To solve each equation with rational coefficients, we will isolate the variable on one side of the equation. Let's go through each problem step by step.
---
1. \( 0.5m = 3.5 \)
- Divide both sides by \( 0.5 \):
\[
m = \frac{3.5}{0.5} = 7
\]
-
Answer: \( m = 7 \)
---
2. \( -1.8 = -0.6x \)
- Divide both sides by \( -0.6 \):
\[
x = \frac{-1.8}{-0.6} = 3
\]
-
Answer: \( x = 3 \)
---
3. \( 0.4y = 2 \)
- Divide both sides by \( 0.4 \):
\[
y = \frac{2}{0.4} = 5
\]
-
Answer: \( y = 5 \)
---
4. \( 1.86 = -6.2z \)
- Divide both sides by \( -6.2 \):
\[
z = \frac{1.86}{-6.2} = -0.3
\]
-
Answer: \( z = -0.3 \)
---
5. \( 1.67t = 10.02 \)
- Divide both sides by \( 1.67 \):
\[
t = \frac{10.02}{1.67} = 6
\]
-
Answer: \( t = 6 \)
---
6. \( 0.9x = -4.5 \)
- Divide both sides by \( 0.9 \):
\[
x = \frac{-4.5}{0.9} = -5
\]
-
Answer: \( x = -5 \)
---
7. \( \frac{1}{13}a = 2 \)
- Multiply both sides by \( 13 \):
\[
a = 2 \times 13 = 26
\]
-
Answer: \( a = 26 \)
---
8. \( -\frac{8}{9}x = 24 \)
- Multiply both sides by \( -\frac{9}{8} \):
\[
x = 24 \times \left( -\frac{9}{8} \right) = -27
\]
-
Answer: \( x = -27 \)
---
9. \( \frac{3}{8}r = 36 \)
- Multiply both sides by \( \frac{8}{3} \):
\[
r = 36 \times \frac{8}{3} = 96
\]
-
Answer: \( r = 96 \)
---
10. \( \frac{3}{4}t = \frac{1}{2} \)
- Multiply both sides by \( \frac{4}{3} \):
\[
t = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}
\]
-
Answer: \( t = \frac{2}{3} \)
---
11. \( -16 = \frac{1}{4}h \)
- Multiply both sides by \( 4 \):
\[
h = -16 \times 4 = -64
\]
-
Answer: \( h = -64 \)
---
12. \( \frac{1}{8}m = 12 \)
- Multiply both sides by \( 8 \):
\[
m = 12 \times 8 = 96
\]
-
Answer: \( m = 96 \)
---
13. \( \frac{5}{8}n = 45 \)
- Multiply both sides by \( \frac{8}{5} \):
\[
n = 45 \times \frac{8}{5} = 72
\]
-
Answer: \( n = 72 \)
---
14. \( 10 = \frac{1}{10}b \)
- Multiply both sides by \( 10 \):
\[
b = 10 \times 10 = 100
\]
-
Answer: \( b = 100 \)
---
15. \( -\frac{1}{7}x = -7 \)
- Multiply both sides by \( -7 \):
\[
x = -7 \times (-7) = 49
\]
-
Answer: \( x = 49 \)
---
Final Answers:
\[
\boxed{
\begin{array}{lll}
1. & m = 7 & \\
2. & x = 3 & \\
3. & y = 5 & \\
4. & z = -0.3 & \\
5. & t = 6 & \\
6. & x = -5 & \\
7. & a = 26 & \\
8. & x = -27 & \\
9. & r = 96 & \\
10. & t = \frac{2}{3} & \\
11. & h = -64 & \\
12. & m = 96 & \\
13. & n = 72 & \\
14. & b = 100 & \\
15. & x = 49 &
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of equations with rational numbers worksheet.
