This worksheet is titled
“Evaluating Expressions with Variables”, and the task is to
solve each proportion — that is, find the value of the variable in each equation.
Each problem is a proportion: two fractions set equal to each other. To solve for the variable, we use
cross-multiplication:
> If \(\frac{a}{b} = \frac{c}{d}\), then \(a \cdot d = b \cdot c\)
Let’s solve each one step by step.
---
Row 1
1. \(\frac{1}{2} = \frac{3}{x}\)
→ Cross-multiply: \(1 \cdot x = 2 \cdot 3\) → \(x = 6\)
2. \(\frac{h}{4} = \frac{1}{2}\)
→ \(h \cdot 2 = 4 \cdot 1\) → \(2h = 4\) → \(h = 2\)
3. \(\frac{2}{y} = \frac{3}{6}\)
→ First simplify \(\frac{3}{6} = \frac{1}{2}\), so \(\frac{2}{y} = \frac{1}{2}\)
→ \(2 \cdot 2 = y \cdot 1\) → \(4 = y\) → \(y = 4\)
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Row 2
4. \(\frac{3}{2} = \frac{t}{4}\)
→ \(3 \cdot 4 = 2 \cdot t\) → \(12 = 2t\) → \(t = 6\)
5. \(\frac{s}{5} = \frac{4}{8}\)
→ Simplify \(\frac{4}{8} = \frac{1}{2}\), so \(\frac{s}{5} = \frac{1}{2}\)
→ \(s \cdot 2 = 5 \cdot 1\) → \(2s = 5\) → \(s = \frac{5}{2} = 2.5\)
6. \(\frac{1}{v} = \frac{4}{8}\)
→ Simplify \(\frac{4}{8} = \frac{1}{2}\), so \(\frac{1}{v} = \frac{1}{2}\) → \(v = 2\)
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Row 3
7. \(\frac{1}{3} = \frac{3}{a}\)
→ \(1 \cdot a = 3 \cdot 3\) → \(a = 9\)
8. \(\frac{r}{6} = \frac{1}{3}\)
→ \(r \cdot 3 = 6 \cdot 1\) → \(3r = 6\) → \(r = 2\)
9. \(\frac{10}{j} = \frac{5}{6}\)
→ \(10 \cdot 6 = j \cdot 5\) → \(60 = 5j\) → \(j = 12\)
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Row 4
10. \(\frac{2}{1} = \frac{x}{2}\)
→ \(2 \cdot 2 = 1 \cdot x\) → \(4 = x\) → \(x = 4\)
11. \(\frac{b}{4} = \frac{3}{6}\)
→ Simplify \(\frac{3}{6} = \frac{1}{2}\), so \(\frac{b}{4} = \frac{1}{2}\)
→ \(b \cdot 2 = 4 \cdot 1\) → \(2b = 4\) → \(b = 2\)
12. \(\frac{m}{1} = \frac{4}{2}\)
→ Simplify \(\frac{4}{2} = 2\), so \(m = 2\)
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Row 5
13. \(\frac{1}{9} = \frac{9}{v}\)
→ \(1 \cdot v = 9 \cdot 9\) → \(v = 81\)
14. \(\frac{y}{3} = \frac{3}{1}\)
→ \(y \cdot 1 = 3 \cdot 3\) → \(y = 9\)
15. \(\frac{1}{w} = \frac{3}{9}\)
→ Simplify \(\frac{3}{9} = \frac{1}{3}\), so \(\frac{1}{w} = \frac{1}{3}\) → \(w = 3\)
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Row 6
16. \(\frac{8}{4} = \frac{a}{2}\)
→ Simplify \(\frac{8}{4} = 2\), so \(2 = \frac{a}{2}\) → \(a = 4\)
17. \(\frac{d}{6} = \frac{6}{3}\)
→ Simplify \(\frac{6}{3} = 2\), so \(\frac{d}{6} = 2\) → \(d = 12\)
18. \(\frac{10}{y} = \frac{5}{2}\)
→ \(10 \cdot 2 = y \cdot 5\) → \(20 = 5y\) → \(y = 4\)
---
##
✔ Final Answers (in order):
1.
x = 6
2.
h = 2
3.
y = 4
4.
t = 6
5.
s = 2.5 or \(\frac{5}{2}\)
6.
v = 2
7.
a = 9
8.
r = 2
9.
j = 12
10.
x = 4
11.
b = 2
12.
m = 2
13.
v = 81
14.
y = 9
15.
w = 3
16.
a = 4
17.
d = 12
18.
y = 4
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## 💡 Tip:
Always check if you can
simplify fractions first before cross-multiplying — it makes solving easier!
You can now fill in these values on your worksheet. Let me know if you want them formatted for printing or checking!
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions worksheet 9th grade.
