{34}$
* Cross-multiply: $34 \cdot x = 24 \cdot 44$
* $34x = 1056$
* Divide by 34: $x = \frac{1056}{34} \approx 31.06$ (or as a fraction $\frac{528}{17}$)

8) $\frac{x}{33} = \frac{41}{47}$
* Cross-multiply: $47 \cdot x = 33 \cdot 41$
* $47x = 1353$
* Divide by 47: $x = \frac{1353}{47} \approx 28.79$

9) $\frac{x}{53} = \frac{23}{29}$
* Cross-multiply: $29 \cdot x = 53 \cdot 23$
* $29x = 1219$
* Divide by 29: $x = \frac{1219}{29} \approx 42.03$

10) $\frac{x}{26} = \frac{18}{23}$
* Cross-multiply: $23 \cdot x = 26 \cdot 18$
* $23x = 468$
* Divide by 23: $x = \frac{468}{23} \approx 20.35$

11) $\frac{x}{25} = \frac{14}{37}$
* Cross-multiply: $37 \cdot x = 25 \cdot 14$
* $37x = 350$
* Divide by 37: $x = \frac{350}{37} \approx 9.46$

12) $\frac{x}{19} = \frac{11}{22}$
* Notice that $\frac{11}{22}$ simplifies to $\frac{1}{2}$. So, $\frac{x}{19} = \frac{1}{2}$.
* Cross-multiply: $2 \cdot x = 19 \cdot 1$
* $2x = 19$
* Divide by 2: $x = 9.5$

Final Answer:
1) 17.5
2) 42.86 (or 300/7)
3) 11.4
4) 26.84 (or 510/19)
5) 34.76 (or 1008/29)
6) 14.55 (or 160/11)
7) 31.06 (or 528/17)
8) 28.79 (or 1353/47)
9) 42.03 (or 1219/29)
10) 20.35 (or 468/23)
11) 9.46 (or 350/37)
12) 9.5